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Studies of the K⁺ → π⁺π0 background for the measurement of K⁺ → π⁺νν ̄and π0 → νν ̄ decays Fu, Jie 2016

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Studies of the K+ → pi+pi0 backgroundfor the measurement of K+ → pi+νν¯and pi0 → νν¯ decaysbyJie FuB.Sc., Shandong University, 2010A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCEinThe Faculty of Graduate and Postdoctoral Studies(Physics)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)August 2016c© Jie Fu 2016AbstractThe NA62 experiment aims at measuring the branching ratio of the ultra-rare decayK+ → pi+νν¯ with 10% precision. To achieve the desired precision,high levels of background rejection must be accomplished using techniquessuch as high-resolution timing, kinematic rejection, particle identification,and hermetic vetoing of photons. K+ → pi+pi0 (Kpi2) decays, one of thelargest background sources, are mainly rejected by kinematics reconstruc-tion and photon vetoing in NA62. To evaluate Kpi2 background rejectioncapabilities of the NA62 system, we studied the inefficiency of these twotechniques. Kpi2 and K+ → µ+ν (Kµ2) events were selected from 2015minimum bias data runs using Kpi2/Kµ2 separation cuts whose efficiencywas also studied in details. The inefficiency of kinematics suppression wasfound to be (2.16 ± 0.21) × 10−3, and the upper limit of the photon vetoinefficiency was 7×10−7 at 90% confidence level. Combined with correctionfactors from Monte Caro simulations, a preliminary result, S/B > 0.2, wasestimated for Kpi2 background in the measurement of K+ → pi+νν¯. Also, anupper limit on the branching ratio of the invisible decay pi0 → νν¯, 4.3×10−7,was obtained at 90% confidence level.iiPrefaceThis thesis is based on the experimental apparatus and data of the NA62experiment.The NA62 collaboration has 337 members from 30 different institutions.I joined the experiment in January 2015 when the 2014 pilot run finished.Since then I mainly focused on the data analysis and tried to evaluate Kpi2background rejection capabilities of the NA62 system. I also worked with theSTRAW working group during my stay at CERN. Under the supervision ofHans Danielson, I conducted several tests using the STRAW prototype: gasleak measurements, experimenting with methods of decreasing the ambientnoise signal, examining the signal threshold using the scanning data andalso gain measurement presented in Appendix A. In addition, I participatedin a few data taking shifts in 2015 and 2016.The apparatus description in Chapter 3 is mainly based on the NA62technical design [1] and papers on related detectors. The corrections (section4.1), one track selection cuts (section 4.2) and additional LKr reconstructionalgorithm (section 5.1.2) are developed by Giuseppe Ruggiero. With thehelp of Douglas Bryman and Giuseppe Ruggiero, I set photon veto cuts inChapter 5. I completed all the data analysis of 2015 minimum bias dataand Monte Carlo data presented in this thesis except reconstruction of dataruns which was conducted by Antonino Sergi.iiiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiGlossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiiDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Overview of the NA62 experiment . . . . . . . . . . . . . . . 11.1.1 Motivation for the NA62 experiment . . . . . . . . . 11.1.2 Decay-in-flight technique . . . . . . . . . . . . . . . . 21.1.3 Main background sources and rejection techniques . . 41.2 Kpi2 background study . . . . . . . . . . . . . . . . . . . . . 81.3 pi0 → νν¯ study . . . . . . . . . . . . . . . . . . . . . . . . . . 81.4 Outline of the thesis . . . . . . . . . . . . . . . . . . . . . . . 102 NA62 Experimental Apparatus . . . . . . . . . . . . . . . . . 112.1 Beam line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.2 Tracking devices . . . . . . . . . . . . . . . . . . . . . . . . . 142.2.1 GTK . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.2.2 STRAW spectrometer . . . . . . . . . . . . . . . . . . 162.3 Particle identification and timing . . . . . . . . . . . . . . . . 182.3.1 CEDAR . . . . . . . . . . . . . . . . . . . . . . . . . 182.3.2 RICH . . . . . . . . . . . . . . . . . . . . . . . . . . . 19ivTable of Contents2.3.3 CHOD . . . . . . . . . . . . . . . . . . . . . . . . . . 222.4 Veto system . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.4.1 CHANTI . . . . . . . . . . . . . . . . . . . . . . . . . 232.4.2 Photon veto . . . . . . . . . . . . . . . . . . . . . . . 252.4.3 Muon veto . . . . . . . . . . . . . . . . . . . . . . . . 293 Analysis strategies . . . . . . . . . . . . . . . . . . . . . . . . . 333.1 Kpi2 background evaluation . . . . . . . . . . . . . . . . . . . 333.1.1 Kinematics suppression . . . . . . . . . . . . . . . . . 333.1.2 pi0 suppression . . . . . . . . . . . . . . . . . . . . . . 343.2 Upper limit on the branching ratio of the decay pi0 → νν¯ . . 344 Data sample selection . . . . . . . . . . . . . . . . . . . . . . . 364.1 Corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364.1.1 Spectrometer momentum correction . . . . . . . . . . 364.1.2 LKr correction . . . . . . . . . . . . . . . . . . . . . . 374.2 One track event selection cuts . . . . . . . . . . . . . . . . . 384.3 Kpi2 and Kµ2 separation cuts and efficiency evaluation . . . . 484.3.1 Overview of separation cuts . . . . . . . . . . . . . . 484.3.2 Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . 514.4 Final cuts used for selecting the data sample . . . . . . . . . 574.4.1 Cuts for kinematics suppression study . . . . . . . . . 574.4.2 Cuts for the pi0 suppression study and pi0 → νν¯ study 585 Photon veto cuts . . . . . . . . . . . . . . . . . . . . . . . . . . 605.1 LKr photon . . . . . . . . . . . . . . . . . . . . . . . . . . . . 605.1.1 LKr standard photon . . . . . . . . . . . . . . . . . . 605.1.2 LKr extra photon . . . . . . . . . . . . . . . . . . . . 615.2 LAV photons . . . . . . . . . . . . . . . . . . . . . . . . . . . 625.3 SAC and IRC photons . . . . . . . . . . . . . . . . . . . . . . 625.3.1 SAV-LAVFEE photons . . . . . . . . . . . . . . . . . 635.3.2 SAV-CREAM photons . . . . . . . . . . . . . . . . . 635.4 False veto effect . . . . . . . . . . . . . . . . . . . . . . . . . 646 Analysis results . . . . . . . . . . . . . . . . . . . . . . . . . . . 676.1 Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 676.1.1 Kinematics rejection for Kpi2 . . . . . . . . . . . . . . 676.1.2 Kinematics acceptance for Kpiνν¯ . . . . . . . . . . . . 686.2 pi0 rejection using photon veto cuts . . . . . . . . . . . . . . 706.3 Kpi2 background . . . . . . . . . . . . . . . . . . . . . . . . . 71vTable of Contents6.4 Branching ratio of the decay pi0 → νν¯ . . . . . . . . . . . . . 717 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75AppendicesA Gain measurement of the STRAW spectrometer . . . . . . 80B Study of the false Kpi2 rejection caused by additional pi+ LKrclusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84viList of Tables1.1 Most frequent K+ decays . . . . . . . . . . . . . . . . . . . . 41.2 Photon destinations in NA62 . . . . . . . . . . . . . . . . . . 92.1 Comparison between the measured properties of full intensitybeam in 2015 run with the design values . . . . . . . . . . . . 144.1 Geometrical acceptance cuts for detectors. . . . . . . . . . . . 424.2 Efficiency of LKr and MUV3 cuts for selecting Kpi2 and Kµ2events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 595.1 Number of Kµ2 events passing photon cuts . . . . . . . . . . 666.1 Number of Kpi2 events in two momentum ranges passing thephoton veto cuts. . . . . . . . . . . . . . . . . . . . . . . . . . 71viiList of Figures1.1 A bird’s-eye view of the SPS and NA62 site . . . . . . . . . . 11.2 The box and penguin diagrams contributing to the K+ →pi+νν¯ decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 The seven candidate events of the BNL E787 and E949 ex-periments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.4 Kinematics of the decay K+ → pi+νν¯ . . . . . . . . . . . . . . 51.5 M2missing distribution for the signal and the kinematically con-strained K+ decays. . . . . . . . . . . . . . . . . . . . . . . . 61.6 M2missing distribution for the signal and generic K+ decays. . 71.7 Diagrams contributing to the pi0 → νν¯ decay . . . . . . . . . 92.1 Layout of the NA62 experimental setup . . . . . . . . . . . . 122.2 Scheme of the primary and secondary beams . . . . . . . . . 132.3 Schematic layout of the GTK . . . . . . . . . . . . . . . . . . 152.4 Schematic view of the magnetic spectrometer . . . . . . . . . 172.5 Schematic drawing of the four views of each straw chamber . 182.6 Schematic layout of the CEDAR . . . . . . . . . . . . . . . . 192.7 Schematic layout of the RICH . . . . . . . . . . . . . . . . . . 202.8 Fitted RICH ring radius for different downstream particles in2015 run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.9 Sketch of two planes of the CHOD . . . . . . . . . . . . . . . 222.10 Schematic layout of the new CHOD . . . . . . . . . . . . . . 242.11 Beam induced background rejected by the CHANTI . . . . . 252.12 A layout of a complete CHANTI station . . . . . . . . . . . . 262.13 Picture of the first LAV station . . . . . . . . . . . . . . . . . 272.14 Details of the ribbons and electrodes . . . . . . . . . . . . . . 282.15 Shashlyk technology . . . . . . . . . . . . . . . . . . . . . . . 292.16 Layout of a scintillator plate in MUV1 and MUV2 . . . . . . 312.17 A view of the MUV1 and MUV2 . . . . . . . . . . . . . . . . 324.1 Number of straw chambers hit by downstream track . . . . . 394.2 Straw momentum difference before and after fit . . . . . . . . 40viiiList of Figures4.3 Diagrams for matching the CHOD Candidate with the Spec-trometer track . . . . . . . . . . . . . . . . . . . . . . . . . . 414.4 Criteria for matching the LKr Cluster with the Spectrometertrack . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434.5 Criteria for matching the CEDAR Candidate with the Spec-trometer track . . . . . . . . . . . . . . . . . . . . . . . . . . 434.6 Criteria for matching the CHANTI Candidate with the Spec-trometer track . . . . . . . . . . . . . . . . . . . . . . . . . . 444.7 Diagrams for matching a multi-ring RICH Candidate withthe Spectrometer track . . . . . . . . . . . . . . . . . . . . . . 464.8 Diagrams for matching a single-ring RICH Candidate withthe Spectrometer track . . . . . . . . . . . . . . . . . . . . . . 474.9 CDA and Z position distribution of decay vertex reconstructedwith nominal kaon . . . . . . . . . . . . . . . . . . . . . . . . 484.10 CDA and Z position distribution of decay vertex reconstructedwith GTK kaon . . . . . . . . . . . . . . . . . . . . . . . . . . 494.11 RICH mass distributions for one track events . . . . . . . . . 504.12 EP distribution for one track events . . . . . . . . . . . . . . . 514.13 M2missing−pi distribution for one track events . . . . . . . . . . 524.14 M2missing−µ distribution for one track events . . . . . . . . . . 534.15 M2missing−pi and M2missing−µ distributions for both Kpi2 andKµ2 decays . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554.16 Efficiency of M2missing−pi cut for selecting Kpi2 sample . . . . . 554.17 RICH mass distributions for Kpi2 and Kµ2 decays . . . . . . . 564.18 Efficiency of RICH mass cuts for selecting Kpi2 and Kµ2 events. 574.19 EP distributions for Kpi2 and Kµ2 decays . . . . . . . . . . . . 585.1 Time difference between the LKr photon candidates and theassociated CHOD track . . . . . . . . . . . . . . . . . . . . . 625.2 Time difference between the LKr extra photon candidate andthe associated CHOD track . . . . . . . . . . . . . . . . . . . 635.3 Time difference between LAV photon candidate and the as-sociated CHOD track . . . . . . . . . . . . . . . . . . . . . . 645.4 Time difference between LAVFEE based SAV photon candi-date and the associated CHOD track . . . . . . . . . . . . . . 655.5 Time difference between CREAM based SAV photon candi-date and the associated CHOD track . . . . . . . . . . . . . . 656.1 M2missing−pi distribution for Kpi2 MC events . . . . . . . . . . 68ixList of Figures6.2 M2missing−pi distribution for Kpi2 events using GTK kaon andspectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . 696.3 M2missing−pi distribution for Kpiνν¯ MC events . . . . . . . . . . 696.4 Kpi2 events surviving each photon veto cut . . . . . . . . . . . 70A.1 Straw prototype with Gas and HV Input Connected . . . . . 81A.2 Gain v.s. Voltage for Ar − CO2(70-30) at 970 mbar . . . . . 81A.3 Gain v.s. Voltage for Ar − CO2(85-15) at 970 mbar . . . . . 83A.4 Gain v.s. Voltage for Ar − CO2(93-7) at 970 mbar . . . . . . 83B.1 Distance of the selected LKr cluster to the projected positionof pi+ in the LKr . . . . . . . . . . . . . . . . . . . . . . . . . 85B.2 The reject efficiency distribution for different radii of themasked region . . . . . . . . . . . . . . . . . . . . . . . . . . . 85xGlossaryBNL Brookhaven National LaboratoryBR branching ratio, fraction of particles which decay by anindividual decay mode with respect to the total number ofparticles which decayCEDAR CErenkov Differential counter with Achromatic Ring focusCERN European Organization for Nuclear Research, the world’slargest particle physics laboratory located in Geneva on theFranco-Swiss borderCHANTI CHarged ANTIcounterCHOD Charged particle HODoscopesC.L. confidence levelGTK GigaTrackerIRC Inner Ring CalorimeterLAV Large Angle VetoLHC Large Hadron Collider, the world’s largest and highest-energyparticle accelerator at present.LKr Liquid Krypton CalorimeterMIPs Minimum Ionizing ParticlesMUV Muon VetoNAHIF North Area High Intensity FacilityRICH Ring Imaging CHerenkov detectorSAC Small Angle CalorimeterxiGlossarySM Standard Model of Particle physicsSPS Superconducting Proton Synchrotron (see Signal-to-background RatioxiiAcknowledgementsFirstly, I would like to express my sincere gratitude to my supervisor, DougBryman, for the support and advice. He was always available when I raninto a problem and had questions on detectors and analysis. His guidancehelped me in all the time of research and writing of this thesis.I would also like to thank Tommaso Spadaro and Giuseppe Ruggiero fortheir help on data analysis. My particular thanks go to Giuseppe Ruggierowho provided the initial analysis code example and helpful comments. I amalso grateful to Antonino Sergi for the reconstruction of physics data andanswering questions on the NA62 experiment. Special thanks go to HansDanielson for his supervision when I was working in STRAW group.Furthermore, many thanks go to all the other NA62 members for thedetector construction and the development of the simulation and recon-struction packages.I would like to acknowledge Reiner Krucken as the second reader of thisthesis.Finally, I have to express out appreciation to my family and friends foralways supporting me throughout my years of study.xiiiTo my parents.xivChapter 1Introduction1.1 Overview of the NA62 experimentThe NA62 experiment [2] is a fixed target kaon experiment driven by Su-perconducting Proton Synchrotron (SPS) at the European Organization forNuclear Research (CERN). Its primary goal is to measure the branchingratio (BR) of the ultra-rare kaon decay K+ → pi+νν¯ with 10% precisionby collecting O(100) K+ → pi+νν¯ events with less than 10% background,for testing Standard Model (SM) predictions where new physics effects mayinduce a deviation.Figure 1.1: A bird’s-eye view of the SPS and NA62 site ( Motivation for the NA62 experimentAmong many rare flavour changing neutral current K and B decays, theextremely rare kaon decay K+ → pi+νν¯ is very sensitive to new physics11.1. Overview of the NA62 experimentthrough the underlying mechanisms of flavour dynamics and can be used toexplore the short-distance scales up to O(1,000 TeV) [3]. This decay is oneof the best probes for new physics effects complementary to Large HadronCollider (LHC) searches, especially within Non-Minimal Flavour Violationmodels [4, 5].The K+ → pi+νν¯ decay is the strongly suppressed second order weak de-cay in the SM. It arises at the quark level from s→ dνν¯ decay, which receivesone-loop contributions from electroweak W-box and Z-penguin diagrams inthe SM as shown in Figure 1.2 [6].Figure 1.2: The box and penguin diagrams contributing to the K+ → pi+νν¯decay.The predicted SM branching ratio of this decay has been calculated tohigh precision [7, 8, 9]:Br(K+ → pi+νν¯)SM = (0.781± 0.075± 0.029)× 10−10 (1.1)where the first error comes from quark-mixing parameter uncertainties andthe second error is the theoretical input uncertainty, while the most preciseexperimental result so far is,Br(K+ → pi+νν¯)exp = (1.73+1.15−1.05)× 10−10 (1.2)obtained by the E787 and E949 experiments [10] at the Brookhaven NationalLaboratory (BNL) based on only 7 observed candidate events shown inFigure 1.3. Although this result agrees with the SM theoretical prediction,the experimental error is quite large. A measurement of the rate with atleast 10% precision is needed for a significant test of new physics. Thismotivates the next generation rare kaon decay experiment, NA62.1.1.2 Decay-in-flight techniqueUnlike E797 and E949 which used a stopped-K+ technique, the NA62 Col-laboration tries a decay-in-flight technique at beam momentum of 75 GeV/c.21.1. Overview of the NA62 experimentNS61CH14-Tschirhart ARI 15 September 2011 7:33Energy, E (MeV)Range, R (cm)101520253035404550 60 70 80 90 100 110 120 130 140 150E949-PNN2E949-PNN1E787-PNN2E787-PNN1SimulationFigure 2The seven candidate events of the BNL E787 and E949 experiments. The background population fromK+→π+π0 is evident at E = 110 MeV and R = 32 cm, and the simulated signal population is indicatedalong the diagonal as small gray dots. PNN1 refers to the signal region indicated as a box in the upper right,and PNN2 refers to the signal region indicated as a box in the lower left.The Superconducting Proton Synchrotron (SPS) at CERN will drive the NA62 experimentwith 400-GeV protons. Similar to the stopped-K+ experiments, the NA62 initiative reliescritically on high-resolution timing, kinematic rejection, particle identification, hermetic vetoing,and redundancy of measurements. To realize the necessary sensitivity with an in-flight technique,NA62 plans to (a) perform low-mass tracking of the incident unseparated beam with a ∼1-GHztotal rate, 40 MHz cm−2; (b) achieve positive kaon identification in this high-rate environmentby means of a differential Cherenkov counter that is insensitive to pions and protons withminimal accidental mistagging; (c) achieve a muon rejection of at least 105 with a samplinghadron calorimeter; (d ) achieve>2-σ π/µ separation up to a momentum of 35 GeV/c with a ringimaging Cherenkov (RICH) counter system; and (e) veto the charged particles originating fromthree- and four-body kaon decays. Initial running of the K+ → π+νν¯ configuration is expectedto occur between 2012 and 2013 and will be followed by an estimated two-year exposure to reacha sensitivity of 80 SM events.3. EXPERIMENTAL PURSUIT OF KL → π0νν¯The first dedicated experiment in pursuit of the KL → π0νν¯ process was KEK E391a, whichrecently established a limit<2.6 × 10−8 (30) at 90%CL; compare this limitwith the SMprediction(10) of B(KL → π0νν¯) = (2.43± 0.39± 0.06)× 10−11. Measuring this highly suppressed processat the SM level requires very intense kaon sources and is a driver of the J-PARC research programin Japan. The KOTO experiment at J-PARC is pursuing K 0L → π0νν¯ discovery with an initiallyproposed sensitivity of a few events at the SM level; a higher-sensitivity experiment is planned forthe future. The very high beam power available with the Project X (23) evolution of the • Rare Kaon and Pion Decays 337Annu. Rev. Nucl. Part. Sci. 2011.61:331-354. Downloaded from Access provided by University of British Columbia on 04/30/16. For personal use only.Figur 1.3: This figur shows seven K+ → pi+νν¯ candidate events o theE787 and E949 experiments in the PNN1 and PNN2. Two signal regionswere indicated as boxes. The points near E = 110 MeV are backgroundK+ → pi+pi0 events which survive photon veto cuts, and the small grey dotsrepresent the simulated K+ → pi+νν¯ events passing the trigg r [10].This new technique brings in some advantages. First, it allows us to gethigh momentum kaons nd decay particles, which leads to a mor efficientdetection of decay particl s, partic larly photo ar sing from pi0 (pi0 → γγ)1in the K+ → pi+pi0 (Kpi2) de ay. Besides, this approach does not requiretagging of the pi → µ → e decay chain as needed in stopped-K+ technique[10]. The decay-in-flight technique hence permits a higher rate, which makesit possible to detect more candidate events in a short time.A detailed description of the NA62 experimental setup is presented inChapter 2. The 400 GeV/c SPS proton beam at a rate of 1.1 × 1012 Hzproduces a secondary charged beam by impinging on a beryllium target.After passing a rigorous selecting system, the secondary beam’s momentumis confined to (75.0 ± 1%) GeV/c with a small angular deviation. Then the1Br(pi0 → γγ) ≈ 98.82%, Br(pi0 → e+e−γ) ≈ 1.17% [11].31.1. Overview of the NA62 experimentDecay Channel BR (%) Rejection StrategiesK+ → µ+νµ 63.55± 0.11 µ-ID, kinematicsK+ → pi+pi0 20.66± 0.08 Photon veto, kinematicsK+ → pi+pi+pi− 5.59± 0.04 Charged Particle Veto, kinematicsK+ → pi0e+νe 5.07± 0.04 Photon veto, e-IDK+ → pi0µ+νµ 3.353± 0.034 Photon veto, µ-IDK+ → pi+pi0pi0 1.761± 0.022 Photon veto, kinematicsTable 1.1: List of the six most frequent K+ decays with correspondingrejection techniques.high intensity hadron beam (∼750 MHz) enters an 117 m long cylindricalvacuum tank with a diameter of 1.92 to 2.8 m and decay there. Nearly4.5× 1012 kaons per year are expected to decay in a 60 m long useful decayregion starting from the beginning of the tank. Assuming a branching ratioof 10−10 and a 10% detection acceptance for K+ → pi+νν¯ decay, we candetect ∼90 signal events over two years of date taking.In order to study the extremely rare decay in this high rate environment,we need powerful background suppression techniques with precise timingability.1.1.3 Main background sources and rejection techniquesThere are two main kinds of background sources. Primary backgroundscome from K+ decays; the other sources are beam-related.Generic K+ decay backgroundsK+ decays with high branching ratio, shown in Table 1.1, can mimic signalevents in some cases. Although the very rare decay K+ → pi+νν¯ is three-body decay, see Figure 1.4, only one secondary particle is detectable. Thesignature of the signal event is a pi+ track matched in time with a K+track. So if only one decay particle, pi+, in K+ decays were detected withother particles escaping the detection, it might produce the same signal as aK+ → pi+νν¯ event. It happens when the pi0 from Kpi2 decay is undetected.Besides, backgrounds are also contributed by decay modes which have onlyone detectable decay particle, like K+ → µ+ν (Kµ2). If µ+ were tagged aspi+ by mistake, it would also mimic a signal event.41.1. Overview of the NA62 experimentθπKPKPπPνPνFigure 1.4: Kinematics of the decay K+ → pi+νν¯. ~PK is the kaon momen-tum detected by GTK, ~Ppi is the pion momentum detected by STRAW, andθKpi refers to the angle between two tracks.To achieve the goal of NA62, the Signal-to-background Ratio (S/B) can-not be lower than 10 so that the suppression factor for these kaon decaysneeds to reach the order of 1012. For this, several techniques were exploitedto veto generic K+ decay backgrounds as shown in Table 1.1: accuratekinematic reconstruction, rigorous particle identification, and powerful de-cay particle vetoing.Firstly, kinematics is one of the most discriminating variables for sup-pressing generic K+ decay backgrounds. Since K+ decays have differentneutral decay products with each other, we can calculate and use a squaredmissing mass for backgrounds rejection:m2missing ≡ (PK+ − Ppi+)2 (1.3)where PK+ and Ppi+ are four-momentum of the kaon detected by the Giga-Tracker (GTK, section 2.2.1) and the pion track detected by the STRAW(section 2.2.2). The missing particles are neutral particle which cannot bedetected by the STRAW. Given particles are relativistic, and the anglesbetween two tracks are quite small (order of mrad), m2missing can be easilycalculated as:m2missing ≈ m2K(1−| ~ppi|| ~pK |) +m2pi(1−| ~pK || ~ppi|)− | ~pK || ~ppi|θ2Kpi (1.4)It should be noted that the detected decay particle is normally assumed as apion for calculating the m2missing. But in some cases, we also assume it hasmuon mass, i.e. m2missing−µ = (PK+ − Pµ+)2, for convenience. As shown inFigure 1.5, three largest background decays, Kµ2, Kpi2 and K+ → pi+pi+pi−(Kpi3), are well kinematically constrained in the m2missing spectrum. Twosignal regions can be defined to reject these decay events:• Region I : 0 < m2missing < m2pi0 − σ(m2pi0)51.1. Overview of the NA62 experiment• Region II : m2pi0 + σ(m2pi0) < m2missing < min([m2missing(Kpi3)])where σ(m2pi0) represents the resolution of the Kpi2 peak to exclude the Gaus-sian tails. The region I and region II were set to be 0 ∼ 0.01 GeV 2/c4 and0.026 ∼ 0.068 GeV 2/c4 [12]. Due to factors like the resolution effects, themultiple Coulomb scattering and the non-Gaussian tails, backgrounds of thekinematically constrained decays may leak into defined signal regions. A de-tailed Monte Carlo (MC) simulation of the whole tracking system, based onGEANT4 [13], shows the inefficiencies of kinematics rejection on the decaysKpi2 and Kµ2 are about 5× 10−3 and 1.5× 10−4, respectively [2]. However,10−4 is insufficient to achieve the necessary rejection ability (10−12). Letalone there are other decay modes, like K+ → pi0e+νe, which cannot beconstrained as can be seen in Figure 1.6. 1.1   Physics Objectives and Detector Overview 13   Figure 2 Shape of the                     for signal (thick solid line) and background events under the hypothesis that the charged track is a pion. These background sources refer to decays which are kinematically constrained.  Figure 3 Shape of the                     for signal (thick solid line) and background events under the hypothesis that the charged track is a pion. These background sources refer to decays which are kinematically not constrained. The experiment, therefore, needs tracking devices for both K+ and S+, and also calorimeters in order to veto photons, positrons and muons. In addition, particle identification systems to identify the incident kaons and to distinguish S+ from P+ and e+ must complement the tracking and veto detectors to reach the ultimate sensitivity and to guarantee redundancy. The guiding principles for the construction of the NA62 detectors are, therefore: accurate kinematic reconstruction, precise particle timing, efficiency of the vetoes and excellent particle identification. Figu 1.5: M2missing distribution under the ypothesis that the det cteddownstream particle is a pion, for the signal (solid curve) and the kine-matically constrained K+ decays (dotted curves). The spectra are plottedin arbitrary units, not weighted with the branching ratios, and neglectingresolution effects [1].Further techniques are needed to achieve the rejection goal. Muon vetosystem described in section 2.4.3 and pi/µ separation achieved by a RingImaging Cherenkov (RICH, see section 2.3.2) counter further suppress thedecay modes with muons. A powerful photon veto system described in sec-tion 2.4.2 is used to detect photons and electrons generated by pi0 decays.It rejects the decay modes with γ and pi0. Not only does the liquid Kryp-ton (LKR, see section 2.4.2 ) electromagnetic calorimeter provide the great61.1. Overview of the NA62 experimentPoS(KAON13)032The NA62 Experiment: Prospects for the K+! p+nn¯ Measurement Giuseppe RuggieroFigure 1: Layout of the NA62 experiment.beam. The m2miss ⌘ (PK Pp+)2, with PK and Pp+ the four momenta of the K+ and the chargedpion, fully describes the kinematics of the decay. Backgrounds come from all the K+ decay modesand from accidental single tracks matched with a K+-like track.The distribution of the m2miss allows a separation of the signal from the main K+ decay modesby defining two signal regions where a minimum background is expected: region I between 0 andthe K+! p+p0 peak, region II between the K+! p+p0 peak and the K+! p+p+p threshold(see figure 2). Nevertheless, the total background in these regions is still several order of magnitudelarger than the K+! p+nn¯ , as a consequence of the main decay modes leaking there via resolutioneffects and radiative tails, semileptonic decays and even rare decays like K+! p+pe+n .Possible interactions of the beam with the material along the beam line and in the residual gasin the vacuum region are the main sources for accidental single track background.]4/c2 [GeVmiss2m-0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 0.12miss2dmΓd totΓ1-710-610-510-410-310-210-1101)γ(µν+µ→+Keν0π+ e→+Kµν0π+µ→+K)γ(0π+π→+K)1010× (νν+π→+K-π+π+π→+K0π0π+π→+Keν+e-π+π→+KRegion IRegion IIFigure 2: m2miss distribution for signal and backgrounds from the main K+ decay modes: The backgroundsare normalized according to their branching ratio; the signal is multiplied by a factor 1010.3Figure 1.6: M2missing distribution under the hypothesis that the detecteddownstream particle is a pion, for the signal (red line) and generic K+decays (both kinematically constrained and not constrained) indicated inother colours. The backgrounds are normalized according to their branchingratio, and the signal is multiplied by a factor of 1010 [14].photon veto ability, but it can also act as a powerful particle identifier forµ+ and e+ which suppress the decays with muons and positrons.Beam related backgroundBesides generic K+ decays, there are several beam related backgrounds. Forexample, beam particles undergoing inelastic interaction in the GTK mayproduce a low-angle pi+ detected by the STRAW, which may mimic a signalevent. Thanks to the CHANTI, this inelastic interaction can be detected asdiscussed in section 2.4.1. Besides, mistagging beam particles can also con-tribute to the accidental background in high rate environment. Like, a beamparticle, pion or proton, may be accidentally mistagged as a decaying kaonin the upstream and is unexpectedly associated to a downstream pi+ comingfrom interactions of beam with the residual gas. To avoid this, we need maindetectors to have high-resolution timing ability and also an upstream kaonidentification detector, a Cerenkov threshold detector (CEDAR, see section2.3.1), for precisely tagging K+.71.2. Kpi2 background study1.2 Kpi2 background studyAs shown in Table 1.1, there are two techniques for rejecting the Kpi2 back-ground: kinematics suppression and pi0 vetoing2. Although MC simulationswere conducted for evaluating the rejection inefficiency of these two tech-nique, no experimental result has been achieved so far. In this thesis, weanalyzed the 2015 physics run data and several MC event samples to achievethe experimental evaluation for two suppression factors, providing the esti-mated S/B for the Kpi2 background in NA62.Previous simulation resultsA MC study suggests that the kinematics inefficiency for rejecting Kpi2 back-ground is 5× 10−3 as mentioned in section 1.1.3.For photon vetoing, a simulation using an estimation of the inefficiency ofphoton veto detectors based on NA48 experimental measurements indicatesthat the average pi0 veto inefficiency with (without) pi+ momentum cut3 is1.6 × 10−8 (8.4 × 10−8) [1]. The momentum cut on pi+, 15 to 35 GeV/c,guarantees the pi0 has at least 40 GeV . There are four photon veto modules,which are LKr, LAV, SAC, and IRC (see Section 2.4.2), providing a hermeticcoverage for photons up to 50 mrad and down to 100 MeV in NA62. Twosimulation studies show that destination of photons from Kpi2 decay canonly have three possible configurations: both photons hit the LKr, SACor IRC; one photon hits the LKr, SAC or IRC and the other one hits theLAV; and one photon hits the LKr, SAC or IRC, and the other one withan angle larger than 50 mrad is undetected. Corresponding fractions ofconfigurations are shown in Table 1.2. The major contribution to the overallphoton veto inefficiency comes from the third configuration, containing 0.2%events, where only one photon is detected in the forward direction. Althoughonly one photon is detected, this photon normally has an energy in the 10GeV range or even more, which makes it easier to be detected.1.3 pi0 → νν¯ studyThe NA62 experiment is like a unique pi0 “factory” due to abundant Kpi2decays in the fiducial region which provide a great number of tagged pi0. Wecan take advantage of this enormous pi0 sample and powerful photon veto2pi0 vetoing totally depends on photon veto detectors in NA62.315 to 35 GeV/c, see section pi0 → νν¯ studyStudy 1 [1] Study 2 [15]Destination of two photons Fractions (%)Both LKr, IRC, SAC 81.22 80.05LAV / one of LKr, IRC, SAC 18.58 19.90One of LKr, IRC, SAC/ Undetected 0.2 0.05aLAV / Undetected 0 0Both undetected 0 0Table 1.2: Destinations of photons from Kpi2 decay in NA62 from previoussimulationsasmaller than the result of study 1 since beam pipe is not considered hereability of the NA62 photon veto system to improve the measurement on thebranching ratio of the rare decay pi0 → νν¯.This decay is forbidden by angular momentum conservation if the neu-trino is the purely massless left-handed particle. As demonstrated by thediscovered neutrino oscillation [16, 17], neutrinos do have a finite mass.Hence the SM-forbidden decay pi0 → νν¯ can occur due to Z-boson exchangeshown in Figure 1.7.3In contrast, as is well-known, minimal substitutiondoes not work in gauging the WZW action. The so-calledtrial and error Noether method [20] gives the gaugedWZW actionΓ˜WZW(U,ALµ ,ARµ )= ΓWZW(U) + 5Ci∫M4Tr(AˆLLˆ3 + AˆRRˆ3)−5C∫M4Tr((dAˆLAˆL + AˆLdAˆL)Lˆ+(dAˆRAˆR + AˆRdAˆR)Rˆ)+5C∫M4Tr(dAˆLdUAˆRU † − dAˆRd(U †)AˆLU)+ · · · . (8)Here we have shown only the terms relevant for the pro-cesses involving single neutral pion and one or two gaugebosons. A complete list of terms can be found in [20].The leptonic part of the Lagrangian isLlept.Zνν¯ = −g2 cos θWZµν¯eγµ1− γ52νe + ν¯e(i∂/)νe+(e→ µ, τ terms). (9)Here again, we have presented only the relevant termsfor the process of our concern, that is, Z → νν¯. Theneutrino field νe is constrained to the left-handed one;γ5νe = −νe.Finally, the Lagrangian should be complemented bythe terms for the dynamics of the gauge bosons, namelyLγ,Z,W± = −14Tr(FALµν FALµν + FARµν FARµν)−12(M2W (W+µ W+µ +W−µ W−µ) (10)+M2ZZµZµ),where FL,Rµν are field strength tensors and MW and MZare the masses of the gauge bosons.III. π0 → νν¯ IN BARYON-FREE SPACEThe lowest static energy configuration for baryon freespace is simply a constant U . Without loss of a generalitywe can set U = 1. Thus, the Lagrangian constructed inthe previous section governs the dynamics of the pionsin baryon free space as it is. By expanding U = exp(iτ⃗ ·π⃗/fπ) up to a given order in the pion field we obtain thehadronic part of the lagrangian for the weak decay of theneutral pion asL = 12∂µπa∂µπa − 12m2ππaπa+fπg2 cos θWZµ∂µπ0 (11)− Nc48π2fππ0 tan2 θW cos 2θW g2εµναβ∂µZν∂αZβ+ · · · .π0 π0(a)ZZZννννν(b)__FIG. 1: π0 → νν¯ processes.The Lagrangian yields proper vertices for π0 → Z andπ0 → ZZ, which contribute to the processes π0 → νν¯as shown in Fig.1. Observe that there does not appeara term such as π0 → W+W− despite fulfilling chargeconservation.The amplitude for the process shown in Fig.1a isMπ0→Z→νν¯ = GF fπ√2u¯ν(p1)p/(1 − γ5)vν(p2), (12)where we have approximated the Z-boson propagatorsimply as i/(p2 −M2Z) ∼ −i/M2Z and GF = g2/(8M2W ).p1 = (ω1, p⃗1) and p2 = (ω2,−p⃗2) are the energy-momentaof outgoing neutrinos and p = p1+p2 is that of the incom-ing pion. For massless neutrinos u¯ν(p1)/p1 = /p2v(p2) = 0so that the amplitude vanishes identically.The process of Fig.1b leads toMπ0→ZZ→νν¯=−i Ncg248π2fπtan2 θW cos 2θW×εµναβ∫d4k(2π)4kα1 kβ2 (13)× u¯(p1)γµ(1− γ5)(k2/− p2/)γν(1 − γ5)v(p2)(k21 −M2Z)(k22 −M2Z)(k2 − p2)2where k1 = k+p/2, k2 = −k+p/2 represent the momentaof the two internal Z-boson lines. The loop-momenta areintegrated only up to a cut-off Λ ∼ 1GeV for the low-energy effective theory. Taking the square of the ampli-tude and tracing over the spinor structure gives|Mπ0→ZZ→νν¯ |2= N2c g4144π4f2πtan4 θW cos2 2θW (14)×IΛ(p, p1, p2)(p2p1 · p2 − 2p · p1p · p2)where IΛ(p, p1, p2) comes from the loop-integration butwhose form is not important in view of the next result: inthe pion rest frame (p2p1 · p2 − 2p · p1p · p2), which arisesfrom the spinor traces for massless neutrinos, vanishesidentically, consistent with the helicity selection rule.IV. π0 → νν¯ IN THE DENSE SKYRMIONMATTERThe Skyrme Lagrangian supports classical soliton solu-tions, skyrmions, whose topological winding number canFigure 1.7: Diagrams contributing to the pi0 → νν¯ decay. [18]Theoretical and experimental branching ratioThe theoretical branching ratio of this rare decay depends on the neutrinomass[19, 20, 21]. It can be given asBr(pi0 → νν¯) = 3× 10−8( mνmpi0)2 ×√1− 4( mνmpi0)2 (1.5)91.4. Outline of the thesisfor a single neutrino type in the case of Dirac neutrino [22]. Using the upperlimit of neutrino mass, mν < 0.23 eV, reported by Planck collaboration [23],the branching ratio of the pi0 → νν¯ decay is constrained to be lower than1.65 × 10−24, while another study shows it should be lower than 3 × 10−15assuming mν ∼ 1eV [24].The present experimental upper limit on the branching ratio of this SM-forbidden decay was set by the E949 experiment with Br(pi0 → νν¯) <2.7×10−7 at 90% confidence level (C.L.) to all possible νν¯ states [22], whichis much larger than what above studies suggested. In E949, the upper limitis entirely determined by how well photons, coming from pi0 decays, can berejected.In this thesis, we used the similar method but with pi0 samples from theNA62 for exploring a new upper limit. With a much more powerful photondetection system in NA62, we are expected to lower this limit to 10−8.1.4 Outline of the thesisThe setup of the NA62 experiment is described in Chapter 2. Chapter 3presents strategies for studying the Kpi2 background, and the branching ratioof the rare decay pi0 → νν¯. A set of selection cuts is illustrated in Chapter 4,where the efficiency results of several pi+/µ+ suppression techniques are alsopresented. Chapter 5 shows how we set photon veto cuts using a small partof data taken in 2015. Finally, Chapter 6 presents analysis results based ondifferent runs taken in 2015 and Monte Carlo simulations.10Chapter 2NA62 ExperimentalApparatusThe layout of the NA62 experimental setup is shown in Figure 2.1. Beamproperties are described in section 2.1. There are two tracking detectors formeasuring the momentum and position of the K+ track (section 2.2.1) andpi+ track (section 2.2.2). Besides, a particle identification system is usedto tag the incident K+ (section 2.3.1) and distinguish pi+ from µ+ (section2.3.2) and e+ (section 2.4.2). Furthermore, veto modules for rejecting beambackground (section 2.4.1), photons (section 2.4.2) and muons (section 2.4.3)are designed to reach the required sensitivity. A detail description of theapparatuses and their working status during the 2015 data taking can befound below.11Chapter2.NA62ExperimentalApparatusLiquid KryptoncalorimeterMuonvetoIRCSACCEDARRICHGigatrackercollimatortargetLarge anglephoton vetoLarge anglephoton vetotaxachromatachromatvacuumStraw chambersspectrometer1 m0 m 50 m 100 m 150 m 200 m 250 mSpectrometer magnetCHODCharged anti counterFigure 1. NA62 experimental layoutStraw spectrometer: Four chambers of straw tubes separated by the MNP33 dipole mag-net will be operated in vacuum in order to provide momentum resolution of σ(p)/p = (0.3 ⊕0.008p[GeV/c]))% with a minimal material budget.RICH: A ring imaging Cherenkov detector will measure the velocity of the charged particlesallowing to separate pions from muons and will provide time resolution better than 100 ps [4].CHOD: A plastic scintillator charged hodoscope will be used in the trigger.IRC and SAC: Shashlyk type veto detectors covering photon angles down to zero (SAC) and alsoserving to veto converted in the upstream material photons (IRC).LKr: The NA48 liquid krypton calorimeter with renewed readout electronics will serve as aphoton veto for photons with angles from 1.5 to 8.5 mrad with inefficiency less than 10−5 for photonwith energies above 10 GeV.MUV: Three muon veto stations based on iron and scintillator sandwich will provide separationbetween pions and muons better than 10−5.Both KTAG and Gigatracker are exposed to the full 800 MHz hadron beam while the rate seen bythe downstream detectors is at most 10 MHz.3 Probing the lepton universality with K± → l±ν decaysWithin the Standard Model the dilepton charged pseudoscalar meson decays proceed as tree levelprocesses through a W exchange. However, the helicity conservation leads to a strong suppressionof the electron mode. The Standard Model (SM) expression for the ratio RK = Γ(Ke2)/Γ(Kµ2) is afunction of the masses of the participating particles and is given byRK =m2em2µ⎛⎜⎜⎜⎜⎜⎝m2K − m2em2K − m2µ⎞⎟⎟⎟⎟⎟⎠ (1 + δRK), (1)where the term δRK = −(3.79±0.04)% represents the radiative corrections. In the ratio RK the theoret-ical uncertainties on the hadronic matrix element cancel resulting in an extremely precise predictionRK = (2.477 ± 0.001) × 10−5 [5].Due to the impossibility to distinguish the neutrino flavour the experimentally measured ratio issensitive to possible lepton flavour violation effects. In particular, various LFV extensions of the SM(MSSM, different two Higgs doublet models) predict constructive or destructive contribution to RK ashigh as 1 % [6].Experimentally, the ratio RK can be expressed asRK =1D· N(Ke2) − NB(Ke2)N(Kµ2) − NB(Kµ2) ·A(Kµ2) × ϵtrig(Kµ2) × fµA(Ke2) × ϵtrig(Ke2) × fe ·1fLKr, (2)QCD@Work 201400003-p.3Figure 2.1: Layout of the NA62 experimental setup (scaled model) [25].122.1. Beam line2.1 Beam lineThe SPS is a particle synchrotron accelerator with a circumference of nearly7 km. It takes particles from the Proton Synchrotron and accelerates themup to 400 GeV/c , providing beams for the LHC and the other three fixed-target experiments including the NA62 in the North Area. As shown inFigure 2.2, the proton beam extracted from the SPS is split onto threetarget stations (T2, T4, and T6) to generate secondary beams for thoseexperiments. Not all beam particles interact in T4 and T6 stations dueto the presence of the magnets. The non-interacted proton beam is thentransported via a series of tunnels (P42 beamline 4) for approximately 823 mto the North Area High Intensity Facility (NAHIF) [26]. At the beginning ofthe P42, there are two vertically-motorized beam-dump/collimator modules,TAX 1 and TAX 2, whose apertures can be changed to get different protonbeam flux intensity.Figure 2.1: Scheme of the primary and secondary beams, from SPS to NA62; lines P42and K12 are visible2.1.2 Kaon-beam momentum selectionThe NA62 experiment receives a high-intensity beam of 750 MHz, K12, with a6% average content of K+, a 20% content of pions and a great majority of protons[13]. The choice of K+ instead of K is made, since the production of K+ with anaverage momentum of 75 GeV/c, in the secondary beam, is about twice the negativeone.In an experiment looking for ultra-rare decays, the tuning of the beam line isone of the most important studies to be performed. An empirical formula gives aprediction of the secondary-beam particle content produced by the interactions of aproton beam on a beryllium target. If the primary protons have a fixed momentump0, the maximum content of K+ in given momentum and solid angle is pK = 0.35p0;for a proton beam of 400 GeV/c, pK = 140 GeV/c.Only the K+ decaying inside a vacuum fiducial region can be studied since,outside of it, the kaons could interact and their decay products could lead to particlemismatching; for this reason, the maximisation has not to be evaluated on thetotal kaon production, but only on the kaons decaying inside that region, thesebeing 4.5 · 106 K+/s, decreasing pK/p0 to 0.23. 75 GeV/c is the momentum whichmaximises the acceptance for K+ ! ⇡+⌫⌫¯. In a K+ decay with an energy of 75GeV/c, particles associated with a ⇡+ must therefore carry an energy greater than40 GeV, sucient to prevent their escape without detection.16Figure 2.2: This diagram shows how extracted proton beam from the SPSfeeds the NA62 experiment.On the exit of the P42, the proton beam is focused and directed onto aberyllium target in the T10 target station at a zero angle. This berylliumtarget is a 400 mm long cylinder with a diameter of 2 mm. After interactingwith the target, a secondary hadron beam is produced and passes the two4An alternative path for the protons is available via target T6, which joins P42 after∼130 m132.2. Tracking devicesParameter Measured Design valueAverage particle momentum (GeV/c) 74.9 75Proton flux on T10 target per 4.8s spill(full intensity)3.3× 1012 3.3× 1012Total flux per pulse (full intensity) 2.2× 109 2.25× 109RMS divergence at CEDAR horizontal (mrad) 0.07 0.07Fraction of proton in beam (%) 22.4 23Fraction of K+ in beam (%) 6.6 6Fraction of pi+ in beam (%) 70.2 70Fraction of µ+ in beam (%) N.A. < 1Table 2.1: Comparison between the measured beam properties in 2015 runwith designed values [27]collimators with an adjustable aperture which select particles with the anglelower than ∼ 4 mrad. Beam optics consist of quadrupole magnets (Q1, Q2,and Q3) and a beam dump element consisting of a momentum-definingslit are used to select hadrons with a central momentum of 75 GeV/c (±1%). Also, another series of quadrupole magnets (Q4, Q5, and Q6) serve topreserve the beam alignment and sweep aside external muons and positrons.The choice of momentum at 75 GeV/c is a result of the trade-off betweenseveral factors mentioned in the NA62 technique design [1]. In one word,the purpose is to maximize the accepted rate of the K+ → pi+νν¯ events inthe useful 60 m fiducial region. At the momentum of 75 GeV/c, the ratio ofproduction rate K+/K− is about 2.1, and the ratio of K+/pi+K−/pi− equals ∼1.2,which is the reason why we chose to use a positive hadron beam ratherthan negative one. Only 6% of the secondary particles are K+, the othersare protons and pi+. During the 2015 data taking, the K12 beam line wassuccessfully commissioned. Its properties at full intensity can be checked inTable 2.1. Although it could reach the full intensity, most of the data weretaken in low intensity to protect the electronics from the radiation.2.2 Tracking devicesThere are two tracking spectrometers; one is placed in the upstream of thedecay region for measuring the momentum and position of beam particles,and the other is put in the downstream for detecting charged decay par-ticles. The whole experiment cannot succeed without knowing the precise142.2. Tracking devicesmomentum of two tracks, which makes the tracking system an essentialpart in NA62. Not only does it give the signature of K+ → pi+νν¯ events,but it also provides the m2missing to veto backgrounds of the kinematicallyconstrained decays. Besides, the decay vertex reconstructed by two tracks’momentum is useful for checking whether the decay happens in the fiducialregion or not, further suppressing accidental beam background caused byhadronic interactions. With the precise position and direction of the decayparticles, tracks can be propagated to other detectors, providing more crosscheck criteria to reject the background.2.2.1 GTKThe GigaTracker (GTK), operating in the vacuum, measures the momentumof beam particles with a total rate ∼750 MHz. It was placed along thebeam line behind the kaon tagging detector (CEDAR) but before the fiducialregion. It is composed of three stations interleaved within four achromatmagnets, as shown in Figure 2.3. Each station is a silicon pixel detectorwith a total number of 18000 pixels (300µm× 300µm) arranged in a matrixof 90×200 elements. This configuration provides the precise positions of thecharged particles with a spatial resolution of ∼0.087 mm. The thickness ofthe pixel is set to be 200 µm corresponding to 0.22 X0 (radiation length).2. The NA62 experimental setup 38detail in chapter GigaTrackerThe GigaTracker (GTK) is a core detector in the NA62 experimental strategy for the track-ing of kaons, needed for the missing mass based kinematic rejection of the background kaondecays.It is a spectrometer composed of three stations mounted in between four achromat magnetsas shown in figure 2.4. The detector is placed along the beam line, just before the fiducialregion in the decay vacuum pipe.Figure 2.4: Layout of the GigaTracker stations.The measurement of the particle momentum and direction is obtained through a magneticfield: the path of the particle is bent depending on its momentum. As indicated in figure2.4, the second station is displaced by 60mm from the beam axis.Each GTK station is a hybrid silicon pixel detector with a total size of 63.1mm ⇥ 29.3mm,thus matching the expected beam dimensions (table 2.1). The pixel size is (300⇥300) µm2.A total number of 18 000 pixels, arranged in a matrix of 90⇥ 200 elements, make one sta-tion. The pixel thickness is 200 µm and corresponds to 0.22% X0: a minimal amount ofmaterial is in fact required not to spoil the beam divergence and limit the rate of beamhadronic interactions. Including the material budget for the pixel readout and cooling, thetotal amount per station remains below 0.5% X0.The expected beam rate of 750MHz is not uniform over the detector area, and presents apeak value over 1.4MHz/mm2. The beam intensity distribution over the GTK station 3is shown in figure 2.5.Figure 2.3: Here is the GTK schematic layout. Three GTK stations (inblue) and four dipole magnets (in grey) are visible. The yellow line showthe path of the K+ beam.To mea ure the direction and momentum of the charged particles, thefirst two ma nets (Mag1 and Mag2) bent the beam off-axis, and then the152.2. Tracking devicesother two magnets (Mag3 and Mag4) reflect it back to its original path.We can measure the value of the momentum by checking how much the off-axis displacement of the beam particle is. The GTK provides a 0.2% RMSmomentum resolution and nearly 16 µrad angular resolution [1].Due to the high rate of particles, and the fact that kaons are ten timesless than pions in the beam, a time resolution lower than 200 ps of the GTKmust be achieved to avoid accidental background mentioned in section 1.1.3.Thanks to the fast readout electronics consisting of ten Application SpecificIntegrated Circuit (ASIC) chips [28], the estimated track time resolutionusing all three stations can be better than 150 ps. In order to reduce theradiation-induced leakage current on sensors, an innovative cooling systemcirculating a flow of liquid C6F14 in micro-channels was designed to keep thetemperature of the detector at 0 Co (upper limit: 5 Co).There are three more beam elements between GTK2 and GTK 3: amuon scraper for sweeping away most of the muon halo from the beam lineby means of a toroidal magnetic field, a collimator to clean up the residualhadron halo, and a dipole magnet (TRIM5) to deflect the beam by 1.2 mradtowards positive X 5.During 2015 data taking, all three GTK stations were installed but notfully commissioned. Since the readout channels of GTK are noisy in 2015run, more than 90% events were lost if requesting GTK candidate. But thedata with GTK is still enough for investigating the detect’s performance,such as the kinematic suppression efficiency for the Kpi2 background. Exceptnoisy readout, all infrastructure, such as vacuum, mechanics, and cooling,worked properly. The time resolution of three GTK stations measured underthe bias voltage 6 in 2015 run is: σGTK1 = 235 ps, σGTK2 = 233 ps, andσGTK3 = 257 ps [27]. This is a little bit worse than the required value, 200ps, which is caused by the systematic errors of the time offsets.2.2.2 STRAW spectrometerThe STRAW is a spectrometer placed nearly 80 m downstream away fromthe GTK3 for tracking charged decay particles and vetoing decays, whichhave multiple charged tracks, like Kpi3 decay. The Straw spectrometer alsoworks in vacuum to minimize multiple scattering. It consists of four cham-bers intercepted in the middle by a high aperture dipole magnet (MNP33)providing a vertical B-field of 0.36T for measuring the momentum. A5The NA62 reference frame is right-handed, with the Y axis pointing to the zenith andthe Z axis on the direction of the beam line.6GTK1 and GTK2 were at 300 V, and GTK3 was at 216V.162.2. Tracking devicesschematic view of the detector is shown in Figure 2.4. Each chamber ismade of 1792 straw tubes has two modules providing the measurement offour coordinates (x, y) and (u, v) [29], see Figure 2.5. For each coordinateview, it has four layers each with 112 straws. The layout configuration ofstraws was designed to make sure that at least two hits per view are alwayspresent. Straw tubes are filled with working gas Ar/CO2(70/30). They aremade of 30 µm tungsten anode wire and 36 µm thick polyethylene tereph-thalate film coated on the inside with 0.05 µm of Cu and 0.02 µm of Au.Internal diameter and length of tubes are 9.8 mm and 2.1 m, respectively.3.5   Straw Tracker   241  3.5 Straw Tracker 3.5.1 Introduction The purpose of the STRAW Tracker is to measure with good accuracy the direction and the momentum of secondary charged parti les originating from the decay region. The spectr meter (see Figure 220) consists of four chambers interc pted in the middle by a high aperture dipole magnet providing a vertical B-field of 0.36T.  Each chamber is equipped with 1’792 straw tubes, which are positioned in four “Views” providing  measurements of four coordinates (see Figure 221).      Figure 220. Schematic view of the magnetic spectrometer.  The main building block of the detector is an ultra-light straw tube which is 2.1m long and 9.8 mm in diameter.  The tubes are manufactured from 36 Pm thin PET27  foils, coated –on the inside of the tube- with two thin metal layers (0.05 Pm of Cu and 0.02 Pm of Au) to provide electrical conductance on the cathode.  The anode wire (Ø=30 Pm) is gold-plated tungsten. Straw Tracker Detector Requirements As illustrated in the proposal [12], kinematical constrains in the events allow the rejection of the majority of the background provided the kaon and pion tracks are reconstructed with good accuracy. Two principal performance requirements –for secondary particles- follow from this:           and                                                             27 PET = polyethylene terephthalate Figure 2.4: Schematic view of the magnetic spectrometer.MNP33 provides a momentum kick of 270 MeV/c towards negative X,roughly compensating for the 1.2 mrad deviation introduced by GTK, seesection 2.2.1.To provide enough kinematical constraints, the straw tracker should sat-isfy two requirements: ∆PP < 0.01 and ∆θKpi < 60 µrad. For this, thespatial resolution should be better than 130 µm per coordinate. The spatialresolution highly depends on the detector’s gain, one of the most importantparameters of gaseous chamber. Different working voltage and the gas mix-tur would e up with different gain values. The first gain measurementof the straw is shown in Appendix A. Besides, a detailed description of thestraw readout system can be found in reference [30].During 2015 date taking, all four straw chambers were commissioned,and all straws except one participated on a regular basis. The time resolutionof the STRAW is not so good, ∼ 5 ns, that we usually use other downstreamdetectors, such as RICH or CHOD, to provide the time of downstream track.172.3. Particle identification and timingNA62 TD Document      242  In addition to the above, it is important to stress that the overall physics performance of NA62 depends on a number of experimental necessities for the Straw Tracker:  x Use of ultra-light material along the particle trajectory in order to minimize multiple Coulomb scattering, in particular, near the first chamber. x Integration of the tracker inside the vacuum tank. x An intrinsic spatial resolution that allows a precise reconstruction of the intersection point between the decay and parent particle. x Average track efficiency near 100%. x Capability to veto events with multiple charged particles x Sufficient lever arm between the four chambers allowing to re-use the exiting dipole magnet.     a) X Coordinate View b) Y Coordinate Viewc) U Coordinate View d) Overlay of four Views  Figure 221. Schematic drawing of the four "Views" that compose each straw chamber. a) the x-coordinate view with vertical straws, b) Y-coordinate View with horizontal straws, c) the U-coordinate view (the V-coordinate view is rotate by 90 degrees compared U-Coordinate), d) A full chambers consisting  of the X,Y,U and V Views; the active area of the chamber covers a diameter of 2.1m. The gap near the middle of each layer is kept free for the beam passage.  From these constrains follow the main requirements of the detector:  x Spatial resolution ≤ 130 Pm per coordinate and  ≤ 80Pm per space point x ≤ 0.5% of a radiation length (X0) for each chamber x Installation inside the vacuum tank  (P = 10-5 mbar) with minimum gas load for the vacuum system                               ) Figure 2.5: Schematic drawing of the four views of each straw chamber. a,b, c show the views of x coordinate with vertical tubes, y coordinate withhorizontal tubes and u coordinator with 45o oriented tubes7, respectively. dshows a full ch mber with all four v ews.2.3 Particle identification and timing2.3.1 CEDARTo distinguish kaons from pions and protons in the incoming beam of about750 MHz particles, a CErenkov Differential counter with Achromatic Ringfocus (CEDAR) was placed before the GTK. The CEDAR is designed toonly detect the Cerenkov light produced by particles of kaon mass becausethe Cerenkov light produced by particles of different masses would havedifferent angles so that it cannot pass optics selection and is absorbed on itsway. Overall, the particle rate that the CEDAR observes is nearly 45 MHz.The CEDAR is a ∼ 7 m long vessel filled with hydrogen or nitrogengas at room temperature, which reduces multiple Coulomb scattering. The182.3. Particle identification and timinginternal optical system consists of a Mangin mirror, a chromatic corrector,lenses and a diaphragm as shown in Figure 2.6. The Cerenkov light emittedby particles is reflected by a spherical Mangin mirror at the end of the vessel;then it passes through a chromatic corrector which makes sure that light ofall wavelengths arrives at the same radius onto a ring-shaped diaphragm of100 mm radius with adjustable aperture width. The aperture was set toonly allow the light produced by kaons to hit on the photodetector made of384 photomultipliers (PMTs) divided into 8 light boxes called octants.  2.2   CEDAR   49     Figure 17 Schematic layout of the Standard West-Area CEDAR.  Two versions of the CEDAR counter have been built for use at the SPS (1). The North CEDAR, filled with Helium gas, is optimized for high energies and the West CEDAR, Nitrogen filled, for lower beam momenta. The difference is related to the Cerenkov angle, determined by the beam momentum and the refractive index of the gas, and the optical correction, which relates to the dispersion of the gas used. It has been verified by a ray tracing program that the West version of this instrument would function well for our application using Hydrogen at room temperature instead of Nitrogen, thus reducing significantly the scattering of the beam in the gas. The optical design minimises the dispersion of Cerenkov light and enables   the aperture of the diaphragm to be reduced. Thus, photons produced by charged kaons pass through while light from pions and protons is blocked.  During 2006, a test run was performed on one of the CEDAR-West Cerenkov counters (filled with N2) and validated its ability to distinguish kaons from pions and protons in the NA62 experiment, as well as the light spot shape predicted by a simulation program.  It was also found from the simulation that the upstream 1.2 metre section of beam pipe containing hydrogen contributes only marginally to the efficiency and can thus be replaced by an extension of the beam vacuum pipe. In addition to a small reduction in multiple Coulomb scattering, such a modification is helpful in the redesign of the optical system necessary to handle the increased photon flux. The main parameters of the proposed Hydrogen-filled CEDAR-W counter are listed in Table 10.  The main effects that broaden the light spot at the diaphragm are: 1. optical aberrations, limited to about 6 microns and therefore negligible; 2. chromatic dispersion, largely corrected for by the chromatic corrector; 3. multiple scattering of the beam during its traversal of the gas, minimised by the choice of Hydrogen gas; Figure 2.6: Schematic layout of the CEDAR.The CEDAR detector is required to achieve a kaon tagging efficiencyabove 95%, with a time resolution of 100 ps, and a contamination of thekaon sample smaller than 10−4 [31].2.3.2 RICHT e Ring Imaging CHere kov (RICH) is ano her article identification de-tector placed after th urth straw chamber along the beam lin . I s mainpurpose is to provide a further muon suppression factor of more than 100by identifying pi+ and µ+. The RICH consists of a 17 m long, 4 m widecylindrical vessel, filled with neon gas at atmospheric pressure. There is abeam pipe inside the vessel to allow free passage to the undecay beam.A mosaic of 20 mirrors plac d at the end of the vess l i used to r flectthe Cherenkov light a d focus it onto photon detector placed in the front.The mirror mosaic is composed of 18 spherical mirrors of hexagonal shape(350 mm side) and 2 mirrors of semi-hexagonal shape located close to the192.3. Particle identification and timingbeam pipe. The semi-hexagonal mirrors have a thickness of 2.5 cm. Thesemirrors have a focal length of 17 m. And the photon detector is made of2000 photomultipliers (PMT) arranged into two groups to avoid the shadowinduced by the beam pipe. A schematic layout of the-the RICH detector isshown in Figure 2.7.NA62 TD Document      290  The number of emitted photons  through a radiator thickness    per unit of photon energy   is predicted by the Franck-Tamm equation as a function of the Cherenkov angle (assuming a charged particle of unit charge):                                         The actual number of photoelectrons      (i.e. electron produced by photons impinging on the PM photocathode) is a convolution of the previous equation, the spectral response of the PM, the reflectivity of the mirror, the transparency of the gas and of any medium in front of the PM, the geometrical acceptance of the PM, multiplied by the radiator length L, i.e. the mirror focal length. Each of these quantity depends on the photon energy. Even if the index of refraction depends on it, it is traditional to summarize the performances of a RICH through a quality factor N0:                   where a good detector can have N0 around 100 cm1. If the probability to produce more than one photoelectron in the same PM is not negligible (as in our case) what is really meaningful is the number of fired PM Nhit which will be smaller than Np.e.. 3.6.1 Expected Performances The RICH performance expectations have been validated testing a full length prototype with particle beams. These results are described in section 3.6.6.  3.6.2 The Vessel The RICH vessel must contain the Neon gas without leak and ill be operated in slight overpressure w.r.t. the external atmosphere. The gas density must remain constant (within 1%) over long time. The PM will be located at the upstream end of the vessel: together with their support structure they must be outside the fiducial acceptance of the apparatus, bringing the diameter of the vessel to 3.8 m.  Figure 282 Schematic drawing of the RICH detector; the downstream section of the vessel is cut to show the mirrors and the beam pipe. The Vessel Functional Requirements (FR) FR.1. Develop a rational installation strategy with in-situ part assembly and alignment possibilities for this large size vessel. FR.2. Provide a tight, clean and non-reflective containment to the radiator gas. Provide a stiff gas containment, keeping in mind possible pressure variations, between 0 and 150mbar overpressure. Figure 2.7: Schematic layout of the RICH. A beam pipe is shown in red line,and a mosaic of 20 mirror is visible.The Cherenkov light emitted by a par icle would form a rin on thephoton detector. The radius of this ringr = f tan θ = f tan(arccos(cnv)) (2.1)only depends on the velocity of the particle assume the refractive index (n)of gas medium and focal length (f) is set. So particles with different massat same momentum would end up with different radius shown in Figure 2.8.From knowledge of the ring radius in the RICH and particle’s momentummeasured by the STRAW, the mass of the detected particle can be deducedas,m =P√1− β2cβ, therein β =1n cos(arctan( rf ))(2.2)This is how RICH detector works to identify particles with different masses.A particle can emit Cherenkov radiation once its momentum is greaterthan a threshold, Pt =m√n2−1 . For the neon gas at atmospheric pressure, thisthreshold is nearly 12.5 GeV/c. Hence, the pi+ momentum should be greaterthan 15 GeV/c in order to have a full efficiency of detecting pi+. As momen-tum (velocity) increase, the radius signal of the pi+ and µ+ would become in-distinguishable from each other as shown in Figure 2.8. At same momentum,particles with lower mass, like electrons, are corresponding to larger radiusas indicated by Equation 2.2. However, as particle momentum increases,202.3. Particle identification and timing110210310410Straw momentum [GeV/c]0 10 20 30 40 50 60 70 80 90 100Ring radius [mm]050100150200250300KaonPionMuonElectronFigure 2.8: Here is the events distribution of fitted RICH ring radius ofdecay particle versus its straw momentum for a 2015 data run.the ring radius will reach a limit. When momentum is above ∼ 35 GeV/c,it is difficult to distinguish the radius between pions and muons. Hence, theupper limit of track momentum is set to be 35 GeV/c for K+ → pi+νν¯ study.Overall, the momentum range of straw track for pi+/µ+ separation is from15 and 35 GeV/c. A test on a RICH prototype shows the µ+ suppressioninefficiency is 0.7%, and the time resolution is better than 100 ps averagedover the momentum range [32]. The remarkable timing ability of the RICHmakes it a perfect timing device for decay particles. Besides, it can alsobe used to reject multi-track events and provide a cross-check to the pi+momentum measured by the straw spectrometer assuming the particle is apion.It should be noted that mirrors alignment was not optimal during the2015 run. The taken data indicates that the pion-muon separation factor ofRICH is worse than expected; a cut on reconstructed rich mass, [0.1325, 0.2]GeV/c2, rejects 98.51% muons with the pion passing efficiency at 85.31%,see section Particle identification and timing2.3.3 CHODThe Charged particle HODoscopes (CHOD), also was used at NA48, is a fastscintillator system which produces signals when crossed by charged particles.It provides information on the positions of the track impact point and precisetime with a resolution of nearly 200 ps [33]. This powerful timing abilitycan be used in the trigger to select decay events with charged particles inthe final state. It can also be used to detect photonuclear reactions in theRICH mirror plane. Since the RICH mirror system amounts to nearly 20%of radiation length, it is possible that the high energy photon produced bypi0 in Kpi2 decay would undergo photonuclear interactions with mirror andproduce lower energy hadrons which cannot be detected by the LKr, henceincrease the photon veto inefficiency. Fortunately, the CHOD, placed afterthe RICH tank and before the LKr, can detect low energy charged hadronsand re-establish the photon veto sensitivity of the LKr.3.7   The CHOD   313    Figure  302 Schematic view of the CHOD detector   3.7 The CHOD   The existing NA48 charged hodoscope is a system of scintillation counters with high granularity and excellent time resolution (200ps) [15].  It will be re-used to detect possible photo-nuclear reaction in the RICH mirror plane and to back-up the RICH in the L0 trigger for charged tracks. The detector consists of 128 detection channels which are arranged in two planes of 64 horizontal and vertical scintillators. Each plane is divided in four quadrants with 16 counters (see Figure  302), so that the acceptance in the X-Y plane covers a radius of 121 cm.  The scintillator dimensions are summarized in Table 45. The counters are made with BC408 plastic scintillators which have fast light output and good attenuation properties.  The scintillation light from each counter is collected via a short fishtail, (made of Plexiglas) light guide, followed by a Photonis XP2262B photomultiplier. Table 45 Figure 2.9: Sketch of two planes of the CHOD.CHOD is composed of 128 plastic scintillator counters which are arrangedin two planes, providing x and y coordinates, see Figure 2.9. The upstreamplane has 64 vertical counters, while the downstream plane has 64 horizontal222.4. Veto systemcounters. Each plane is divided into four quadrants with 16 counters so thatspecific triggers could require various combinations of hit locations in eachplane. Two planes are separated by around 30 cm. The time differencebetween two planes’ signal can be used to reject fake coincidences caused bythe back-scattering from the LKr calorimeter. Each counter has a thicknessof 2 cm corresponding to 0.05 radiation length. The length of counters variesfrom 60 cm to 121 cm and the width changes from 6.5 cm to 9.9 cm [6]. Thescintillation light produced by the cross of a charged particle in each counteris read by a Photonis XP2262B photomultiplier (PMT) through a fishtailplexiglass light guide. Four modules of the front-end electronics developedfor the LAV are exploited to process CHOD signals [34].During the 2015 run, the CHOD provides level 0 trigger signal and level 0reference time to select events. A loose trigger selection requires at least twocounter hits within a time window, while a strict one required the coincidencebetween the signals of at least one vertical and one horizontal counter ofadjoining quadrants. The coincidence allows track time to be corrected forthe hit impact point. Since the CHOD cannot handle a high hit rate, a newCHOD with a higher level of segmentation was built, see Figure 2.10. It hasbeen installed and is ready for the 2016 run.2.4 Veto system2.4.1 CHANTIThe CHarged ANTIcounter (CHANTI), placed behind GTK, is used toidentify inelastic interactions of the beam with the collimator and the GTKstations as well as to tag beam halo muons in the region immediately closeto the beam. The critical events are the ones in which inelastic interactionsof the hadron beam with the silicon detector of the GTK3 take place. Thisinelastic interaction would bring in the beam related background in caseonly pi+ of the produced particles is detected by the STRAW. The presenceof the CHANTI can reject this event as shown in Figure 2.11. It is shown bya GEANT4 simulation that around 0.1% beam kaons may undergo inelasticinteractions with GTK3 [35], so left rejection factors contributed by theCHANTI veto and analysis cuts must reach the 108 in order to sufficientlysuppress this background.The CHANTI is composed of six square shape stations, placed inside thevacuum tube respectively at 27 - 77 - 177 - 377 - 777 - 1577 mm distancefrom the GTK3. Each station has a length of 300 mm and a rectanglehole (95 mm×65 mm) present in the centre. It is made of two layers, x232.4. Veto system9 NewCHODThe lateral acceptance region for charged particles downstream of the RICH and upstreamof the LKr calorimeter is defined by the LAV12 detector with an inner radius of 1070 mm,and the IRC detector with an outside radius of 140 mm. The CHOD is a two-dimensionalarray of scintillator tiles installed upstream of the LAV12 with the main function ofproviding a basic element for the L0 trigger when at least one charged particle crossesthe circular crown with the dimensions defined above. The subdivision of the acceptancesurface into two-dimensional tiles leads to an optimized distribution of hit rates, anddi↵erent groups of tiles can be selected to contribute to specific trigger requirements.Figure 29: The new CHOD detector is mounted on the front face of LAV12 (left). Itconsists of one detection layer with 152 scintillating tiles. The tiles are mounted frontand back of the thin G10 support panel (bottom right). At the periphery the structureis sti↵ened with honeycomb and aluminium construction profiles (top right).In each quadrant, a 30 mm thick plastic scintillator is divided into 38 tiles. Exceptfor three tiles near the external circular edge, their heights are 108 mm and their centresare spaced vertically by 107 mm, resulting in a 1 mm overlap. This is possible by placingalternatively one row of tiles on the upstream and the next on the downstream side of a3 mm thick central support foil (G10 with 35 micron Cu lining on both sides), suitablyperforated for the passage of 4.4 mm wide, 0.25 mm thick, 316L steel panduits (two pertile) to secure the tiles firmly in their positions (see Figure 29). Laterally most tiles areeither 134 mm or 268 mm wide. The scintillation light, collected and transmitted by1 mm diameter KurarayTM Y11 S wavelength shifting fibers, is detected by arrays of3 ⇥ 3 mm2 SensLTM SiPMs on mother-boards located on the periphery of the CHOD.38Figure 2.10: Schematic layout of the new CHOD [27].(y) layer, which is co posed of 24 (22) scintillator bars arranged in thevertical (horizontal) di ection. Each lay as two sublayers, made of 10+12(10+14) bars. A schematic layout of a complete CHANTI station in shownin Figure 2.12. For particles hitting the centre of the GTK3, the CHANTIcovers hermetically the angular region between 38 mrad and 1.38 rad, whilea coverage betwe n 57 mrad and 1.16 rad is exp cted for the particle hittingthe corner of the GTK [35].To work in the expected detect rate around 2 MHz, the CHANTI musthave a time resolution better than 2 ns to keep the random veto rate atan acceptable level. The CHANTI is able to veto about 95% of all kaoninelastic interactions with the GTK3. This vetoing efficiency reaches almost99% if restricting to potentially signal-like events [35].During the 2015 data taking period, CHANTI has been working smoothly,and its time resolution is steadily better than 1 ns. The single layer efficiencyhas been measured to be higher than 99% for straight tracks.242.4. Veto system    2.4     CHANTI   149  2.4 CHANTI 2.4.1 CHANTI Detector Requirements  The Charged ANTI (CHANTI) detector is required in order to reduce critical background induced by inelastic interactions of the beam with the collimator and the Gigatracker (GTK) stations as well as to tag beam halo muons in the region immediately close to the beam. The most critical events are the ones in which the inelastic interaction takes place in the last GTK station (GTK-3). In such cases, pions or other particles produced in the interaction, if emitted at low angle, can reach the straw tracker and  mimic a K decay in the fiducial region. If no other track is detected, these events can appear like a signal event, i.e. one single π+ in the final state.   A GEANT4 simulation has shown that kaon inelastic interactions with GTK-3 happens in about 1/103 cases, so that the combined rejection factors of the analysis cuts and the CHANTI veto must lead to a remaining inefficiency of 10-8. The purpose of the CHANTI is to identify inelastic interactions in the GTK  by  tagging  particles at higher angles w.r.t. to the beam. This can be achieved by placing a number of guard counters right immediately after GTK3. At the same tim  the CHANTI can also veto beam halo (muons) in the region closest to the beam.   Figure 123 Despite the ulltra thin GTK detectors, beam particles can create accidental background if they undergo inelastic interaction in the GTK material. The scattered particles are revealed in the CHANTI which is placed immediately after the third GTK station.  Finally a veto for charged and neutral particles placed just downstream of the last GTK station, provides additional rejection of the accidental background coming from hadronic interactions of the beam particles in the last GTK station, as previously discussed. This detector, called CHANTI, consists of scintillators assembled in a rectangular shape surrounding the beam. The CHANTI detector must be able to tag inelastic events with high efficiency.  Given that it will be sensitive to the muon halo and to the inelastic interactions the expected rate of particles that release enough energy to be detected will be around 2 MHz.  Even if it is not intended as a trigger veto at L0, the CHANTI must have a good time resolution (≤ 2 ns) to keep the random veto rate at an acceptable level:  for instance, assuming a 5 sigma (10 ns) time coincidence window with the event fine time at reconstruction level, a 2% inefficiency on the signal would be induced by CHANTI Figure 2.11: This figure illustrates how inelastic interactions of beam withthe GTK3 can mimic an event signal. The interactions produces multipleparticles including low angle pi+ whose path is indicated in green lines. Ifpi+ is the only particle reaching the STRAW, it may mimic a K+ → pi+νν¯event signal (pi+ matches with K+). However, with the presence of CHANTIshown in blue colour, this event would be rejected due to hits on CHANTIfrom other particles.2.4.2 Photon vetoThe photon veto system is composed of several calorimeters providing nearlycomplete hermeticity for decay photons with polar angles from 0 to 50 mrad.The large angle region, from 8.5 to 50 mrad, is covered by a system of12 calorimeters (LAV), while a Liquid-Krypton electromagnetic calorimeter(LKr) covers the angular region between 1 mrad and 8.5 mrad. The othertwo calorimeters, the IRC and SAC, are used for the angular region below1 mrad. Overall, the photon veto system must provide a suppression factorof 108 for rejecting Kpi2 decays.LAVThe LAV is composed of 12 stations situated between 120 and 240 m (seeFigure 2.1). The first eleven calorimeters incorporated into the decay tankwork in the vacuum, while the last one is placed after the RICH detectorand exposed to air. Each station is made up of four or five rings of leadglass blocks, recycled from the OPAL electromagnetic calorimeter [36]. Fig-ure 2.13 is the picture of the first station, A1, with lead glass installed.The number of the blocks in each station increases from 160 to 256 as thediameter of the stations increases.252.4. Veto system F. Ambrosino et al. /  Physics Procedia  37 ( 2012 )  675 – 682 677Figure 1: The NA62 detector layout.of 65 mm in y and 95 mm in X due to the rectangular shape of the beam. For particles hitting the GTK-3 centerthe CHANTI covers hermetically the angular region between 38 mrad and 1.38 rad w.r.t the beam axis, for particleshitting one of the GTK-3 corners the coverage is hermetic between 57 mrad and 1.16 rad. This must be comparedto the highest angle under which a Large Angle Veto (LAV) station is possibly able to detect particles producedin the GTK-3 that is 49 mrad for particle produced at GTK-3 corner, so that LAV complements at low angles theinformation given by CHANTI. The CHANTI, by itself, is able to veto about 95% of all inelastic interactions ofK in GTK-3 regardless of the final state. This vetoing efficiency reaches almost 99% if one restricts to potentiallysignal-like events, namely the ones where the kaon either did not survive the inelastic interaction or did not decay inthe fiducial volume, and one track is reconstructed by the straw spectrometer. Each station is made up of two layers,called layer x and y respectively. A y(x) layer is composed of 22 (24) scintillator bars arranged parallel to the x(y)direction and individually shaped at the appropriate length. Each layer is composed by two sublayers, made of 10+12(10+14) bars, and staggered by half bar. Each bar is triangularly shaped, and two staggered bars face oppositely asshown in fig. 2. Light is collected by means of one WLS fiber placed inside each bar and read at one side by a siliconphotomultiplier (SiPM).Figure 2: Left: Layout of a complete CHANTI station. Right: Jig used to align bars during gluing; on top Teflon mask to distribute glue spotsThe basic building block of the CHANTI is a scintillator bar in form of a triangular prism similar to the onesused in the D0 pre-shower detectors [9] and in the MINERVA experiment [10]. It is produced at the NICADD-FNALextruded scintillator facility [11] and consists of an extruded polystyrene core (Dow Styron 663 W) doped with blue-emitting fluorescent compounds (PPO 1% by weight and POPOP 0.03% by weight) and a co-extruded TiO2 coatingFigure 2.12: A layout of a complete CHANTI station.The particles crossing the LAV d tector mainly are photons from kaondecays, as well as muons and pions in the beam halo. When photons tra-verse the lead glass block, produced electromagnetic showers would emit theCherenkov light which is detected by the PMTs via a 4 cm long cylindri-cal light guide. A test on the prototype with lead glass modules shows theinefficiency for the detection of the electron is 1.2+0.9−0.8 × 10−4 at 203 MeVand 1.1+1.9−0.7×10−5 at 483 MeV [37], which satisfies the requirement that thedetection inefficiency of LAV for photons with energies as low as 200 MeVshould reach 10−4.The LAV provide time and energy measurements based on the time-over-threshold (ToT) technique. Results [6] show the time resolution of a singleblock isσt =220ps√E(GeV )⊕140 ps (2.3)and the energy resolution isσEE=9.2%√E(GeV )⊕ 5%E(GeV )⊕2.5% (2.4)The readout chain for the LAV is composed of two different types of boards, adedicated front-end board (LAV-FEE) board and a common digital readoutboard called TEL62, used by many of the NA62 detectors.262.4. Veto system2. The NA62 experimental setup 50spectively; the blocks are 37 cm in length. Each block is read out at the back side by aphotomultiplier, which is optically coupled via a 4 cm long cylindrical light guide of thesame diameter as the PMT. A complete module (block plus PMT, see figure 2.16) is acommon assembly; the block and PMT cannot be independently replaced.Figure 2.16: A module from the OPAL calorimeter (left). The 1st LAV station with 32⇥5wrapped OPAL lead glass calorimeter elements (right).A LAV station is made by arranging these blocks around the inside of a segment of vacuumtank, with the blocks aligned radially to form an inward-facing ring. Multiple rings areused in each station in order to provide the desired depth for incident particles. The blocksin successive rings are staggered in azimuth; the rings are spaced longitudinally by about1 cm. Figure 2.16 shows the completed first station of the LAV system.The LAV system consists of a total of 12 stations, the diameter of which increases withdistance from the target. The geometry of the LAV stations is summarised in table 2.2.As a result of the staggering scheme, particles incident on any station are intercepted byblocks in at least three rings, for a total minimum effective depth of 21 radiation lengths.The vast majority of incident particles are intercepted by four or more blocks (27 X0). Thestations with five layers (A1-A8) are 1.55m in length, while those with four layers (A9-12)are 1.43m in length.The LAV provide time and energy measurements with a readout scheme based on thetime-over-threshold (ToT) technique. This is implemented using a dedicated front-enddiscriminator board [34] which converts the analog signals to low-voltage differential sig-Figure 2.13: Here is the first LAV station which has 5 rings of OPAL leadglass blocks. The glasses are wrapped.LKrThe Liquid Krypton Calorimeter (LKr) is a key detector for the NA62 ex-periment. First, it has powerful photon veto ability. To meet the requiredph ton r jection factor, LKr must have a detected inefficiency better than10−5 for photon with energy larger than 35 GeV. A tudy shows its photonveto inefficiency is lower than 0.9× 10−5 at 90% C.L. for detecting photonswhos are energies greater than 10 GeV [38]. It also plays an importantrole in sep rati g muons, pions and electrons which have different depositedproperties, such as the size of particle showers and deposited energy overSTRAW momentum (EP ).The LKr calorimeter is a quasi-homogeneous ionization chamber [39],filed with liquid krypton at the temperature of 120 K. Its volume is anoctagonal cylinder with surface area of 5.3 m2 and depth of 1.27 m. Thevolume was divided into 13248 ionization cells of a cross section 2 cm × 2cm by 18 mm wide, 40 µm thick copper-beryllium ribbons which are used aselectrodes to collect the ionization signal. An anode was set in the centre oftwo cathodes as shown in Figure 2.14. A photon or an electron entering theLKr produces an electromagnetic shower composed of low energy photonsand electrons which produce a certain number of electron-ion pairs propor-tional to the deposited energy. The shower is called a cluster, normallyencompassing quite a few LKr cells. The number of radiated cells depend272.4. Veto systemon the incident angle and the type of particles.2011 JINST 6 C12017Figure 2. Assembled LKr calorimeter structure and electrode details.The calorimeter active medium consists of a bath of ⇠10m3 of liquid krypton at 120K witha total thickness of 125 cm (⇠27 radiation lengths) and an octagonally shaped active cross-sectionof 5.5m2. An 8 cm radius vacuum tube goes through the centre of the calorimeter to transportthe undecayed beam. Thin copper-beryllium ribbons (of dimensions 40 µm⇥18mm⇥127 cm)stretched between the front and the back of the calorimeter form a tower-structure readout. The13248 readout cells each have a cross-section of about 2⇥2 cm2 and consist (along the horizontaldirection) of a central anode (kept at high voltage) in the middle of two cathodes (kept at theground). The assembled LKr calorimeter structure and details of the ribbons and spacer platelayout are shown in figure 2.2.2 Readout electronicsThe front-end part of the calorimeter readout was built for the NA48 experiment and comprises twocircuits. The initial current is derived from the charge measured by a preamplifier mounted insidethe cryostat at liquid Kr temperature and connected to the anode electrode by a blocking capacitor.The integration time constant of the charge preamplifier is 150 ns. The signal from the pream-plifier is transmitted to a combined receiver and differential line driver mounted outside the calori-meter close to the signal feed-through connectors. The receiver amplifies the preamplifier signaland performs a pole-zero cancellation. The signal after pole-zero cancellation has a rise-time ofabout 20 ns and a fall-time of 2.7 µs. The maximum signal level, 50GeV, corresponds to±1V into100W at the digitizer electronics input. The required signal to noise ratio is 15000 to 1.– 3 –Figure 2.14: Details of the ribbons and electrodesThe LKr also provides the energy, position and time measurement ofthe particle. The energy resolution of the LKr, measured using an electronbeam, can be presented as:σEE=3.2%√E(GeV )⊕ 9%E(GeV )⊕0.42% (2.5)For particle energy at 20 GeV , the energy resolution is around 1%. On theother hand, the space resolution is 1.1 mm in each coordinator, using thetest result:σx,yE= (0.42√E(GeV )⊕0.06)cm (2.6)The time resolution of a singl shower is nearly 500 ps.For working at high rate nvironment, a new readout system, the Calorime-ter REAdout Module (CREAM), is designed and used to provide 40 MHzsampling of 13248 cal rimeter channels, zero suppression, nd programmabletrigger sums for the experiment trigger processor [40].IRCThe Inner Ring Calorimeter (IRC) is situated before the LKr. It is a cylin-drical tube consisting of two parts: the first one has 25 layers of lead andscintillator, while another has 45 layers. The layout of lead and scintillator isbased on the Shashlyk technology: alternating lead and plastic scintillator282.4. Veto systemplates as shown in Figure 2.15. The incoming electron or photon inter-acts with the lead and produces an electromagnetic shower where chargedparticles produce scintillation light. Then light is then absorbed by fluo-rescent material and re-emitted to longer wavelengths which can transversethe plastic as attenuation length increases. Finally, the longer wavelengthlight can be detected by four PMTs via the wavelength shifting fibers. IRCis segmented into 4 parts, hence it has 4 channels.3.4   The Photon Veto Detectors   229 Description of the Shashlyk Technology  A detector of “shashlyk” type is based on consecutive lead and plastic scintillator plates. The first such detector was suggested in 1991 by Atoyan et al. as an electromagnetic calorimeter for the E-865 BNL experiment devoted to the search for lepton flavour violating decay K+ → S+Pe-  [63]. The incoming electron or photon interacts with the lead and develops an electromagnetic shower. The charged products of the shower produce scintillation light inside the plastic material which then could be absorbed and re-emitted to longer wavelengths by fluorescenting additions. At these longer wavelengths, the attenuation length of the plastic is lengthened considerably. The light is taken out by wavelengths shifting fibres (WLS) where a second wavelength shifting takes place usually to the green part of the spectrum to a photodetector (most commonly photomultiplier). The fibres pass through the plastic scintilla or and lead plates via holes in the pl tes. A schematic view of the layout is shown in Figure  208. Figure  208 Shashlyk technology The choice of lead for radiator and photon converter is motivated by the fact that lead has the maximal radiation to interaction length ratio. For a full general description of this type of calorimeter see [64]. A single module of shashlyk type calorimeter is also a single channel detector. The attenuation length of the emitted scintillation light in the plastic scintillator is much longer than the actual transverse size of the module which leads to light in all the fibres. It is important to note that splitting of the total number of fibres into bunches to be readout by different photodetectors doesn't diminish the single channel rate but only matches the geometry and the surface of the active photocathode area to the total surface of WLS fibres.  The shashlyk module has an internal particle detection inefficiency connected with the presence of the holes for the WLS fibres. Concerning the present application of such detectors this inefficiency is not an issue since if can be recovered by tilting or rotating the single shashlyk module as will be discussed in Section for the SAC and section for the IRC. Results from the Prototype Tests  A Small Angle Calorimeter (or SAC) prototype was constructed and tested during a 2006 test run. The active part of the constructed prototype was assembled from 70 lead plates with thickness of 1.5mm Figure 2.15: Shashlyk technology.SACThe Small Angle Calorimeter (SAC) is placed at the end of the experimentto cover small angular region not covered by the IRC. A magnet located at248 m from the target is used to deflect the non-interacting charged particlesof the beam so that only neutral particles, like photons, can reach the SAC.It also exploits the Shashlyk technology and has four channels.Both the SAC and IRC re exposed to photons with en rgi s hig er than5 GeV, and must p ovid the det ction inefficiency bet er than 10−4. During2015 run, both det to s readout was con cted to LAV-FEE and CREAMso they have tw r adout m dules.2.4.3 Muon vetoMuon veto system consists of three detectors, called the MUV1, MUV2,and MUV3, expected to provide a further µ+ suppression of the order of105 with respect to pi+.292.4. Veto systemAlthough the MUV1 and MUV2 are a part of muon veto system, theyare actually hadronic calorimeters instead of fast veto detectors like MUV3.They are used as complementary calorimeters to the LKr, measuring addi-tional deposited energy and also shower shapes of incident particles. Mostmuons deposit less energy in the LKr and these two hadronic calorimetersthan pions do. This can be exploited as a criterion, not significant de-posited energy, for distinguishing muons from pions. However, in some cases,muons may also deposit a major fraction of their energy via catastrophicbremsstrahlung or direct pair production. To distinguish these muons frompions, we should compare the difference between the shape of the electro-magnetic muon cluster and that of the hadronic pion cluster and find acut.The MUV3 is a hodoscope, similar as the CHOD, for detecting non-showering muons. It can act as a fast veto in the level 0 trigger to suppressthe high rate of the Kµ2 decays.MUV1-2The MUV1 and MUV2, placed after the LKr, are classic iron-scintillatorsandwich calorimeters with 24 (MUV1) and 22 (MUV2) layers of scintil-lator strips which are alternatively oriented in the horizontal and verticaldirections. Each scintillator layer consists 48(44) scintillator strips in MUV1(MUV2), the layout of one scintillator plate of both detectors is shown inFigure 2.16.In the MUV1, there are 23 inner steel layers with a dimension of 2700×2600×25 mm3 and 2 outer steel layers with a dimension of 3200×3200×25mm3. The larger outer layers serve as support for the whole structure andfor the WLS fibers, the photon detectors, and the read-out. Each iron plateis separated by 12 mm and contains a central hole of 212 mm diameter toallow the passage of undecayed beam particles. While for MUV2, 23 steellayers have a similar dimension of 2600× 2600× 25 mm3 and also have 12mm gap and 212 mm diameter central hole. The MUV1 and MUV2 areconstructed by simply stacking alternating iron and scintillator layers ontoeach other. A view of the MUV1 and MUV2 is shown in Figure 2.17.In the MUV1, the scintillator light is collected by WLS fibers, while theMUV2 routes the light by light guides. The MUV1 and MUV2 calorime-ters are read via the same ADC-based CREAM module used by the LKrcalorimeter [40].302.4. Veto system3.8   The Muon Veto Detector (MUV)   319  3.8.3 Scintillators and Light Transport MUV1 Scintillators The MUV1 module houses 2 x 12 layers of scintillators, alternatively oriented in the horizontal and vertical directions. Except for the strips close to the central beam hole and the very outer strips, the size of the scintillator strips is 2616 x 60 x 10 mm3. They thus cover the whole width of the MUV1 module, allowing a light read-out on both sides. Each scintillator layer consists in total of 48 scintillator strips (Figure 307 left): 34 strips of 2616 mm length, 6 somewhat shorter (with 2496, 2376, and 2256 mm length, respectively) to accommodate the support rods in the corners, and 8 strips of about half length and 54 mm width around the beam hole. The total number of scintillator strips in all 24 layers is 1152.   Figure 307 (Left) Layout and sizes of one (horizontal) scintillator layer of the MUV1 module. (Right) Drawing of the spacers in the MUV1 beam pipe region.              In the beam pipe region, the scintillator strips are terminated by a steel spacer ring around the beam pipe. To achieve the maximum acceptance in the region close to the beam pipe, for each orientation the four scintillator strips closer to the beam pipe are cut in two parts and read out at only one end. The ends of four of the eight scintillator strips so obtained are shaped in steps to match the circular shape of the beam pipe as shown in Figure 307 right. The strip width of 6 cm is a compromise between the need of high granularity and the affordable number of PMTs and read-out channels. Monte Carlo studies showed that a smaller strip width of 4 cm would increase the muon rejection only at a percent level.  The MUV1 scintillators are produced at IHEP in Protvino. They are made of polystyrene (Styron 143E) as carrier substrate with 2% scintillating fluors (p-terphenyl) and 0.05% POPOP. While p-terphenyl emits scintillation light at about 300 – 400 nm in the ultra-violet, POPOP shifts the wavelength to   380 – 500 nm. The procedure used to fabricate the scintillators was newly developed: the mixture of polystyrene pellets, p-terphenyl, and POPOP is melted under a 10-4 bar vacuum at about 250 °C. This procedure allows the fabrication of large numbers of long scintillator strips in a relatively short time. One production cycle of heating, melting and cooling needs about 14 hours.  NA62 TD Document      320  Compared to commercially available scintillators (e.g. Bicron BC 408), the MUV1 scintillators have a shorter attenuation length (< 1 m). However, because of the read-out by WLS fibers (see below), the attenuation length is not an important issue for the detector performance. It was therefore decided to fabricate all MUV1 scintillators at IHEP. MUV1 Light Collection and Transport For the read-out of MUV1, wavelength-shifting (WLS) fibers are used. This choice was taken to compensate the short attenuation length of the scintillators and also to comply with the space requirements from the surrounding MUV2 PMTs. Each scintillating strip is read out by two WLS fibers, placed in grooves at 15 and 45 mm along the 60 mm strip width. Several different fiber types from Bicron and Kuraray (Y-11) have been investigated. The preliminary choice is 1.2 mm diameter, multi-cladded fibers BC-91A from Bicron. The fibers shift the scintillator output light to wavelengths between 470 and 570 nm. They are optically connected to the scintillators with optical cement BC-600. It was decided not to use epoxy glue because of possible aging of the fiber cladding. All fibers have a length of about 500 cm with small variations (< 10 cm), depending on the longitudinal position of the corresponding scintillator. The 12 x 2 fibers of one longitudinal row of scintillators are bundled to direct the light to one single PMT; therefore no longitudinal segmentation exists. The connection to the PMT is made by a matrix, which holds all 24 fibers within the active PMT area of 26 mm diameter. MUV2 Scintillators and Light Transport The scintillators of the MUV2 module, which is the NA31/NA48 HAC back/front module, were replaced for the start of the NA48 experiment and for NA62 the module is being reused. The scintillators are of type BC-408 from Bicron. Each scintillator plane, inserted between the iron plates, consists of 44 strips. Each strip spans only half the calorimeter so that each plane is made of two half-planes. The two central strips of each half-plane are also three step shaped at one end to wrap around the central hole for the beam pipe (as in MUV1), so they have a width of 108 mm with a length of 1194 mm at the first step and 1243 mm at the third step. All other strips are 1300 mm long and 119 mm wide. The thickness of each scintillator is 4.5 mm (Figure 308).   Figure 308 Layout of one (horizontal) scintillator layer of the MUV2 module. Figure 2.16: Layout f a scintillator plate in MUV1 (left) and MUV2 (right).The dimension of the scintillator strips is indicat d in blue number with aunit of mm.MUV3The MUV3 is located after MUV2 and an 80 cm thick iron wall filter. Itconsists of 12 × 12 scintillator tiles with a dimension of 220 × 220 × 50mm3. The light produced by traversing charged particles is collected byPMTs positioned about 20 cm downstream. Due to this geometry, themaximum time jitter between photons from particles hitting different pa tsof the scintillator tiles i less han 250 ps, t us preserving the required timeresolution of this detector.312.4. Veto systemNA62 TD Document      316  x Space requirements: Due to the need of a beam deflecting magnet before the end of the beam-line, the longitudinal space available for the HAC modules is less than in NA48. Since light guides and PMTs of the NA48 HAC back module need about 80 cm of longitudinal space in addition to the iron/scintillator layers, a new light collection system had to be built in any case. The restricted longitudinal space also led to the decision to turn the NA48 HAC front module (MUV2) by 180°. After this rotation, the MUV2 light guides and PMTs point up-stream, surrounding the MUV1 module, leaving the MUV2 downstream space completely free. After MUV1 and MUV2 and an 80 cm thick iron wall, the MUV3 module, or Fast Muon Veto, has the aim of detecting non-showering muons and acts as muon veto detector at trigger level. To achieve the required time resolution of less than 1 ns at each transversal position, a design is chosen, which employs scintillator tiles arranged to minimize differences in the light path trajectories.    Figure 303 Right: Three-dimensional view of the MUV1 module. Left: View of MUV1 (grey) and MUV2 (blue). The beam is coming from the left. The number of  detection channels is summarized in  Table 46. Table 46 Number of read-out channels of the MUV detector. Module Number of Channels MUV1 176 MUV2 88 MUV3 Design A (B) 296 (252) Total 560 (516)  Figure 2.17: A view of the MUV1 (grey) and MUV2 (blue).32Chapter 3Analysis strategies3.1 Kpi2 background evaluationWe have two tools to suppress the Kpi2 background: pi0 vetoing and kine-matics suppression. Almost all pi0 decay into two photons, so pi0 rejectionentirely relies on the photon rejection ability in NA62 and is usually referredas photon vetoing. Assuming there is no correlation between rejection fac-tors, the overall rejection level for the Kpi2 background can be obtained bymultiplying two rejection factors with the branching ratio for Kpi2 decay.The estimated the S/B for the Kpi2 background in NA62 is:S/B ≈ Br(Kpiνν¯) ·Akinematics ·APV ·AKpiνν¯Br(Kpi2) · Skinematics · SPV ·AKpi2=8× 10−11 ·Akinematics ·APV ·AKpiνν¯0.207 · Skinematics · SPV ·AKpi2(3.1)To get the S/B, we first need to assess suppression factors of the kinematics(Skinematics) and photon veto cuts (SPV ) for Kpi2 events. Then MC simu-lations should be generated to evaluate the acceptance of selection cuts forboth decays (AKpi2 and AKpiνν¯ ) and the acceptance factor of kinematics cuts(Akinematics) for K+ → pi+νν¯ events. Moreover, the acceptance factor ofthe photon veto cuts for K+ → pi+νν¯ events, APV , can be estimated bystudying the efficiency of photon veto cuts for rejecting Kµ2 decays sinceboth decay modes do not have photons in decay products.3.1.1 Kinematics suppressionThe kinematic cut we used is squared missing mass, M2missing, defined inEquation 1.3. To get the kinematics suppression factor, Skinematics, of thekinematic cut for Kpi2 decay, we first need a pure Kpi2 sample identifiedby a series of Kpi2 selection cuts, listed in section 4.4.1. The momentumof the pi+ in the Kpi2 sample must be within the range from 15 GeV/cto 35 GeV/c, which defines K+ → pi+νν¯ signal region. To make sure weget the accurate result, we used the GTK tracks, rather than the nominal333.2. Upper limit on the branching ratio of the decay pi0 → νν¯kaons, for calculating M2missing even though this costs more than 90% dataas mentioned in section 2.2.1. Once acquiring the pure Kpi2 decay sample,we just need to check how many Kpi2 events leak into the M2missing signalregions. Based on that we can estimate the Skinematics for Kpi2 decay.3.1.2 pi0 suppressionFor studying the pi0 suppression, SPV , we also need a pure Kpi2 sample in theright momentum range to provide tagged pi0. But Kpi2 selection cuts usedhere are different from those for the kinematics study (see section 4.4.2 forthe details of selection cuts). The pi0 suppression factor in NA62 is expectedto reach 10−8, much lower than the expected kinematicsKpi2 rejection factor,10−3. So we have to use the nominal kaon tracks with the momentum ofnear 75 GeV/c in order to get a large number of Kpi2 events.The critical part for the pi0 suppression study lies in how we set photonveto cuts. Unlike the above kinematics study where M2missing signal regionsare set in advance (see section 1.1.3), we need to set photon identificationcuts based on the response of photon detectors for Kpi2 events. This pro-cess can be biased and brings in large uncertainties. Certainly, wider cutscan increase photon veto efficiency, but it also leads to large accidental vetoeffects. Fortunately, we can use a Kµ2 data sample and a Kpi2 MC samplewhere pi0 was forced to decay into νν¯ to estimate the false veto effect. More-over, to avoid bias we can use a set of Kpi2 events as a training sample toset the photon veto cuts first. And then we can apply these cuts on other(unbiased) Kpi2 events to check their suppression inefficiency SPV :SPV =NleftNK+ ·Br(Kpi2) ·AKpi2 · CFalse=NleftNKpi2 · CFalse(3.2)where AKpi2 is the acceptance of Kpi2 events, NKpi2 is the total number ofKpi2 events in the unbiased data sample, Nleft is the number of remainingevents surviving photon veto cuts, and the correction factor CFalse whichcorrects the signal losses due to the false rejection of the photon veto cuts.3.2 Upper limit on the branching ratio of thedecay pi0 → νν¯This study is similar to the above pi0 rejection study because the upper limiton the branching ratio of the SM-forbidden decay is entirely determined by343.2. Upper limit on the branching ratio of the decay pi0 → νν¯how efficient we can detect pi0 in tagged Kpi2 events as shown below:NK+ =Npi0→νν¯Br(Kpi2) ·Br(pi0 → νν¯) ·AKpi2(pi0→νν¯) · CFalse=NKpi2Br(Kpi2) ·AKpi2Br(pi0 → νν¯) = Npi0→νν¯ ·AKpi2NKpi2 · CFalse ·AKpi2(pi0→νν¯)=NleftNKpi2 · CFalse ·AKpi2(pi0→νν¯)AKpi2(3.3)Hence, it follows the same analysis strategy as the pi0 suppression study,except that we need to consider the difference between acceptance factors ofselection cuts,AKpi2(pi0→νν¯)AKpi2. It can be computed by comparing the acceptanceof select cuts in Kpi2 MC sample which had common pi0 decays with that inanother Kpi2 MC sample where pi0 were forced to decay into neutrino pairs.Besides, the other difference between is that we do not have to applya pi+ momentum cut, [15, 35] GeV/c, for selecting Kpi2 events here, whichenables us to get more pi0 events in this study. However, requesting eventswith high pi+ momentum would potentially weaken the photon detectionefficiency and the RICH identification ability, so a cut on momentum, ≤ 40GeV/c, is still needed for studying the branching ratio of the decay pi0 → νν¯.Our study is sensitive to any decays of the form pi0 → “nothing”, where“nothing” refers to any system of weakly interacting neutral particles.35Chapter 4Data sample selectionIn this chapter, we go through all cuts we used to acquire pure Kpi2 and Kµ2samples. These cuts consist of two parts. The first part contains various cutsused for getting one track events, where a valid straw track is required tomatch with an upstream CEDAR track and also track candidates of the sev-eral downstream detectors. It is a prerequisite step for getting the Kpi2 andKµ2 events samples since both decay modes only have one observable decaytrack. The second part of cuts contain different combinations of the Kpi2 orKµ2 identification cuts which are applied on one track events to select desiredevents for different study purposes. There are a few Kpi2 and Kµ2 separa-tion techniques contributed by kinematics, photon detection, calorimetersand the RICH. Before setting suitable separations cuts for different studies,we check the efficiency of these identification cuts using one minimum biasrun 8 taken in 2015.4.1 CorrectionsBefore selecting one track events, we need to correct the reconstructed mo-mentum of the candidate in order to account for the change in the fieldintegral of the dipole bending magnet, and for misalignment of the driftchambers. Besides, the reconstructed energy of the LKr cluster must becorrected for non-linearity (zero suppression), energy loss in the entrancewindow of the cryostat and the global energy scale. The position of LKrcluster should also be shifted for alignment.4.1.1 Spectrometer momentum correctionThe magnetic field correction (parameterized by β) has the same sign for alltracks, while the correction required for the chamber misalignment (param-eterized by α) depends on the charge of the track so the correction has the8Run: A series of SPS bursts taken under uniform data collection conditions; Each runhas its own ID number (a 32-bit unsigned integer).364.1. Correctionsform:Pafter = Pbefore(1 + β)(1 + α · q · Pbefore) (4.1)Therein, q is the charge of the track, and the values of α and β for each runwere determined by reconstructing the invariant mass in the decay K+ →pi+pi+pi− and comparing it with the nominal kaon mass provided by theParticle Data Group (PDG) [41]. It should be noted that α and β valuesvary between runs and can be acquired in the online table 9. For run 3811,α = −10.85× 10−8, β = 1.57× 10−3 when the unit for momentum is MeV.4.1.2 LKr correction1. Energy (GeV)• Non-linearity correction if the number of cells in the cluster isgreater than 9 [42]:Ecorr1 =Euncorr0.7666 + 0.0573489 · ln(Euncorr), if Euncorr < 22Euncorr0.828962 + 0.0369797 · ln(Euncorr), if 22 ≤ Euncorr ≤ 65Euncorr0.828962 + 0.0369797 · ln(65), if Euncorr ≥ 65(4.2)• Global scale factor:Ecorr2 = Ecorr1 · 1.03 (4.3)• Energy loss in the hole depends on the distance of cluster to thecentre(D):Ecorr3 =Ecorr2 · 0.99990.97249 + 0.0014692 ·D, if 140 ≤ D ≤ 185 mmEcorr2, otherwise(4.4)Ecorr4 = Ecorr3 · (1− r) (4.5)9 One track event selection cutsTherein,r =0.0042− 3.7 · 10−4 ·D, if 140 ≤ D < 180 mm−0.00211, if 180 ≤ D < 200 mm−0.01694− 7.769 · 10−4 ·D, if 200 ≤ D < 220 mm• Energy loss at low energy:Efinal =(Ecorr4 + 0.015) · 15 · 0.999915 + 0.015, when Ecorr4 < 15(4.6)2. Position (mm)xafter = xbefore + 1.3 (4.7)yafter = ybefore + 0.8 (4.8)4.2 One track event selection cutsIn this section, we used data from Run 3811, taken in 2015 with protonbeam at 1% nominal intensity10, to demonstrate how we set the one trackevent cuts. We also used the data to check the efficiency of Kpi2 and Kµ2separation cuts in section 4.3.Nearly four hundred official reconstructed bursts11 were analyzed. Theyare reconstructed by the NA62Reconstruction package (version 834). Afterreconstruction we can easily get access to the information like positions,momentum, and energy of the hits or clusters produced by particles in de-tectors.The trigger schemes in Run 3811 are minimum bias triggers: CHOD/3and CHOD×!MUV3/1, where 3 and 1 are downscale factors. The CHODtrigger, requiring a coincidence of hits from the same quadrant in the hori-zontal and vertical planes of the CHOD plastic scintillator slabs, guaranteesthat at least one charged particle reaches the CHOD in the event. The!MUV3 trigger rejects events with the MUV3 hit whose energy is above thethreshold. Although the CHOD×!MUV3 trigger kills most Kµ2 events, both10All 2015 minimum bias run were taken with proton beam at 1% nominal intensity11Burst: the basic data-taking time unit; each burst lasts 3-4 s and is delivered every30 s (the SPS duty-cycle).)384.2. One track event selection cutstriggers contribute to Kpi2 events sample. Hence, we do not have to just se-lect data with CHOD trigger but requesting all data for the analysis. Other2015 minimum bias runs also have same triggers.Selection criteria for getting one track event are as follows:1. Select events with at least one but less than ten spectrometer tracks.The event should have at least one LKr hit and one CHOD hit.2. Loop over every spectrometer candidate in each event. Select validspectrometer candidate which satisfies following requirements:(a) Good spectrometer track:• Track leaves hits on four straw chambers, i.e. Nchamber == 4,see Figure 4.1.Entries  563928Mean    4.336Std Dev    0.3704Number of Chambers having track hits3 4 5Number of Tracks100150200250300350400450310×ProjectionX of biny=[1,200] [y=0.0..200.0]~ 83.6%~83.6%Figure 4.1: Number of straw chambers hit by downstream track.• χ2 ≤ 20• |Pbefore-fit − Pafter-fit| ≤ 20 GeV/c, see Figure 4.2• Track has less than two common hits with another spectrom-eter track(b) Track doesn’t form a good vertex12 with another not fake spec-trometer track1312Good vertex: (CDA < 15) mm && (60 < V ertex.Z < 200) m && (|Ttrack1 −T (tracks2)| < 50 ns)13Fake spectrometer track: (Nchamber! = 4) && [(χ2 ≥ 30) or (has less than twocommon hits with another spectrometer track)]394.2. One track event selection cutsEntries  552411Mean  224.3− Std Dev      2187   [MeV/c]after-fit|-Pbefore-fit|P60000− 40000− 20000− 0 20000 40000 60000Number of Tracks110210310410510ProjectionX of biny=[1,200] [y=0.00..20.00]Figure 4.2: Straw momentum difference before and after fit.(c) Its linear extrapolated positions on other detectors are withindetectors’ geometrical acceptance shown in Table 4.1(d) Spectrometer track should match with a CHOD candidate. TheCHOD candidates are reconstructed at analysis level by pairingtwo hits from vertical and horizontal planes. Hits are required tobe in the same quadrant. Time of the candidate is corrected forT0 and slewing using the same corrections applied at reconstruc-tion level. A best CHOD candidate is selected by minimizing adiscriminant DCHOD [42] which depends on the time differencebetween two CHOD hits, the time difference between spectrom-eter time and reconstructed CHOD time, and the distance ofextrapolated CHOD position to reconstructed CHOD position.DCHOD =(TCHOD − Ttrack)2(3 · σδT )2 +(TV hit − THhit)2(3 · σδThits2)+D2CHOD−to−trackD2cutTherein, σ is the parameter of the fitted gaussian function andDcut = 60 mm as shown in Figure 4.3. A cut on discriminant,D < 1.1, is set to check whether the spectrometer track matchwith the selected CHOD candidate or not. If no, then reject thisthe spectrometer track.(e) Spectrometer track should match with a LKr cluster• Look for a LKr cluster which is closest to the extrapolatedtrack position at LKr from all reconstructed clusters. And see404.2. One track event selection cutsEntries  6487360Mean    2.302 / ndf 2χ  2.3638e+05 / 2395Prob        0Constant  4.9± 9073.3 Mean      0.0029± 1.7004 Sigma     0.0024± 6.6998  [ns]track-TCHODCandidateT30− 20− 10− 0 10 20 30Number of CHOD Candidates0200040006000800010000Entries  6487360Mean  0.1−    / ndf 2χ  6.2419e+05 / 797Prob        0Constant  19.8±  31942 Mean      0.00144±0.12993 − Sigma     0.0015± 3.3205  [ns]HHit-TVHitT20− 15− 10− 5− 0 5 10 15 20Number of CHOD Candidates010000200003000040000500006000070000Distance [mm]0 10 20 30 40 50 60 70 80 90 100Number of CHOD Candidates210310410Entries  6487360Mean    37.04CHOD Discriminant0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5Number of CHOD Candidates110210310410 Entries  341990Mean   0.3138a) b)d)c)Figure 4.3: Diagrams for matching the CHOD Candidate with the Spec-trometer track. a) to c) show the parameters for calculating the CHODdiscriminant: a) Time difference between CHOD candidate and spectrom-eter track with the fitted gaussian distribution whose fitted parameters areshown in statistics table parameters. b) Time difference between CHODV-plane-hit and H-plane-hit. c) The distance of extrapolated CHOD posi-tion to reconstructed CHOD position. The parameter, Dcut = 60 mm, isindicated with red arrow line. d) CHOD discriminant distribution. Red lineshows the cut value.414.2. One track event selection cutsDetector Geometrical Acceptance CutSTRAW(4 Chamber Stations) 75 < Da < 1000 mmRICH (Front and end surface) 90 < D < 1100 mmCHOD (V and H plane) 125 < D < 1199 mmLKr D > 150 mm and within a octagonbMUV1 130 < D < 1100 mmMUV3 130 < D < 1100 mmTable 4.1: Geometrical acceptance cuts for detectors.aDistance of extrapolated impact point on a detector’s station to the centre of thatstation. It should be noted that the centre of station is not exact (0,0), it varies betweendetector’s station even for the same detector. The position of each centre can be found inReference [1]bThe surface of the LKr is a regular octagon with 1130 mm apothem. It also has acircle hole with the radius of 150 mm in the centre to let undecayed beam particle pass.whether this cluster can pass the following matched criteriaas shown in Figure 4.4:– |Ttrack − TLKr−cluster| ≤ 20ns– The distance from extrapolated LKr position of the strawtrack to the position of the reconstructed LKr cluster isless than 150 mm.• If no LKr cluster were found, a new LKr cluster is recon-structed at the analysis level by grouping valid LKr hits 14around the extrapolated impact point of the track on theLKr. The reconstruction succeeds if there is at least onevalid LKr hit, and the energy of the most energetic hit isgreater than 40 MeV. If this new reconstructed LKr cluster15 also does not satisfy the above LKr matching criteria, thenveto the spectrometer track.(f) Spectrometer track should match with a CEDAR candidate. Aclosest in-time CEDAR candidate is chosen among candidateswith NSector ≥ 4. Time different distribution is shown in Figure4.5. The spectrometer track would be rejected unless the chosenCEDAR track pass the time cut, −2 ≤ (TCEDAR − TCHOD) ≤4 ns.14Valid LKr hits should satisfy: D < 150 mm && |Thit − Ttrack| ≤ 40ns.15Its position is the average valid hit positions weighted with energy. Its energy is thesum of all valid hits. Its time is the time of the energetic hit.424.2. One track event selection cutsEntries  340756Mean   0.4025 / ndf 2χ  317.2 / 37Prob       0Constant  5.40e+01± 2.51e+04 Mean      0.0093± 0.4233 Sigma     0.007± 5.392  [ns]track-TLKrClusterT40− 30− 20− 10− 0 10 20 30 40Number of Selected LKr Clusters02000400060008000100001200014000160001800020000220002400026000Entries  340756Mean       11Distance [mm]0 20 40 60 80 100 120 140 160 180 20010210310410a) b)Figure 4.4: Criteria for matching the LKr Cluster with the Spectrometertrack. a) time difference between LKr clusters and spectrometer tracks, redline indicates the fitted gaussian distribution b) The distance of extrapolatedposition of track on the LKr to the centre of the LKr cluster.Entries  182548Mean   0.09773Std Dev    0.5721 [ns]CHOD-TCedarT10− 8− 6− 4− 2− 0 2 4 6 8 10Number of Cedar Candidates110210310ProjectionY of binx=[3,200] [x=1.0..100.0]Figure 4.5: Here is the distribution of the time difference between theselected Cedar candidate and the matched CHOD candidate.434.2. One track event selection cutsEntries  162323Mean   0.1244Std Dev     1.762 / ndf 2χ  9296 / 378Constant  17.4±  4750 Mean      0.00349± 0.03708 Sigma     0.003± 1.233   [ns]CHOD-TCHANTIT20− 15− 10− 5− 0 5 10 15 20Number of CHANTI010002000300040005000ProjectionX of biny=[1,20] [y=0.0..20.0]Figure 4.6: Here is the distribution of the time difference between theselected Cedar candidate and the matched CHOD candidate.(g) Spectrometer track should not match with a CHANTI candidate.If a CHANTI candidate passed a time cut, −6 ≤ (TCHANTI −TCHOD) ≤ 7 ns, then reject the straw track. Time differencedistribution is shown in Figure 4.6.(h) Spectrometer track should match with a RICH candidate (op-tional). The matching process is similar to that of CHOD can-didate. But we considered two types of RICH candidate recon-structed by two different algorithms: multi-ring RICH candidatesand single-ring RICH candidates. Multi-ring RICH candidatesare reconstructed based on Ptolemy theorem [43] in the stan-dard reconstruction process. A valid multi-ring RICH candidateshould have more than three RICH hits and fitted χ2 < 10. Inaddition, an offset was applied to ring centre to correct the mir-ror misalignment assuming the light coming from the mirror hitby the spectrometer track. To get a single-ring RICH candidate,the offset corrections were first applied for every hit from a RICHTime candidate16 at the analysis level and then a least squaresfit was redone using these corrected hits. For each type, a best16A group of RICH hits near in time444.2. One track event selection cutscandidate is selected by minimizing a discriminant [42] :DRICH =(Tcandidate − Ttrack − µT )2(3 · σT )2 +(Dcandidate −Dtrack)2D2cutAs shown in Figure 4.7 and 4.8. For multi-ring RICH candidate,σT = 5.12 ns and µT = 0.6 ns, while for single-ring RICH can-didate σT = 5.08 ns and µT = 0.65 ns. And Dcut = 13 mm isset for both types. The distribution of the calculated discrimi-nant is shown in Figure 4.7 c) and 4.8 c) for both types. Cuts onthe discriminant, DRICH−multi ≤ 1.8 (DRICH−single ≤ 2.5), andfitted chi-squared, χ2 ≤ 3, are set as match cuts.3. After getting valid spectrometer tracks, we need to check whether thedecay happened in the fiducial region or not. We can set cuts on thedecay vertex. If straw track passed following vertex cuts, then theywould become a one track event.A decay vertex is defined as the middle of the closest distance (CDA)between the kaon track and selected spectrometer track after blue fieldcorrection. There are two ways for setting the kaon track. Firstly,we can select it from GTK candidates which have three hits in threedifferent GTK stations. Among those candidates, a closet in-timeGTK track relative to the time of CHOD track was selected to bea GTK kaon candidate. To become a valid GTK kaon track, thecandidate must satisfy requirements: χ2 ≤ 40, |TGTK − TCHOD| ≤1.5 ns, 72.7 ≤ Pkaon ≤ 77 GeV , θx ≤ 0.0002 and θy ≤ 0.0002. Ifno valid GTK kaon track is found, the event would be rejected. Theother way is to set the kaon track as the nominal kaon track assumedusing the average momentum near 75 GeV/c, θx and θy from the runmonitor information in the online table. Obviously, it is more preciseto use the GTK kaon track but it costs plenty of data due to noisyGTK readout in 2015. In order to get enough events, the nominalkaon track was assumed for photon veto study in this thesis.For these two kaon cases, different cuts on the decay vertex were usedto select one track event from valid straw tracks.• Nominal kaon track:(1) CDA < 35 mm(2) 110 ≤ Vertex.Z ≤ 165 m, to avoid the decays in the collima-tor, as shown in Figure 4.9454.2. One track event selection cutsEntries  398434Mean   0.5984 / ndf 2χ  2500.8 / 1969Prob  15− 2.5809eConstant  1.22± 611.74 Mean      0.00819± 0.60321 Sigma     0.0062± 5.1288  [ns]track-TRICHCandidateT20− 15− 10− 5− 0 5 10 15 20# of Multi-ring RICH Candidate0100200300400500600700 Entries  398434Mean     6.14Distance [mm]0 5 10 15 20 25 30# of Multi-ring RICH Candidate050010001500200025003000350040004500Entries  219387Mean   0.4127RICH Discriminant0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5# of Multi-ring RICH Candidate10210310410RingChi20 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5# of Multi-ring RICH Candidate110210310410Entries  216603Mean   0.3116a bc dFigure 4.7: Diagrams for matching a multi-ring RICH Candidate with theSpectrometer track. a) time difference between the multi-ring RICH can-didate and spectrometer track with the fitted gaussian distribution, fittedsigma is shown in the statistics table b) The distance of extrapolated RICHposition to the position of the selected RICH multi-ring Candidate. c) Dis-tribution of the multi-ring RICH discriminant d) Distribution of the fittedχ2. Red lines with an arrow in c) and d) show the match cut.464.2. One track event selection cutsEntries  333443Mean   0.6479 / ndf 2χ  2231.8 / 1946Prob  06− 5.8196eConstant  1.13± 517.13 Mean      0.00887± 0.64727 Sigma     0.0067± 5.0785  [ns]track-TRICHCandidateT20− 15− 10− 5− 0 5 10 15 20# of Single-ring RICH Candidate0100200300400500600 Entries  333443Mean     7.59Distance [mm]0 5 10 15 20 25 30# of Single-ring RICH Candidate050100150200250300350400Entries  222436Mean   0.5363RICH Discriminant0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5# of Single-ring RICH Candidate10210310410RingChi20 1 2 3 4 5 6 7 8 9 10# of Single-ring RICH Candidate210310410Entries  221595Mean    1.147a bc dFigure 4.8: Diagrams for matching a single-ring RICH Candidate with theSpectrometer track. Similar as Figure 4.7.474.3. Kpi2 and Kµ2 separation cuts and efficiency evaluationEntries  4364888Mean    8.943Std Dev      8.98CDA [mm]0 10 20 30 40 50 60 70 80Events / 0.25 mm210310410510Entries  4364888Mean   1.289e+05Std Dev   2.285e+04Vertex.z [mm]80 100 120 140 160 180310×Events / 600 mm0100002000030000Figure 4.9: Left figure shows CDA of the decay vertex of one track candi-dates in Run 3811. The vertex was reconstructed using the nominal kaontrack and the spectrometer track. Right figure shows the vertex.z distribu-tion.• Valid GTK kaon track.(1) CDA < 7 mm(2) 105 ≤ Vertex.Z ≤ 165 m , see Figure 4.10.Once applying above criteria on the data, we get one track events andcan start to identify Kpi2 and Kµ2 events from them.4.3 Kpi2 and Kµ2 separation cuts and efficiencyevaluationIn this section, we present techniques for identifying Kpi2 and Kµ2 events.Before using them we should check their efficiency of separating Kpi2 andKµ2. We used one track events, surviving the above one track event cutsassuming nominal kaon track, from Run 3811 for this study.4.3.1 Overview of separation cutsAlthough both Kpi2 and Kµ2 decays can survive one track event cuts, thereare a few methods to distinguish them. Some are used to identify pi+ and484.3. Kpi2 and Kµ2 separation cuts and efficiency evaluationEntries  85528Mean    1.452Std Dev    1.835CDA [mm]0 5 10 15 20 25Events / 0.1 mm110210310Entries  97318Mean   1.348e+05Std Dev   1.956e+04Vertex.z [mm]90 100 110 120 130 140 150 160 170 180310×Events / 600 mm02004006008001000Figure 4.10: Same as Figure 4.9 but the vertex was reconstructed using theGTK kaon track and the spectrometer track.µ+, while other cuts are contributed by distinct properties of pi0 and ν.First, different mass between pi+ and µ+ leads to the discrepancy inRICH signal. We can use Equation 2.2 to calculate the mass of RICH track.The calculated RICH mass distributions of one track events in Run 3811are shown in Figure 4.11. The left plot shows the mass of RICH multi-ringtracks, and the right is the plot for RICH single-ring tracks. Kpi2 eventsare corresponding to the pion peak near 0.1349 GeV/c2, while Kµ2 eventsare near the muon mass peak. It can be noticed that though the number ofRICH single-ring tracks is less than that of multi-ring tracks, multi-ring masshas worse pi+ and µ+ separation efficiency. So we only use MassRICH-singleto set the Kpi2 and Kµ2 identification cut.Apart from the RICH, the electromagnetic calorimeter LKr and themuon veto detector, MUV3, can also be exploited to identify pi+ and µ+.As mentioned in Section 2.4.2, different types of particles would depositdifferent energy in the LKr even though they have same energy. Electronsdeposit almost all of energy in the LKr while muons act like Minimum Ion-izing Particles (MIPs) and typically deposit only a small fraction of theirenergy through ionization. Hence, we can use ELKrPSTRAW (a ratio of depositedenergy of track in the LKr to track’s straw momentum, EP ), to distinguishe+/pi+/µ+. As shown in Figure 4.12, electron normally has EP ≈ 1, while494.3. Kpi2 and Kµ2 separation cuts and efficiency evaluationEntries  2065551Mean   0.1178Std Dev   0.03174]2 [GeV/cRICH-multiMass0 0.05 0.1 0.15 0.2 0.25Events #050001000015000200002500030000350004000045000Entries  1807852Mean   0.1173Std Dev   0.03118]2 [GeV/cRICH-singleMass0 0.05 0.1 0.15 0.2 0.25Events #0500010000150002000025000300003500040000muonpionmuonpionelectron electronFigure 4.11: Left plot shows the mass distribution of RICH multi-ringcandidate for one track events. Right plot is for RICH single-ring Candidate.Pion and muon peaks can be clearly seen in diagram.muons and pions are corresponding to EP ≤ 0.1 and 0.1 < EP < 0.9. As forMUV3, almost all pions would be stopped before reaching the MUV3, whilemost muons can hit it. Hence, we can use it to check whether the track isµ+ or not.In addition, we can use kinematics reconstruction to separate Kpi2 andKµ2 events. Due to the fact that pi0 and ν, neutral decay product missedby the STRAW spectrometer, have different mass, Kpi2 and Kµ2 eventswould end up with different M2missing, the mass squared of missing parti-cles. As shown in Figure 4.13, the M2missing−pi distributions for Kpi2 andKµ2 decays are distinct from each other. Kpi2 events have the M2missing−pinear the Mass2pi0 ≈ 0.0182 GeV2/c4, while Kµ2 events are corresponding toM2missing less than 0. We can also assume the straw track has muon massto get M2missing−µ for convenience sometimes. For example, it is easy to useM2missing−µ for selecting Kµ2 events since most Kµ2 events lie at 0 GeV2/c4in M2missing−µ distribution as shown in Figure 4.14.Finally, it comes to photon detection. The pi0 from Kpi2 decay can fur-ther decay into photons or electrons which can be detected by photon vetodetectors, LKr, LAV, IRC, and SAC mentioned in Section 2.4.2. However,for Kµ2 events, decay product neutrino cannot be observed, i.e., have nomatched photon. The cuts for finding photons are discussed in Chapter 5.Photon detection plays an important role in getting pure Kpi2 and Kµ2 de-504.3. Kpi2 and Kµ2 separation cuts and efficiency evaluationEntries  2974328Mean   0.2025Std Dev    0.2928STRAW/PLKrE0 0.2 0.4 0.6 0.8 1 1.2Events #10210310410510610muonpionelectronFigure 4.12: The EP distribution for one track events.cay samples for studying the efficiency of above cuts as well as Skinematicsin Section 3.1.1.In next subsection, we check the efficiency of above techniques exceptphoton veto for separating Kpi2 and Kµ2 events.4.3.2 EfficiencyTight cuts for getting Kpi2 and Kµ2 eventsTo study the efficiency of one cut, we need to get pure Kpi2 and Kµ2 decaysamples by applying other three cuts on one track events. The details ofcuts are as follows:• M2missing cutKpi2: 0.013 ≤M2missing−pi ≤ 0.023 GeV2/c4Kµ2: |M2missing−µ| ≤ 0.005 GeV2/c4• RICH singe-ring mass cutKpi2: 0.133 ≤ MassRICH-single ≤ 0.17 GeV/c2Kµ2: 0.05 ≤ MassRICH-single ≤ 0.115 GeV/c2• LKr and MUV3 cutKpi2: 0.1 <EP < 0.8 and no matched MUV3 candidate514.3. Kpi2 and Kµ2 separation cuts and efficiency evaluation]4/c2 [GeV2πmass-Missing0.1− 0.05− 0 0.05 0.1Straw momentum [GeV/c]0102030405060708090100110210]4/c2 [GeV2πmass-Missing0.1− 0.05− 0 0.05 0.1Events #01000020000300004000050000600007000080000Kmu2Kmu2Kpi2Kpi2Figure 4.13: Upper plot shows the momentum of straw track versus thecalculated M2missing−pi of one track event assuming the straw track has pi+mass. Lower plot is the projection of upper plot in x axis, i.e., M2missing−pidistribution. Kpi2 and Kµ2 decay peaks are denoted in both plots.524.3. Kpi2 and Kµ2 separation cuts and efficiency evaluation]4/c2 [GeV2µmass-Missing0.1− 0.05− 0 0.05 0.1Straw momentum [GeV/c]0102030405060708090100110210]4/c2 [GeV2µmass-Missing0.1− 0.05− 0 0.05 0.1Events #010000200003000040000500006000070000Kmu2Kpi2Kmu2Kpi2Figure 4.14: Upper plot shows the momentum of straw track versus thecalculated M2missing−µ of one track event assuming the straw track has µ+mass. Lower plot is the projection of upper plot in x axis, i.e., M2missing−µdistribution. Kpi2 and Kµ2 decay peaks are denoted in both plots.534.3. Kpi2 and Kµ2 separation cuts and efficiency evaluationKµ2:EP ≤ 0.1 and has matched MUV3 candidate• Photon cutKpi2:see pi0 cut in section 4.4.1Kµ2:No matched photon in the LKr, LAV, IRC, and SAC.These cuts are stricter than we normally use in order to get fewer backgroundevents in the samples.M2missingOnce applying the sample selection cuts except the M2missing cut on onetrack events in Run 3811, we got pure Kpi2 and Kµ2 samples to set efficientM2missing cuts to distinguish Kpi2 and Kµ2 events. Figure 4.15 shows theM2missing−pi (right) and M2missing−µ (left) distribution for selected Kpi2 andKµ2 events.We can set a cut, 0.01 ≤ M2missing−pion ≤ 0.026 GeV2/c4, to select Kpi2events. As shown in Figure 4.15 right, the M2missing−pi distribution of Kpi2events has a peak at 0.01819 GeV2/c4 which is close to the square valueof pion mass 0.134982 GeV2/c4, while M2missing−pi for most Kµ2 events isless than 0. The resolution of M2missing of the Kpi2 events is about 4× 10−3GeV2/c4, a little bit worse than the design value because nominal kaonmomentum was used for calculating M2missing rather than that of GTK kaoncandidate. Three times better resolution can be acquired if using GTK kaoncandidate, see Figure 6.2. To choose a suitable cut, we examine several cutswhose range are [0.018-i·n, 0.018+i·n] where i is the step (set it as 0.001GeV/c2 here) and check the Kpi2 and Kµ2 passing efficiency of those cuts.The efficiency plot for two situations, non-momentum cut and moment cut(15 to 35 GeV/c) on straw track, is shown in Figure 4.16. It is clear thatthose cuts are quite efficient, with the maximum muon efficiency at 10−3(10−4) level before (after) momentum cut. In order to get large statisticsand the M2missing signal regions (see section 1.1.3) for K+ → pi+νν¯ events,we chose a cut with wider range, [0.01, 0.026] GeV2/c4. This cut has (95.17±0.07)% Kpi2 selection efficiency and (2.77± 0.32)× 10−4 Kµ2 veto efficiencyafter momentum cut.Similarly, we also set a cut on M2missing−µ to select Kµ2 events. Sincewe do not need a great number of Kµ2 events to obtain Crandom in section544.3. Kpi2 and Kµ2 separation cuts and efficiency evaluation0.04− 0.02− 0 0.02 0.04 0.06050001000015000200002500030000 2piK2µK]4/c2 [GeV2missingM0.06− 0.04− 0.02− 0 0.02 0.04 0.06050001000015000200002500030000350002piK2µKFigure 4.15: TheM2missing distributions forKpi2 (red) andKµ2 (green) decaysamples. The right plot shows M2missing−pi which was calculated assuminga straw track has pion mass, i.e. (PK+ − Ppi+)2, while the left plot showsM2missing−µ = (PK+ − Pµ+)2.Increase the step i[0.01,0.026]Figure 4.16: Here shows the efficiency of several M2missing−pi cuts for select-ing the Kpi2 sample. The arrow shows the direction of increasing steps.554.3. Kpi2 and Kµ2 separation cuts and efficiency evaluation]2Mass of detected track[GeV/c0 0.05 0.1 0.15 0.2020004000600080001000012000140001600018000RICH single-ring candiate Sample2piK Sample2µKFigure 4.17: The RICH mass distributions for Kpi2 (red) and Kµ2 decays(green) sample selected by the other three tight cuts. Only tracks withstraw momentum from 15 to 35 GeV/c were chosen in samples. RICH masswas calculated by using the radius of single-ring RICH candidate and strawmomentum.3.1.2, the cut we chose is [-0.007,0.007] GeV2/c4 which gives 83.9% (84.5%)Kµ2 selection efficiency and 10−4 (2.14 × 10−5) Kpi2 veto efficiency before(after) momentum cut.RICH single-ring mass cutThe efficiency study of RICH single-ring cut follows a similar process, butwe used different selection cuts to select Kpi2 and Kµ2 samples. The cutsinclude M2missing cut, calorimeter cut and photon cuts in section 4.3.2 aswell as the momentum cut (15 to 35 GeV/c). After getting the samples, wecalculated the RICH mass whose distribution is shown in Figure 4.17.As shown in Figure 4.18, we examine the efficiency of a few RICH masscuts, [0.02-i·n, 0.02] GeV/c2 where the step i is set as 0.0005 GeV/c2, forselecting Kpi2 and Kµ2 events. It is obvious that RICH separation cut isworse than the kinematics. The cut we chose for selecting Kpi2 is 0.1325 ≤MassRICH-single ≤ 0.2 GeV/c2, which has 85.31% pion efficiency and 1.49%muon efficiency.While for getting Kµ2 events, we set 0.05 < MassRICH-single < 0.11GeV/c2 which has 70.69% muon efficiency and 1.07% pion efficiency.564.4. Final cuts used for selecting the data sampleMuon efficiency0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04Pion efficiency0.50.550.60.650.70.750.80.850.90.951Cut: [0.1325,0.2] Figure 4.18: This figure shows the efficiency of different RICH mass cutsfor selecting Kpi2 and Kµ2 events.CalorimetersThree tight cuts other than the calorimeter cut were used to select the Kpi2and Kµ2 samples. TheEP distributions for two samples are shown in Figure4.19. We can set a upper limit at 0.85 to decrease the electron contaminationin the pion sample by at least a factor of 200 [44], while a cut EP > 0.1 isneeded to efficiently reject muons. In summary, we can use 0.1 < EP < 0.85and required no MUV3 matched candidate for selecting Kpi2 decays. Theefficiency of this cut is shown in Table 4.2.Since we plan to use Kµ2 events to study the random veto effect of theLKr, we did not use this LKr related cut EP for selecting Kµ2 events. But acut on matched MUV3 candidates can be used.4.4 Final cuts used for selecting the data sampleIn summary, we can use following cuts to select desired events for the dif-ferent study purposes.4.4.1 Cuts for kinematics suppression studyFor the kinematics suppression study, we need to get a pure Kpi2 samplefrom one-track events with valid GTK kaon tracks. Obviously, we cannotuse M2missing−pi for selection. The Kpi2 selection cuts are:574.4. Final cuts used for selecting the data sample0 0.2 0.4 0.6 0.8 1 1.2110210310410510 Sample2piK Sample2µKE/PEvent #Figure 4.19: The EP distributions of Kpi2 (red) and Kµ2 (green) decays forrun 3811. No cut on STRAW track momentum is set.• 15 ≤ PSTRAW−track ≤ 35 GeV/c• 0.1325 ≤ MassRICH-single ≤ 0.2 GeV/c2• 0.1 ≤ EP ≤ 0.85, !MUV3• pi0 cut:– Events with only two LKr standard photons but no other photons(see details in Chapter 5).– Cut on average time of two photons: |Tphotons−TSTRAW | ≤ 12 ns.– Cut on the pi0 decay vertex reconstructed by using the energyand positions of two photons: 105 ≤ Vertex− pi0Z ≤ 180 m.– Cut on the energy of two photons deposited in LKr and MUV1(Etwo-photons) and energy of pi+ track using RICH: ERICH-track +Etwo-photons ≥ 70 GeV.4.4.2 Cuts for the pi0 suppression study and pi0 → νν¯ studySince the pi0 → νν¯ study here entirely depends on the pi0 suppression, theprocedures for studying the pi0 suppression and pi0 → νν¯ are almost thesame. The difference is that a momentum cut, 15 ≤ PSTRAW−track ≤ 35584.4. Final cuts used for selecting the data sampleSeparation cutsµ+ Efficiency15 to 35 GeV/cNon-momentum cutpi+ Efficiency15 to 35 GeV/cNon-momentum cutLKr cut: 0.1 < EP < 0.85(6.45± 0.18)× 10−3(5.67± 0.12)× 10−3(73.58± 0.13)%(73.51± 0.11)%!MUV3(3.38± 0.42)× 10−4(2.64± 0.25)× 10−4(73.56± 0.11)%(73.48± 0.11)%Table 4.2: Efficiency of LKr and MUV3 cuts for selecting Kpi2 events andKµ2 eventsGeV/c, must be applied for the pi0 suppression study. Hence, we used thesame cuts as follows and leave the momentum cut till the last step for thepi0 suppression study. To guarantee the performance of the photon vetodetectors, PSTRAW−track ≤ 40 GeV/c was requested for pi0 → νν¯ study.After applying one-track selection cuts (nominal kaon) on the data sam-ple, we can use the following cuts to select Kpi2 and Kµ2 events:• Kpi2– 0.01 ≤M2missing−pi ≤ 0.026 GeV2/c4– 0.1325 ≤ MassRICH-single ≤ 0.2 GeV/c2– 0.1 < EP < 0.85, !MUV3• Kµ2– |M2missing−muon| ≤ 0.007 GeV2/c4– 0.05 < MassRICH-single < 0.11 GeV/c2– Matched MUV3 candidate59Chapter 5Photon veto cutsWe can set photon identification (veto17) cuts by checking the photon de-tectors’ response in a “training” Kpi2 sample, since almost all photons inthe Kpi2 sample are supposed to leave signals in photon detectors and bedetected. In this study, photon veto cuts are time cuts, which can be usedto check whether there is a photon detected by four photon veto modules,the LKr, LAV, SAC, and IRC. A photon can leave a cluster in the LKr ora hit in the other three detectors. For each detector, one or several photoncandidates were selected for setting photon veto cuts.The “training” Kpi2 sample were identified from four 2015 minimum biasruns (3789, 3799, 3801, 3805), which have the same running and trigger con-ditions as Run 3811, using Kpi2 selection cuts in section 4.4.2. For executinga “blind” analysis, these Kpi2 events were not included in the final result forpi0 rejection.No matter how we set photon veto cuts, there is always false veto effectdue to the presence of additional pi+ clusters in the LKr and the noise inall photon detectors. As it shown in section 5.4, a MC simulation and aKµ2 sample identified by cuts in section 4.4.2 from Run 3809 were usedto evaluate the additional false rejection factor caused by the accidentalrejection of photon veto cuts.5.1 LKr photon5.1.1 LKr standard photonA LKr standard photon is an in-time LKr cluster reconstructed by the stan-dard algorithm. Beside the photon from pi0 decay, a pi+ track can also leaveone or several clusters in the LKr. To make sure a LKr cluster did comefrom a photon rather than a pi+ track, we had to define a circular region,with the centre at the projected position of the pi+ track in the LKr, which17In the pi0 suppression study, the event would be rejected once it has a identifiedphoton. So we consider photon identification as photon veto.605.1. LKr photonwas masked for searching LKr photon candidates. In other words, we be-lieved all LKr clusters inside this circular region were associated with thepi+ track, and all other LKr clusters beyond this region became LKr photoncandidates. However, it is possible that additional LKr clusters left by pi+track may exist outside this region and mimic photons. Hence, we needto consider the rejection effect brought by additional pi+ LKr clusters as acontribution to false veto factor, CFalse. The larger the radius of the maskedregion is, the smaller the chance of the false rejection would be. As demon-strated by a MC study in Appendix B, nearly 5.64% of Kpi2 events were berejected by pi+ clusters if the radius of the circular region were set to be 150mm, which leads to CFalse−pi+ = 94.36%.Figure 5.1 shows the time difference between the LKr photon candidatesand the associated CHOD track of all Kpi2 training events for two energyranges. We can set time cuts to identify a LKr photon among selected LKrphoton candidates. For candidates whose energy is lower or equal to 2 GeVin Figure 5.1 left, a time cut was set as −5 ≤ TLKr-Cluster − TCHOD ≤ 8 ns(i.e. [-5, 8] ns) to check if they are LKr photons, while two time ranges[-11,16] ns and [-30, -20] ns were set for left LKr photon candidates havinglarger energy due to several peaks shown in Figure 5.1 right. As long asonly one LKr photon candidate satisfied time cuts, we believed there was aphoton presented in the event.5.1.2 LKr extra photonSince LKr standard reconstruction for 2015 runs was reported to be ineffi-cient for detecting photons, an alternative LKr reconstruction was used asa supplementary photon veto cut after all LKr, LAV, SAC and IRC photoncuts. Details of the algorithm can be found in meeting report [45]. The al-ternative LKr reconstruction was only activated when there was no standardLKr photon.Among all newly reconstructed clusters which are 150 mm away fromthe projected position of the pi+ track in the LKr, the most energetic clusterwas selected to become a LKr extra photon candidate in every event. Foravoiding large noise, this candidate should have energy greater than 1 GeVotherwise no LKr extra photon was identified. Figure 5.2 shows the timedifference distribution of all LKr extra photon candidates relative to CHODtracks in “training” Kpi2 events. A slightly wider time cut, [-8, 6.5] ns, wasset to identify the LKr extra photon.615.2. LAV photons [ns]CHOD-TLKr-photon-CanT30− 20− 10− 0 10 20 30Number / 0.2 ns110210310 2 GeV≤ LKr-photon-candidateE [ns] CHOD-TLKr-photon-CanT30− 20− 10− 0 10 20 30Number / 0.2 ns110210310410510 > 2 GeVLKr-photon-candidateEFigure 5.1: Distribution of the time difference between the LKr photoncandidates and the associated CHOD track for candidates whose energy is≤ 2 GeV (left), and > 2GeV (right) in all “training” Kpi2 events. There aremore peaks in the right diagram so a wider time window is required.5.2 LAV photonsLAV photon is an in-time LAV hit. Among all reconstructed LAV hits, onlyhits with specific edge-combination types were considered [46]. Besides, avalid hit should not come from the identified noisy LAV channels in 2015run. Among all valid LAV hits in every Kpi2 event, only the closest-in-timehit relative to the CHOD time was selected to become the LAV photoncandidate. Figure 5.3 shows its timing information for corresponding LAVstations. If hit candidates come from the station LAV12, two time cuts,[-3.5, 7] ns and [12, 21] ns, were set for checking whether candidates areLAV photons or not. While for candidates from the other stations, a timecut, [-5, 5] ns, should be set.5.3 SAC and IRC photonsLike the LAV photon, SAC and IRC photons are also in-time hits. Butthere are two readout modules for small angle veto (SAV) detectors: theLAVFEE and the CREAM board [47]. As can be seen in section 6.2, wetreated CREAM based SAC photon veto cut as a supplementary cut andput it after SAV-CREAM photon rejection cut.625.3. SAC and IRC photons [ns] CHOD-TLKrextra-CanT8− 6− 4− 2− 0 2 4 6 8Number / 0.2 ns051015202530354045LKr_extra_photon_CandidateFigure 5.2: Distribution of the time difference between the LKr extra photoncandidates and the associated CHOD tracks in all “training” Kpi2 events.5.3.1 SAV-LAVFEE photonsThere is no reconstructed energy information for LAVFEE based hits. Butwe can exploit the time-over-threshold (TOT) value which is almost pro-portional to deposit energy [48, 49]. Among all LAVFEE based SAC hits inevery event, we selected one hit having the largest TOT value as LAVFEEbased SAC photon candidate. Same for the IRC. Figure 5.4 left and rightshows the timing of LAVFEE based SAC photon candidates and LAVFEEbased IRC photon candidates in Kpi2 events from run 3801, respectively.Time cuts, [-5, 5] ns and [-6.5, 6.5], were set for identifying (rejecting) SACphotons and IRC photons, respectively.5.3.2 SAV-CREAM photonsUnlike LAVFEE, we do have the energy of CREAM based hits. Energy cuts,≥ 1 GeV and ≥ 2.5 GeV, was placed on SAC and IRC hits, respectively, toreduce noise. As a supplementary cut to LAVFEE, we selected the closest-in-time hits instead of the most energetic hits as photon candidates. Asyou can see in Figure 5.5, [-5, 5] ns and [-8, 8] ns can be set for identifyingCREAM based SAC photons and IRC photons.635.4. False veto effect [ns]CHOD-TLAV-photon-CanT10− 8− 6− 4− 2− 0 2 4 6 8 10Number / 0.05 ns110210310410 12 ≠LAV Station-ID  [ns] CHOD-TLAV-photon-CanT10− 5− 0 5 10 15 20 25 30Number / 0.05 ns110210310410LAV Station-ID = 12Figure 5.3: Distribution of the time difference between the LAV photoncandidates and the associated CHOD tracks in all “training” Kpi2 events.The right diagram shows the time difference of LAV photon candidates fromthe LAV12, while the left diagram is for candidates from left eleven LAVstations.5.4 False veto effectApart from the pi+ clusters, false rejection is also contributed by the acciden-tal rejection caused by the photon detector’s noise which was not taken intoaccount in the MC simulation. Hence, we estimated the additional randomveto factor, CFalse−random, by applying above photon veto cuts on the Kµ2sample from Run 3809. As we can see in Table 5.1, there is a tiny differencebetween the CFalse−random for momentum range [15, 35] GeV/c and that for≤ 40 GeV/c. This factor was evaluated to be nearly 0.983, which could alsobe used as APV in Equation 3.1 since photon veto cuts should have almostsame accidental veto effect on K+ → pi+νν¯ events.Combined with CFalse−pi+ in section 5.1.1, total false rejection factorCFalse is estimated to be 92.77%.645.4. False veto effect [ns]CHOD-TSAC-photon-CanT10− 8− 6− 4− 2− 0 2 4 6 8 10Number / 0.25 ns050100150200250SAC_LAVFEE [ns] CHOD-TIRC-photon-CanT10− 8− 6− 4− 2− 0 2 4 6 8 10Number / 0.1 ns0100200300400500600700800900IRC_LAVFEEFigure 5.4: Distribution of the time difference between the LAVFEE basedSAV photon candidate and the associated CHOD track in Kpi2 events fromrun 3801. The left diagram shows the time difference of LAVFEE basedSAC photon candidates, while the right diagram is for LAVFEE based IRCphoton candidates. [ns]CHOD-TSAC-photon-CanT15− 10− 5− 0 5 10 15Number / 0.25 ns0100200300400500SAC_CREAM [ns] CHOD-TIRC-photon-CanT15− 10− 5− 0 5 10 15Number / 0.25 ns0100200300400500600700800900IRC_CREAMFigure 5.5: Distribution of the time difference between the CREAM basedSAV photon candidate and the associated CHOD track in Kpi2 events fromrun 3801. The left diagram shows the time difference of CREAM basedSAC photon candidates, while the right diagram is for CREAM based IRCphoton candidates.655.4. False veto effectKµ2Events number15 to 35 GeV/cEvents number≤ 40 GeV/cTrial events 406560 565836Reject LKr standard photons 405785 564737Reject LAV photons 400148 557111Reject SAV-LAVFEE photons 400044 556963Reject SAV-CREAM photons 399745 556541Reject LKr extra photons 399675 556435CFalse−random 98.31% 98.34%Table 5.1: This table shows how many Kµ2 events from Run 3809 passedeach photon cut.66Chapter 6Analysis resultsIn this chapter, we followed the analysis strategies in Chapter 3 to eval-uate the Kpi2 background and the branching ratio of the decay pi0 → νν¯using other 2015 minimum bias runs and MC data. These runs were re-constructed by the NA62Reconstruction18 package v0.9.1 (latest revision).To estimate Akinematics and Cmissreco, we generated some Kpiνν¯ and Kpi2events using NA62MC package v0.9.1 and reconstructed them with the sameNA62Reconstruction package.6.1 Kinematics6.1.1 Kinematics rejection for Kpi2MC simulation300K Kpi2 MC events were generated for studying kinematics rejection ef-ficiency. After applying selection cuts in section 4.4.1, except the pi0 cut,on MC events, we got 19288 trial events whose M2missing−pi distribution isshown in Figure 6.1, where the NA62 accessible K+ → pi+νν¯ phase spaceregions I and II are roughly indicated by green lines. Almost all events re-side in a narrow core with resolution of 1.14× 10−3 GeV2/c4. There are 21events leaking into two signal regions: 11 events entered in region I, [0, 0.01]GeV2/c4, and 10 events were found in region II, [0.026, 0.068] GeV2/c4. Insummary, MC results suggest that the inefficiency of kinematics rejectionfor Kpi2 events is (1.09± 0.24)× 10−3.DataWe also analyzed nearly 2500 bursts from Run 3821 and identified 49077Kpi2 events using all selection cuts in section 4.4.1. Figure 6.2 shows theM2missing−pi spectrum for these events. It can be seen that the spectrum ofKpi2 events from data has slightly wider distribution than MC simulation18NA62 Software contains NA62MC, NA62Reconstruction, NA62Analysis and NA62DBpackages, see for details676.1. KinematicsEntries  19288Std Dev    0.001275 / ndf 2χ  203.4 / 41Prob  23− 2.128eConstant  31.3±  3338 Mean      0.00001±0.01836 Sigma     0.00001± 0.00114 ]4/c2 [GeV2 πmissing-M0.04− 0.02− 0 0.02 0.04 0.06 0.084/c2 GeV-4 10×Event # / 5 110210310Figure 6.1: The M2missing−pi distribution for Kpi2 MC events. M2missing−piwas calculated using momentum of a GTK kaon track and a spectrometertrack. K+ → pi+νν¯ signal regions were indicated by green lines.and is a little bit noisy. This might be caused by accidentals since part ofthe GTK system suffered from high noise during the run. Of the 49077 trialevents, 52 events entered in region I and 54 events were found in region II,which results in Skinematics ≈ (2.16± 0.21)× 10− Kinematics acceptance for Kpiνν¯In addition to 300K Kpi2 MC events, we also generated 300K Kpiνν¯ MCevents to estimate the Akinematics in Equation 3.1. The analysis processis same as MC study in section 6.1.1. Compared with the Kpi2 MC simu-lation, there are more Kpiνν¯ events surviving one track selection cuts andKpi2 selection cuts, which means those cuts have different efficiency for Kpi2and Kpiνν¯ decays. Based on the simulationAKpiνν¯AKpi2= 2626919288 ≈ 1.362. TheM2missing−pi distribution of selected Kpiνν¯ events in shown in Figure 6.3. Outof 26269 Kpiνν¯ events, 15077 events enter into two signal region, which givesAkinematics = 57.39%.686.1. KinematicsEntries  49077Std Dev    0.001556 / ndf 2χ  648.6 / 75Prob       0Constant  43.5±  7374 Mean      0.00001±0.01806 Sigma     0.00000± 0.00131 ]4/c2 [GeV2 πmissing-M0.04− 0.02− 0 0.02 0.04 0.06 0.084/c2 GeV-4 10×Event # / 5 110210310410Figure 6.2: The M2missing−pi distribution for Kpi2 events in Run 3821.M2missing−pi was calculated using momentum of a GTK kaon track and aspectrometer track. K+ → pi+νν¯ signal regions were indicated by greenlines.Entries  26269Mean   0.03829Std Dev    0.02753]4/c2 [GeV2 πmissing-M0.02− 0 0.02 0.04 0.06 0.08 0.1 0.12 0.144/c2 GeV-3 10×Event # / 2 02004006008001000Figure 6.3: The M2missing−pi distribution for Kpiνν¯ MC events. M2missing−piwas calculated using momentum of a GTK kaon track and a spectrometertrack.696.2. pi0 rejection using photon veto cuts10 20 30 40 50 60 70110210310410510 events2piTrial KVeto LKr standard photonVeto LAV photonVeto SAV-LAVFEE photon Veto SAV-CREAM photonVeto LKr extra photon Straw Momentum [GeV/c]Event #Figure 6.4: This figure shows how Kpi2 events from six 2015 minimum biasruns survived each photon veto cut.6.2 pi0 rejection using photon veto cutsUsing the cuts described in section 4.4.2, we got 7.1M Kpi2 events from sixminimum bias runs (3809, 3810, 3811, 3813, 3818, 3821) before placing themomentum cut. Then we checked the pi0 veto efficiency by applying photonveto cuts one by one on the selected Kpi2 sample. As shown in Figure 6.4,most remaining Kpi2 events (red bars) have high pi+ momentum. This isnot surprising since photon detectors have small efficiency of detecting lowenergy photons. We got no events left in the desired momentum ranges afterplacing all photon veto cuts.Only Kpi2 events with pi+ momentum in [15, 35] GeV/c were used forthis study. As shown in Table 6.1, we got zero events left out of 3553586 trial706.3. Kpi2 backgroundKpi2 15 to 35 GeV/c ≤ 40 GeV/cTrial events 3553586 4735650Final events 0 0Table 6.1: Number of Kpi2 events in two momentum ranges passing thephoton veto When zero events were observed, the number of remaining eventswas limited to be < 2.3 at 90% C.L. using Poisson statistics, which resultsin:SPV =NleftNpi0 · CFalse<2.33553586× 0.9277 = 7.0× 10−7 (90% C.L.)6.3 Kpi2 backgroundPlugging all the factors into Equation 3.1, the S/B ratio for the Kpi2 back-ground should be:S/B >8× 10−11 × 0.574× 0.983× 1.3620.207× 2.16× 10−3 × 7.0× 10−7 = 0.26.4 Branching ratio of the decay pi0 → νν¯We generated another 300K Kpi2 MC events where pi0 was forced to decayinto νν¯ to computeAKpi2(pi0→νν¯)AKpi2. Smaller AKpi2 was expected due to miss-reconstruction of the pi+ track, which may happen when photons or electronsfrom pi0 decays overlap with the pi+ track but doesn’t not occur if pi0 decaysinto neutrino pairs. We got 23479 events surviving the selection cuts insection 4.4.1 (except the pi0 cut) from this MC sample, compared to 19288events from the Kpi2 MC sample where neutral pions went through commondecays. Hence,AKpi2(pi0→νν¯)AKpi2= 2347919288 ≈ 1.217.As shown in Table 6.1, after photon veto cuts no events were left from4735650 Kpi2 events where pi+ momentum is below 40 GeV/c. Actually,we found one interesting event from Run 3813 (burst number:889, eventnumber: 4112) which survived all Kpi2 selection cuts in section 4.4.2, except716.4. Branching ratio of the decay pi0 → νν¯EP cut19, and all photon veto cuts. However, this event is probably notpi0 → νν¯ candidate since it has a few in-time MUV1 candidates with largedeposited energy. We added the energy of all in-time MUV1 candidatesin that event and found that the ratio of total energy deposited in MUV1to the momentum of straw track, (EMUV1Pstraw ) is 2.37. This ratio is abnormallylarge for a pi0 → νν¯ event since the maximum EMUV1Pstraw we acquired from 58073Kpi2(pi0→νν¯) MC events is only 1.24. This event motivated us to set anotherpi0 → νν¯ identification cut, EMUV1Pstraw < 0.6, besides photon veto cuts, for futurepi0 → νν¯ study. The efficiency of this cut for observing pi0 → νν¯ decay intagged Kpi2 event was estimated to be 99.63% using Kpi2(νν¯) MC events.In summary, based on zero remaining events the 90% C.L. upper limitof the branching ratio of the decay pi0 → νν¯ was obtained as:Br(pi0 → νν¯) < 2.34735650× 0.9277× 1.217 = 4.3× 10−719The EPof this event is 0.8993, failing the 0.1 < EP< 0.85 cut. But the mass ofmatched sing-ring RICH candidate is 0.138747 GeV/c2, close to the pi+ mass. It shouldbe noted that this event does not have matched multi-ring RICH candidate and the strawmomentum of pi+ is 15.03 GeV/c.72Chapter 7ConclusionsThis study provided the preliminary result of the S/B for the Kpi2 back-ground in the measurement of K+ → pi+νν¯ in NA62. The S/B was esti-mated to be greater than 0.2 based on the efficiency results of the kinematicssuppression and pi0 veto vetoing and some efficiency factors acquired fromMC simulations. The required S/B should be at least 10 for the success ofthe NA62. Our result was limited by insufficient Kpi2 events, which made itdifficult to determine the real inefficiency of pi0 rejection in NA62.Several 2015 minimum bias runs were analyzed to provide the Kpi2 andKµ2 samples for studying the kinematics and pi0 vetoing factors. To setcuts for identifying Kpi2 and Kµ2 events, the RICH performance for distin-guishing pi+/µ+ in 2015 run was evaluated; a RICH mass cut, 0.1325 ≤MassRICH-single ≤ 0.2 GeV/c2, would kill 98.53% muons with the efficiencyof getting pions at 85.31%. The efficiency of other identification cuts suchas kinematics and calorimeters was also evaluated. The kinematic rejectionof Kpi2 events using GTK kaon tracks was found to be (2.16± 0.21)× 10−3based on 101 survived events out of 49077 trial Kpi2 events. This inefficiencywas at the same level with what MC simulation found, (1.09± 0.24)× 10−3.Nominal kaon tracks were assumed for pi0 veto study to acquire more trialKpi2 events. Based on zero remaining events out of nearly 3.55M Kpi2 events,the pi0 veto inefficiency of < 6.98× 10−7 (90% C.L.) was obtained.Besides, a slightly larger number of identified Kpi2 decays obtained withwider momentum range were used to search for the helicity-suppressed decaypi0 → νν¯. We got zero pi0 → νν¯ candidates out of approximately 4.74M trialevents, which leads to an upper limit of the branching ratio at 4.3 × 10−7(90% C.L.) Although at present this result is 1.6 times larger than whatE949 reported, the limit of pi0 detection in NA62 has not been reached yet.We need more Kpi2 decays from future runs in NA62 to explore the limitof pi0 detection and get the precise results for the S/B of the Kpi2 backgroundin NA62 and the branching ratio of the decay pi0 → νν¯. In future study, ifpossible the GTK kaon tracks rather than the nominal kaon tracks should beused to reconstruct kinematics variable for studying the pi0 rejection. Oncewe get remaining events in future, an estimation of background events in73Chapter 7. ConclusionsKpi2 trial events should be achieved. Also, it should be noted although zeroKpi2 events survived our present photon veto cuts, these cuts may not bethe most efficient for rejecting pi0. 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World Scientific, 2006.79Appendix AGain measurement of theSTRAW spectrometerIn order to value and optimize NA62 straw trackers’ performance, we mea-sured the dependence of the gas gain versus applied voltage at 970 mbarabsolute pressure for three different gas mixtures, Ar−CO2 (70-30 & 85-15& 93-7). Battery and a new method of gas gain measurement were usedto get more accurate current. Our results indicate the gain for Ar − CO2(70-30) gas mixture at 1752 V is (5.479± 0.213)× 104.SetupThe straw prototype at CERN was used to conduct the experiment. 16tubes were connected with flex-rigid circuits borad to one Front-End board.We used one board with high voltage and gas input connected shown byFigure A.1. An auto-ranging Keithley-6487 picoammeter with sensitivity0.01 pA has been connected between the straw cathode and the ground tomeasure the produced currents. Although the sensitivity of picoammeter isquite high, its reading is constantly fluctuating, ± 0.2 nA, once connectedto the high voltage supply. This may be caused by the noisy grounding. Tosolve this problem, we use a 130V battery as power supply, which avoidsparasitic ground loops and then allows us to measure very small current,for detecting primary current. Besides, we took a new method proposed inwhich radiation source rates can be changed without affecting measurementso that we can use high activity source, an 2.7GBq 55Fe source, to get thelarger primary current. Due to space charge effect and safety issue, 0.32 mAcurrent was set as upper limit.Get I v.s. Voltage curvesAfter putting 55Fe source in the nearest distance, we used voltage divisionfor the battery to get different voltage from 45 to 130V and measured the80Get I v.s. Voltage curvesFigure A.1: Straw prototype with Gas and HV Input Connectedcurrent in some points. As shown by Figure A.2 a, we get a plateau (gain≈ 1) for the current within this range, which demonstrates Iprimary equals431.8 ± 4.05. Without moving the source, we replaced battery with highvoltage supply, changed the voltage and got Curve 1. Then the distanceand angel of 55Fe source was adjusted to decrease source rate, Curve 2 wasacquired after this. So was Curve 3. Finally, we got the current v.s. voltageline shown in Figure A.2 a.Using the equation gain = ImeasuredIprimary , gain for Curve 1 is easy to get.Then we can calculate the average constant k1 =gainImeasuredfor Curve 2 usingthe known gain of several points deduced from Curve 1. Gain for otherpoints in Curve 2 can be obtained using known k1. Repeating this, we cangot gain v.s. voltage in Figure A.2 b.0 500 1000 1500Voltage [V]10-1100101102103Current[nA]aPlateauTaken with battery123600 800 1000 1200 1400 1600 1800Voltage [V]10-1100101102103104105106Gainby=10(0.003828±0.000048) ∗x+(−2.012±0.077)) R2 =0.9984Primary Current : 431.80± 4.05 pAFigure A.2: Gain v.s. Voltage for Ar − CO2(70-30) at 970 mbar81Gas gain resultGas gain resultWe followed the above process and got gain v.s. voltage curves for Ar −CO2(70-30, 85-15, 93-7) corresponding with Figure A.2, Figure A.3 andFigure A.4, respectively. Pressure was set at 970 mbar.Due to the fact that current reading fluctuates with high voltage powersupply as mentioned above, we drop the points whose current below 2 nA.Besides, Figure A.3 shows when gain is above 2 × 105 straw tracker entersinto non-proportional counting region, a transition region to the Geiger re-gion. Hence, to get credible linear fit result we use the data whose gain iswithin the region [10, 2×105]. Curves were linear fitted using bivariate cor-related errors and intrinsic scatter (BCES) model. The error in y coordinateequals 1% in current reading plus initial error in primary current.We can use fit parameters to estimate the gain at exact voltage like 1750,but it brings large uncertainty δ(10a)10a = ln(10) ∗ δa. Consequently, we decideto directly use the data point. For Ar − CO2 (70-30) gas, at 1752 V, thegain should be (5.479± 0.213)× 104 assuming total error equals maximum2% in reading plus 0.945% error in constant K (0.655% in K1 and 0.29% inK2) plus error in primary current, 0.938%.It is obvious that with the proportion of Ar increased the gain dramati-cally increases. The corresponding voltage for gain achieving 104 is 1575V,1400V and 1275V for 70-30, 85-15 and 93-18. If we want to achieve 105 ingain for the best resolution, the working voltage should be set at 1825V forthe present working gas mixture, i.e., 70% Ar and 30% CO2, at 970 mbar.Using gas mixtures with denser Ar can decrease the working voltage. 1610Vor 1460V is required if we used Ar−CO2(85-15) or Ar−CO2(93-7) as filledgas.82Gas gain result0 500 1000 1500Voltage [V]10-1100101102103Current[nA]aPlateau123600 800 1000 1200 1400 1600 1800Voltage [V]10-1100101102103104105106107Gainby=10(0.004296±0.000073) ∗x+(−1.962±0.094)) R2 =0.9976Primary Current : 571.8± 5.1 pAFigure A.3: Gain v.s. Voltage for Ar − CO2(85-15) at 970 mbar0 200 400 600 800 1000 1200 1400 1600Voltage [V]10-1100101102103Current[nA]aPlateau123600 800 1000 1200 1400 1600Voltage [V]10-1100101102103104105106Gainby=10(0.004638±0.000113) ∗x+(−1.879±0.130)) R2 =0.9952Primary Current : 540.00± 3.95 pAFigure A.4: Gain v.s. Voltage for Ar − CO2(93-7) at 970 mbar83Appendix BStudy of the false Kpi2rejection caused byadditional pi+ LKr clustersWe generated 300K Kpi2 MC events where pi0 was forced to decay into νν¯.In this MC simulation, LKr clusters were only generated by pi+ track sothat we can use these events to study the false rejection effect caused byadditional pi+ LKr clusters.First, we applied the one track selection cuts and Kpi2 selection cuts(section 4.4.2) on MC event. In each survived MC event, we selected onlyone LKr cluster which is furthest from the pi+ projected position in theLKr from all LKr clusters except the one associated with the pi+ track. Itshould be noted that the distance was set to 0 if no additional LKr clusterwas found. The distance distribution of these selected clusters is shown inFigure B.1. Nearly 75% Kpi2(pi0→νν¯) events in this study only have one LKrcluster, which is associated with the pi+ track.As long as the distance of the selected LKr cluster in a MC event waslarger than the radius of the masked region we set, we treated that LKrcluster as a fake photon cluster and reject the event. The reject efficiencydistribution for different radii is shown in Figure B.2. The efficiency isaround 94.36% if we set the radius of the masked region to 150 mm.84Appendix B. Study of the false Kpi2 rejection caused by additional pi+ LKr clustersEntries  58073Mean    28.62Std Dev     71.49Distance [mm]0 100 200 300 400 500 600Events / 2 mm110210310410Figure B.1: This figure shows the distance of the selected LKr cluster to theprojected position of pi+ in the LKr.0 50 100 150 200 250 300 350 400Radius of the masked region [mm]0.750.800.850.900.951.00EfficiencyFigure B.2: This figure shows the rejection efficiency for different radii ofthe masked region.85


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