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Study of the Decay π0 → vv using Data from CERN Experiment NA62 Feiler, Simon 2019-05-02

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Honours ThesisStudy of the Decay pi0 → νν¯ using Data fromCERN Experiment NA62bySimon FeilerinThe Faculty of Science(Department of Physics and Astronomy)The University of British Columbia(Vancouver)PHYS 449 Honours ThesisCourse Instructor:Prof. Robert KieflSupervisor:Prof. Douglas Bryman02/May/2019c©Simon Feiler, May 2019AbstractThis project is part of the NA62 pi0→ νν¯ analysis and is run on the 2016 datasets.Parts covered in this project, include the trigger efficiency which after variations inthe beginning (runs 6300-6350) maintained a value of around 0.1. The combinedtrigger and filter efficiency was found to be f = 1.507+0.117−0.108×10−4 @99%CL forall runs combined. A study of a possible muon contamination of the signal regionwas conducted. The combined muon acceptance of the RICH, Calo PID, missingmass requirement of the signal region and the MUV was found to be ≈ 10−13. Amuon contamination of the signal region can be ruled out.iiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Theory and Experimental Setup of NA62 . . . . . . . . . . . . . . . 32.1 Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.1.1 pi0→ νν¯ in the Standard Model . . . . . . . . . . . . . . 42.2 Accelerator Complex and Beam of the NA62 Experiment . . . . . 52.3 Detector Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Details on Proposed Experiment/Calculation . . . . . . . . . . . . . 83.1 Overview over the Analysis . . . . . . . . . . . . . . . . . . . . . 83.1.1 Signal Region Selection . . . . . . . . . . . . . . . . . . 103.2 Trigger and Filter Settings of NA62 . . . . . . . . . . . . . . . . 113.2.1 Trigger Settings . . . . . . . . . . . . . . . . . . . . . . . 123.2.2 Filter Settings . . . . . . . . . . . . . . . . . . . . . . . . 133.3 Muon Repression in the Signal Region . . . . . . . . . . . . . . . 133.3.1 RICH . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14iii3.3.2 Calo PID . . . . . . . . . . . . . . . . . . . . . . . . . . 163.3.3 Missing Mass Requirement . . . . . . . . . . . . . . . . 183.3.4 Muon Veto Detector . . . . . . . . . . . . . . . . . . . . 194 Analysis and Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 204.1 Trigger Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . 204.2 Filter Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . 244.3 Study of the Muon Rejection . . . . . . . . . . . . . . . . . . . . 274.3.1 RICH . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.3.2 Calo PID . . . . . . . . . . . . . . . . . . . . . . . . . . 314.3.3 Missing Mass Requirement . . . . . . . . . . . . . . . . 314.3.4 Muon Veto Detectors . . . . . . . . . . . . . . . . . . . . 334.3.5 Combined Muon Acceptance . . . . . . . . . . . . . . . . 345 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38A Supporting Materials . . . . . . . . . . . . . . . . . . . . . . . . . . 40A.1 Trigger Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . 40A.2 Filter Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . 46ivList of TablesTable 2.1 Fundamental fermions of the standard model. . . . . . . . . . 3Table 2.2 Forces and interaction carriers (gauge bosons) of the standardmodel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Table 3.1 Reducible backgrounds of the pi0 → νν¯ analysis. Branchingratios from [13]. . . . . . . . . . . . . . . . . . . . . . . . . . 9Table 3.2 Possible kaon decays (>1%) from [13]. . . . . . . . . . . . . . 10vList of FiguresFigure 2.1 CERNs accelerator complex and the main experimental sitesby Christiane Lefvre [10] ©2008-2019 CERN for informa-tional use. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6Figure 2.2 Schematic of the NA62 detector setup by E. Cortina Gil et al.[7] licensed by CC BY 3.0. . . . . . . . . . . . . . . . . . . . 7Figure 3.1 Illustration of the NA62 data process. In NA62 data is passedthrough a trigger and a filter, saving only a fraction of the data.A small part of the decays is saved regardless of its propertiesas control data. . . . . . . . . . . . . . . . . . . . . . . . . . 12Figure 3.2 Distinct profiles of three particles with masses m1 < m2 < m3in the θ -momentum plane where θ is the opening angle of theCherenkov radiation. . . . . . . . . . . . . . . . . . . . . . . 15Figure 3.3 Radius vs particle momentum in the RICH by E. Cortina Gilet al. [7] licensed by CC BY 3.0. The different particles showdistinct behavior depending on their respective rest mass (eq.3.2) and can therefore be identified. . . . . . . . . . . . . . . 16Figure 3.4 Energy E vs momentum p deposited in the LKr for MC gener-ated muons and pions. . . . . . . . . . . . . . . . . . . . . . 17Figure 3.5 Missing mass spectrum of kaon decays by A. Ceccucci et al.[5] licensed by CC BY 3.0. . . . . . . . . . . . . . . . . . . . 18Figure 4.1 Trigger efficiency per burst and Gaussian fit for run 6614. . . 21viFigure 4.2 Trigger efficiency per burst vs the number of KPi2 per burstfor run 6614. . . . . . . . . . . . . . . . . . . . . . . . . . . 22Figure 4.3 Trigger efficiency per burst and Gaussian fit, after requiringmore than 60 KPi2 per bursts, for run 6614. . . . . . . . . . . 23Figure 4.4 Trigger efficiencies for all the 2016 runs with more than 10bursts after the removal of the bursts smaller than 60 KPi2.The bursts are fitted with a Gaussian fit and the error bars cor-respond to 99% CL. . . . . . . . . . . . . . . . . . . . . . . 24Figure 4.5 Filter efficiencies for the runs 6300 to 6380. A binomial distri-bution of the event passing is assumed. The error bars corre-spond to 99% CL pearson. . . . . . . . . . . . . . . . . . . . 25Figure 4.6 Histogram of all filter efficiencies of the 2016 runs and MonteCarlo simulation of the distribution of filter efficiencies f =k/n, where k is assumed to follow a binomial distribution, withprobability p= 1.507×10−4 and n is the number of trials. . . 26Figure 4.7 Distribution of the RICH likelihood for a pion and a muonsample. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28Figure 4.8 Muon acceptance of the RICH for different likelihood cuts forbinned momenta. . . . . . . . . . . . . . . . . . . . . . . . . 29Figure 4.9 Pion acceptance of the RICH for different likelihood cuts forbinned momenta. . . . . . . . . . . . . . . . . . . . . . . . . 30Figure 4.10 Muon acceptance of the Calo PID for different likelihood cutsfor binned momenta. . . . . . . . . . . . . . . . . . . . . . . 31Figure 4.11 Missing mass distribution of the pion and muon sample andthe missing mass requirement of the signal region with corre-sponding muon acceptance. . . . . . . . . . . . . . . . . . . 32Figure 4.12 Missing mass vs momentum for the muon sample. . . . . . . 33Figure 4.13 Muon identification of the MUV3 detector for different mo-menta by E. Cortina Gil et al. [7] licensed by CC BY 3.0. . . . 34Figure A.1 Trigger efficiency per burst for run 6725 . . . . . . . . . . . . 41Figure A.2 Trigger efficiency per burst and Gaussian fit for run 6356 . . . 42viiFigure A.3 Trigger efficiency per burst vs the number of KPi2 per burstfor run 6356 . . . . . . . . . . . . . . . . . . . . . . . . . . . 42Figure A.4 Trigger efficiency per burst and Gaussian fit for run 6356 . . . 43Figure A.5 Trigger efficiency per burst vs the number of KPi2 per burstfor run 6668 . . . . . . . . . . . . . . . . . . . . . . . . . . . 44Figure A.6 Trigger efficiency per burst and Gaussian fit for run 6483 . . . 45Figure A.7 Trigger efficiency per burst and Gaussian fit for run 6589 . . . 45Figure A.8 Filter efficiencies for the runs 6380 to 6540. The error barscorrespond to 99% CL pearson. . . . . . . . . . . . . . . . . 46Figure A.9 Filter efficiencies for the runs 6540 to 6700. The error barscorrespond to 99% CL pearson. . . . . . . . . . . . . . . . . 47Figure A.10 Monte Carlo simulation of the distribution of filter efficienciesf = k/n, where k is assumed to follow a binomial distribution,with probability p= 1.507×10−4 and n is the number of trials.10000 samples were produced for each run. . . . . . . . . . . 48viiiAcknowledgmentsI would like to thank my supervisor Professor Douglas Bryman and second readerDr. Bob Velghe. Needless to say that this project would not exist without them. Ihad a lot of fun with it, learnt a lot and got to see beautiful British Columbia.What more can you wish for?ixChapter 1IntroductionOne of the most pressing questions for humankind throughout all its history is thequestion of how matter is structured. From the ages of ancient Greece where Dem-ocritus pondered about the smallest, indivisible components of matter. ThroughGerman 1800s Weimar Classicism where Goethes iconic literary figure Dr. Faust[15] nearly goes mad over the question what holds the world together inside. Allthe way to today where the scientific method and technological advance super-sedes the power of imagination in deciphering the mysteries of matter. The partof physics that engages with this conundrum today is particle physics. It has madeincredible progress in the last few of years, summarized in the so called StandardModel (SM). It represents an exceptionally precise description of known particlephenomena and people are finally beginning to feel confident enough about it toteaching it in undergraduate physics courses [9]. However it is known that eventhough the SM is a remarkably successful model, it is not yet complete. For ex-ample, the SM treats neutrinos as massless but it is known from neutrino oscil-lation experiments that they in fact do hold mass [8]. There is also the issue ofdark matter. We can observe its gravitational impacts, but within the SM there areno plausible candidates that fulfills the required properties of being massive andweakly interacting. So there has to be some kind of new underlying physics thatcan’t be understood from the perspective of the SM. It is therefore crucial to designexperiments that are sensitive to this new kind of physics in order to observe thosedeviations and get a better understanding of their magnitude. Such an experiment1is the pi0→ νν¯ analyis, which this project is being a part of. The goal of the analy-sis is to study the rare decay of a pion into neutrino and antineutrino pi0→ νν¯ andpossibly put a new upper limit on the branching ratio of this decay. This decay isforbidden if neutrinos are assumed massless (ref. Sec. 2.1.1). The standard decaysof the pi0 are listed in TABLE 3.1. The current upper limit on the decay was derivedby the E949 Collaboration and is [2]BR(pi0→ νν¯)< 2.7 × 10−7 @ 90% CLThe search for this decay can take place within the CERN NA62 experiment. NA62was originally founded to measure the branching ratio of the very rare decay K+→pi+νν¯ to an accuracy of 10% [5]. A K+ → pi+pi0 data set can be extracted fromtheir 2016 data set. From there on the further decay of the pi0 can be studied. Ashort introduction to the standard model, the pi0→ νν¯ decay and the experimentalsetup is provided in Chap. 2. An outline of the analysis as a whole is drawn inSec. 3.1 and the signal region is defined. The parts of the analysis covered inthis project are the calculation of the trigger and filter efficiency and the study ofa possible muon contamination of the signal region. They are described in Sec.3.2and Sec. 3.3 and conducted in Chap. 4.2Chapter 2Theory and Experimental Setupof NA622.1 Standard ModelThis section will give a brief overview of the essential part of the standard model,based on [11], for a comprehensive introduction one can refer to [9].The fundamental particles of the standard model are quarks and leptons areshown in Tab. 2.1. These fermions (spin-1/2-particles) are divided in 3 generationsof increasing mass. For every of these fermions an antiparticle with same mass andfermionsgeneration electriccolor spin1 2 3 chargeleptonsνe νµ ντ 0 — 12e µ τ -1quarksu c t +2/3r, b, g 12d s b -1/3Table 2.1: Fundamental fermions of the standard model.spin, opposite charge and opposite color exists.Further non fundamental particles are baryons (antibaryons), consisting of 3quarks (antiquarks), and the mesons, consisting of a quark and antiquark.3Particles within the SM can interact through 3 forces, which couple on differentproperties of the particles respectively. Those forces are listed in Tab. 2.2.The forces are mediated through so called gauge bosons (spin-1-bosons). Grav-ity is not included in the standard model.force couples on interaction carriers mass(GeVc2 )stron color 8 gluons (g) 0electromagnetic electric quarge photon (γ) 0weak weak charge W± , Z0 ≈ 102Table 2.2: Forces and interaction carriers (gauge bosons) of the standardmodel.It should be pointed out that gluons and the force carriers of the weak interac-tion can interact among themselves since they themselves carry color respectivelyweak charge.The Higgs mechanism describes how particles in the SM gain mass. Thismechanism predicts the existence of an additional electrically neutral scalar par-ticle (spin-0-particle). Which was eventually experimentally confirmed at a massof 125 GeV.Within the SM energy, momentum, charge, color, baryon number, and leptonnumber are conserved.2.1.1 pi0→ νν¯ in the Standard ModelThe spin of the pion is 0. Therefore a pion at rest in a two body back to back decayhas to decay in two left-handed or two right-handed particles to fulfill angularmomentum conservation. In order to decay into neutrinos the pion has to decay intoa neutrino and antineutrino-pair to fulfill fermion number conservation. Thereforethe decay product has to be a left-handed neutrino and a left-handed antineutrino,or both have to be right-handed. However we know that all neutrinos are left-handed and all anti neutrinos are right-handed. This is known as the maximumparity violation of the weak force [9]. If neutrinos are assumed massless they4are forced to travel at the speed of light. Then the distinction into left and right-handed is not an artificial construct of the frame of reference. Because then wecan’t lorentz-transform into a system faster than the neutrinos. Therefore the pi0→νν¯ decay cannot take place if the neutrinos are assumed massless. If they howevercarry mass they can’t travel at the speed of light. Hence one can lorentz transforminto a reference frame faster then them and thus turn a left-handed neutrino into aright-handed neutrino and vice versa. Then the decay is allowed, however stronglysuppressed depending on how small the neutrino masses are. An estimate, givenby formula 2.1, on how the branching ratio decreases with smaller neutrino massescan be found at [14]. Plugging in the current limit on the tau neutrino mass ofmντ < 18.2MeV [3] one obtainsBr(pi0→ νν¯) = 3×10−8(mν/mpi0)2√1−4(mν/mpi0)2 ≈ 5×10−10 (2.1)This is an estimate on what could be achievable from our current knowledge onneutrino masses. Even though a branching ratio that small will not be achievedby this analysis it is still important to conduct this experiment since it representsa direct measurement and is not requiring the knowledge of the neutrino masses.The current upper limit on the branching ratio by direct measurement is [14]Br(pi0→ νν¯) = 2.7×10−7@90%CLThis value is within reach of this analysis and since more data is at disposal it islikely that that branching ratio can be improved.2.2 Accelerator Complex and Beam of the NA62 Experi-mentA bottle of hydrogen gas is the starting point for the protons used in experimentsat CERN. Those hydrogen atoms get ionized and passed into a linear accelerator(Linac 2). Then they get passed into a row of smaller synchrotrons, the proton syn-chrotron booster (Booster), the proton synchrotron (PS) and eventually the superproton synchrotron (SPS) [1]. The SPS serves as a pre injector to the large hadron5collider (LHC). Fig. 2.1 gives an overview over all the acceleration complex andthe experimental sites.Figure 2.1: CERNs accelerator complex and the main experimental sites byChristiane Lefvre [10] ©2008-2019 CERN for informational use.The proton beam is extracted at a central momentum of 400 GeV/c from theSPS and directed towards Na62’s experimental setup at the North Area. There thebeam hits a 400 mm long, 2 mm diameter beryllium target. From this target apositively charged beam, consisting of secondary particles at 75 GeV/c, is derived.This beam consists of the desired K+ amongst other particles and is then passedinto the detector [7].62.3 Detector SetupFigure 2.2: Schematic of the NA62 detector setup by E. Cortina Gil et al. [7]licensed by CC BY 3.0.A quick overview over the detectors and their function is provided a schematic canbe seen in Fig. 2.2. A more detailed description can be found in [7]. First ofthe kaons in the secondary particle beam get identified by a differential Cherenkovcounter (KTAG). Since the central beam momentum is known the particle identi-fication works in a similar way as the RICH, described in Sec. 3.3.1. The GTKconsists of 3 silicon pixel tracking detectors and measures the coordinates of theidentified kaons. This detector is placed in a magnetic dipole field, therefore themomentum can be calculated from the way the charged kaon beam bends. The par-ticles then enter the decay region. A magnetic spectrometer with tracking detectors(STRAW) can detect and measure the coordinates and momenta of charged decayproducts. The ring-imaging Cherenkov counter (RICH) can be used to identifypions with respect to other charged particle using the independent measurementof their momenta from the STRAW (see Sec. 3.3). A charged-particle hodoscope(CHOD) will be used to detect charged particles and helps setting the trigger (ref.Sec. 3.2). The CHOD is divided into 4 sections. Liquid Krypton electromagneticcalorimeter (LKr), Small-Angle calorimeters (SAC), Intermediate-Ring calorime-ters (IRC) will be used to detect photons from small to intermediate angles. Aseries of annular Large-Angle photon Veto detectors (LAV) will help to detect pho-tons at large angles. The muon-veto detectors (MUV1,2,3) consist of a two-parthadron calorimeter followed by additional iron and a plane of scintillating tiles.They work together with the RICH to identify muons up to a high precision.7Chapter 3Details on ProposedExperiment/Calculation3.1 Overview over the AnalysisAn overview over the entire analysis will be provided in this section. Afterwardsthe parts of the analysis conducted in this project, namely the study of the filter andtrigger efficiency and the study of a muon contamination of the signal region, willbe discussed. Goal of the NA62 pi0→ νν¯ analysis is to put a new upper limit on thebranching ratio of said decay by a direct measurement. The analysis will run on the2016 datasets. First of a signal region selection (Sec. 3.1.1) will be applied to thedata. Afterwards only one of the kaon decay channels, the K+→ pi++pi0 decay1,remains. The remaining events then all contain pi0 which we wish to study. Thetotal number of pi0 N(pi0) then has to be scaled back by the combined trigger andfilter efficiency (Sec. 3.2) as not all of these decays get stored by NA62. That wayN(pi0) will be scaled back to the number of events that would have been obtainedwithout the trigger and filter.Now the background rejection(BGR) can be applied to the signal region. TheBGR simply consists of removing events containing photons. That way one gets1To be precise the SR doesn’t include events where the pi0 decays further into e− or e+. Sincethis decay channel gets removed by the trigger/filter. This will only marginally impair the branchingratio since those decays only take place in less than 2%8Decay Branching-ratio in %pi0 → γ+ γ 98.82pi0 → e++ e−+ γ 1.17pi0 → e++ e++ e−+ e− 3.34×10−5pi0 → e++ e− 6.46×10−8pi0 → 4γ < 2×10−8 CL= 90%Table 3.1: Reducible backgrounds of the pi0→ νν¯ analysis. Branching ratiosfrom [13].rid of all the possible pi0 decays (shown in Tab. 3.1) as all the e+ and e− channelshave already been rejected by the trigger/filter.The leftover events are our signal or irreducible background for pi0 decays intono detectable particles pi0 → nothing. These could either be photons that weresimply missed by the detector, neutrinos or even some weakly interacting particles.Hence dividing the number of leftover events N(pi0 → nothing) by N(pi0) allowsus to obtain an upper limit on the branching ratio of pi0→ νν¯ :BR(pi0→ νν¯)< N(pi0→ nothing)N(pi0).Note that the signal doesn’t have to be scaled by the trigger and filter efficiencysince it’s not being affected by it. Lastly some corrections have to be applied.Since there is a high frequency of hits in the detector it can happen that pi0→ νν¯gets discarded because a muon or photon randomly hits the veto system at roughlythe same time as the decay takes place. What also has to be considered is thata photon can hit the detectors in the same region as a pion and therefore avoiddetection. This influence of the pion on the reconstruction of the photon can besimulated in Monte Carlo simulations and be taken into account. Both of theseeffects can reduce the efficiency by roughly 25%.First, all of these steps will be conducted on roughly 20% of the 2016 data.All the cuts and selections will be optimized on this fraction of the data to find thebackground rejection versus signal acceptance point that gives the best limit on the9Decay Branching-ratio (%)K+ → µ++νµ 63.56K+ → pi++pi0 20.67K+ → pi++pi0 +pi0 1.76K+ → pi++pi++pi− 5.58K+ → pi0 + e++ν 5.07K+ → pi0 +µ++ν 3.35Table 3.2: Possible kaon decays (>1%) from [13].branching ratio. Afterwards the analysis will be carried out on the rest of the data.This procedure is called ”blind” analysis. That way analysis bias introduced by thedecisions of the analysis team can be avoided.3.1.1 Signal Region SelectionIn this section the signal region will be defined. Since the goal of this analysisis the study of a pi0 decay the objective of the signal region is to contain onlythose pi0 which can be studied further. The reason why the analysis is taking placewithin NA62 is that among the possible kaon decays there is a good candidate forsuch a selection, the K+→ pi++pi0 decay. So the signal region selection aims todistinguish this decay channel form the other possible decays, listed in 3.2. Themain reason why this channel was picked is due its two body kinematics. As aresult of those kinematics the decay represents a sharp peak in the missing massspectrum, as shown in Fig. 3.5.By requiring the missing mass to be in a smallwindow one can achieve a good suppression of the other decay channels whileleaving the channel of interest relatively untouched. The reason for this is that themissing mass distribution for a 3 body decay is smeared out over a wider area andthe missing mass distribution of the K+ → µ+ + νµ is at a different value, evenwhen the muon is misidentified as a pion.Another requirement is to require no other charged particle than the pi+. Thissuppresses the other decay channels even further depending on how well the par-ticle identification works. The second condition implies that decays where the pi010decays further into electrons or positrons will get rejected as the pi0 decays instan-taneously (mean life time τ = (8.52 ± 0.18) × 10−17 [13]). This will impair thefinal branching ratio but these small deviations of <2% will be accepted.The m2miss-cuts together with the requirement of no charged particle besides thepi+ define the SR. With those requirements almost only K+→ pi+pi0 decays willremain in the signal region.For the background repression in this SR one can simply require that no pho-tons can be found in the photon veto detectors. Then all the pi0 decays shown Tab.3.1) get rejected2, leaving only the signal and irreducible background.3.2 Trigger and Filter Settings of NA62The goal of the trigger settings of NA62 is to identify and save K+→ pi+νν¯ likeevents in order to save valuable storage space. This signal is very similar to thesignal targeted by this analysis. In both cases there is one charged pion and nofurther particle detected. So K+→ pi+pi0 with a subsequent pi0→ νν¯ will not beaffected and therefore doesn’t have to be scaled.To achieve the goal of saving storage an online trigger is used that has to decideon the spot whether to keep an event or to disregard it. Afterwards a filter will beapplied to refine the selection. Since there is more time available, calculations andparticle identifications can take place at that second step. One small fraction, thecontrol data, will be kept regardless of its properties. This is necessary in order togo back and study what exactly the trigger and the filter are doing. A schematic ofthe data processing in NA62 is shown in Fig. 3.1.2Decays containing electrons and positrons are already rejected through the definition of thesignal region.11Figure 3.1: Illustration of the NA62 data process. In NA62 data is passedthrough a trigger and a filter, saving only a fraction of the data. A smallpart of the decays is saved regardless of its properties as control data.In order to obtain the trigger(filter) efficiency the control data will be passedthrough the trigger(filter). Then the efficiency f is simply defined as the ratio ofnumber of events passing k and number of events before the trigger(filter) n.For the purpose of this analysis it is only of concern how the the trigger(filter)settings affect our signal region. Therefore when the efficiencies are calculated inSec 4 the control data will first be passed through the signal region selection beforeapplying the trigger(filter). Then the efficiency becomes:f =N(Kpi2)passingN(KPi2)original=kn. (3.1)In the following passage the trigger and filter settings used will be introduced.3.2.1 Trigger SettingsThe following trigger settings have been used in 2016: there has to be at leastone flash of light in the RICH indicating that there is at least one charged particleinvolved in the decay. Since the trigger has to act fast there is no time to identifythe particles at this stage. Then all the hits inside the CHOD have to be in the samequadrant. This helps to suppress events with photons or additional pions, since12those arise in more body decays they can usually be found in different quadrantsof the CHOD. Then there has to be less than N hints in the CHOD. This helpsto protect against showers that are caused by the RICH mirror. Following this,there has to be no activity in the MUV and the LAV respectively to discount eventswith mouns or photons. Furthermore, the trigger requires that there is less than20 GeV in the LKr. Since one can be certain that photons deposit all their energyin the calorimeters, energies above 20 GeV indicate most likely a photon. So thiscondition helps to further suppress events with photons in their decay products.3.2.2 Filter SettingsAfterwards the filter will check the event quality and decide whether all the detec-tors were working correctly. Then the track in the STRAWs will get reconstructedand from the direction and momentum, the position where the particle will hit thedownstream detectors will be calculated. Should that position lie out of the accep-tance of those detectors, the event will be disregarded. Then the actual position ofthe track in the CHOD will be validated. Should it deviate from the calculated posi-tion the event will be discarded. Also there has to be a kaon candidate in the KTAGwith at least one 1 hit in every GTK otherwise the momentum can’t be determinedand therefore there will be no use in keeping the event.3.3 Muon Repression in the Signal RegionThe second part of this project is the study of a possible muon contamination of thesignal region. This is crucial because the K+→ µ++νµ decay for example couldleak into the signal region. That would be particularly harmful since that decaycould then be mistaken for our signal, since apart from the muon there is no furtherparticle observed. This could happen through the misidentification of the µ+ as api+. Also the K+→ µ++νµ decay can leak into the defined missing mass regionof the signal region. That could happen since the decay has a radiative componentor is a result of a miss-reconstruction of the tracks by assigning the wrong kaon tothe wrong decay.Luckily the detector was designed to deal with these kind of tasks as NA6213relies on a very accurate distinction between pions and muons as well. The dis-tinction between pions and muons relies on 4 constituents. These four constituentswill be introduced in the following sections.3.3.1 RICHTo better distinguish between pi+ and other particles (mainly µ+) NA62 uses aRICH. This makes use of the fact that Cherenkov radiation has a specific openingangle θ ,ref. [11], for a given velocity. Cherenkov radiation occurs if a chargedparticle moves faster than the speed of light in a dielectric medium. It is the elec-tromagnetic equivalent of a supersonic boom. The RICH is filled with neon gasthat has been chosen as a radiator medium. Knowing the refractive index n of theneon gas the opening angle of the Cherenkov radiation can be obtained:cos(θ) =1nβ=1n pEOne can express the energy E via the momentum p and the mass m of the particlethroughE =√m2 + p2Then one obtains a function θ(p) likeθ = arccos(√1+m2/p2n)(3.2)A plot of this function can be seen in Fig. 3.2 for three different mass valuesm1 < m2 < m3. Each of these mass values corresponds to a certain line in theθ -momentum plane.14Figure 3.2: Distinct profiles of three particles with masses m1 < m2 < m3 inthe θ -momentum plane where θ is the opening angle of the Cherenkovradiation.With this information and knowing what particles are to be expected in thedetector one can start identifying them. This is illustrated in Fig. 3.3. The Graphshows the typical arccos(√1+m2/p2/n). To get the angle from the radius onesimply has to take the tangent and multiply by the focal length of the detector.15Figure 3.3: Radius vs particle momentum in the RICH by E. Cortina Gil et al.[7] licensed by CC BY 3.0. The different particles show distinct behav-ior depending on their respective rest mass (eq. 3.2) and can thereforebe identified.From here on a likelihood can be assigned to every event of containing a pionor a muon. This likelihood value is the RICH hypothesis and ranges from -1, theparticle is with a high certainty a muon, to 1, the particle is with a high certaintya pion. The way this rich hypothesis is ascribed is described in [12]. By cuttingon this likelihood the RICH detector can help distinguish pions from muons andtherefore help to achieve muon suppression in the signal region.3.3.2 Calo PIDFurthermore the information from the LKr, MUV1 and MUV2 can be used foradditional verification of particle identity. A multivariate analysis (MVA) will bedone on all information (e.g. the shape of the shower, the energy deposited, etc.)provided by those detectors. The MVA assigns similar a pion likelihood, ranging16from 0 to 1, and a muon likelihood, ranging from 0 to 1, to every event. The MVAcan make the particle distinction based on the following differences in properties.Electrons and photons deposit their energy almost immediately, they can be distin-guished from the pions and muons. Also, since pions consist of quarks they can,unlike muons, strongly interact with the calorimeters. Therefore the shape and en-ergy they leave behind in the detector can look different. Through those stronginteractions with the detector material pions can generate neutrons which will es-cape the detector undetected as the LKr is an electromagnetic calorimeter. As aresult pions don’t deposit all of their energy but on average they still deposit morethan muons. This can be seen on some Monte Carlo data in Fig.3.4.Figure 3.4: Energy E vs momentum p deposited in the LKr for MC generatedmuons and pions.So in naive manner one could just put a cut on this E/p value and assign ahigher likelihood of the particle being a pion from the right of this cut. The MVPworks in a bit more sophisticated fashion.173.3.3 Missing Mass RequirementAs mentioned earlier the missing mass of an event gives a good indication of whatdecay channel is present. The missing mass defined as the squared difference in4-momenta of the K+ and of the pi+. For our decay of interest m2miss becomes.m2miss = (PK+−Ppi+)2 = P2pi0 = mpi0 2 = 0.0182 GeV2 (3.3)The missing mass spectrum of the kaon decays can be seen in Fig. 3.5. Thewidth of the curve takes the detector resolution into account. By requiring m2missout of a small range around the peak the other possible decays of the kaon can besuppressed.Figure 3.5: Missing mass spectrum of kaon decays by A. Ceccucci et al. [5]licensed by CC BY 3.0.That way muons can be further suppressed in the signal region.183.3.4 Muon Veto DetectorBy simply requiring no hits in muon veto detector (MUV3) further muon suppres-sion can be achieved.19Chapter 4Analysis and Results4.1 Trigger EfficiencyAs stated earlier, in Sec. 3.1, the trigger efficiency f is defined by the ratio betweenthe number of KPi2 passing the trigger (referred as k) and the number of KPi2before the trigger (referred as n). As there are only two possible outcomes ”pass”and ”not pass”, that are mutually exclusive, it can be regarded as a Bernoulli trial.It is therefore assumed that k follows a binomial distribution. In consequence fmust follow a binomial distribution as it is only scaled by a factor 1/n.As a first naive approach to come up with a method to determine the triggerefficiency the assumption is made that the binomial distribution is in the Gaussianlimit. The trigger efficiency is then evaluated on a burst by burst basis on everyindividual run and a Gaussian fit is carried out.f (x) =h√2piσexp((x−µ)22σ2)(4.1)Where h is the height of the curve, σ the standard deviation, and µ the mean, inour case the trigger efficiency. The result can be seen in Fig. 4.120Figure 4.1: Trigger efficiency per burst and Gaussian fit for run 6614.An evaluation of how well a fit is working can be obtained from the reducedχ2ν . A χ2ν of 1 means the fit is working well, much greater 1 means it’s a bad fit andsmaller 1 means we are overfitting. χ2ν is defined asχ2ν =χ2ν=χ2Nb−N fwhere ν is the number of degrees of freedom, meaning the number of occupiedbins Nb in the histogram that are being fitted minus the number of fit parametersNf used. In our case Nf = 3, namely h, σ and µ .As can be seen by the χ2ν = 4.53 the fit is not working well. Which is alsonoticeable by the flank on the right of the histogram and the large amount of burstsin the 0 column. Clearly some of the assumptions don’t hold. To investigate thisfurther the trigger efficiency per burst is drawn vs the number of KPi2 in a burstFig. 4.2.21Figure 4.2: Trigger efficiency per burst vs the number of KPi2 per burst forrun 6614.The first thing that stands out from looking at Fig. 4.2 are the hyperbolas onthe left side of the graph. These are to be expected and correspond to k=1,2,3respectively. As the trigger efficiency, defined as k/n, for a fixed k will drop with1/n. It can also be seen that the flank and the large amount of bursts in the 0 columnare caused by small bursts. For these small bursts the assumption of a Gaussiandistribution doesn’t hold. There are various guidelines/pointers about when it isadequate to use a normal distribution for a binomial distribution. The one used inthis analysis is from [4]:1√n(√qp−√pq)< 0.3 (4.2)where p is the probability of success, q =1-p and n is the number of trials, in ourcase the number of KPi2 per burst. Assuming the trigger efficiency is around 0.12,1the equation holds for approximately n = 60. Meaning that only for bursts with1The trigger efficiency varies a bit from run to run. For some runs it is a bit smaller or larger, butthis only serves as an estimate.22more than 60 KPi2 the use of a Gaussian distribution is justifiable. All the burstswith less than 60 KPi2 will thereby be excluded for the analysis of the triggerefficiency. An updated distribution can be seen in Fig. 4.3. One can see that thefit is now much more accurate, this can especially be seen by the χ2ν which is nowvery close to 1.Figure 4.3: Trigger efficiency per burst and Gaussian fit, after requiring morethan 60 KPi2 per bursts, for run 6614.This is obviously one of the cases where the Gaussian fit worked very well,there are some runs shown in the appendix where this wasn’t the case.Fig. 4.4 shows the acquired trigger efficiencies for all the runs with more than10 bursts after the removal of the smaller bursts. The shown error intervals corre-spond to the standard error @ 99% CL defined by:σx¯ = 2.58× σ√n23Figure 4.4: Trigger efficiencies for all the 2016 runs with more than 10 burstsafter the removal of the bursts smaller than 60 KPi2. The bursts are fittedwith a Gaussian fit and the error bars correspond to 99% CL.After some variations in the beginning (runs 6300-6350) the trigger efficiencymaintains a value of around 0.1. Those changes in the beginning were probablycaused by a change in the definition of the trigger. Consulting the logs revealedthat NA62 was still applying some changes to the calorimetric trigger at that time.4.2 Filter EfficiencyIn this section the combined trigger and filter efficiency will be evaluated. Forconvenience the it will be referred as the filter efficiency from here on. The filterefficiency is defined in eq. 3.1 as ratio between the number of KPi2 passing thefilter (referred as k) and the amount of KPi2 before the filter (referred as n). Similarto the trigger efficiency it is regarded as a Bernoulli trial. It is therefore assumedthat k follows a binomial distribution. In consequence f therefore also follows abinomial distribution as it is only scaled by the factor 1/n.For the filter efficiency eq. 4.2 is not fulfilled since p is of the order of mag-nitude of 10−4 and n goes only up to 105 at most. So a binomial distribution ofthe filter efficiency is assumed. The error intervals are chosen as Clopper-Pearson-24intervals @ 99% CL [6]. Fig. 4.5 shows the filter efficiencies for the runs 6300-6380 with according Clopper-Pearson-intervals. The rest of the runs are shown inappendix in Fig. A.8 and A.9.Figure 4.5: Filter efficiencies for the runs 6300 to 6380. A binomial distribu-tion of the event passing is assumed. The error bars correspond to 99%CL pearson.Combining, by adding up n and k for all the runs, gives us:f = 1.507+0.117−0.108×10−4 @99%CLAs a cross check on the intervals one can also take the Gaussian error @99% CLdefined bys=2.58 f√k=2.58 f√1180= 0.113×10−4The Gaussian error is almost identical for the combined filter efficiency. Fig. 4.6shows the the distribution of the filter efficiency, by projecting Fig. 4.5, A.8 andA.9 on the y-axis.25Figure 4.6: Histogram of all filter efficiencies of the 2016 runs and MonteCarlo simulation of the distribution of filter efficiencies f = k/n, wherek is assumed to follow a binomial distribution, with probability p =1.507×10−4 and n is the number of trials.As there is a lot of runs with a filter efficiency of 0, with 0 KPi2 passing thefilter, it would be nice to have a cross check to see if it’s probable to have thatmany runs with 0 events passing the filter or if in those cases the filter did not workcorrectly. Such a cross check can be provided by doing a Monte Carlo Simulation.For that the assumption is made that k follows a binomial distribution with p =f = 1.507 ×10−4.k =(nk)pk(1− p)n−kThen the filter efficiency is f = k/n. The Monte Carlo simulation is run with 10000samples each, p and n are used to get f. How the distribution of the filter efficiencyfor individual runs looks like is shown in Fig. A.10. By adding up the distributionsfor all the runs and scaling by the number of samples the MC distribution shownin Fig. 4.6 is derived. It can be seen that MC and data are in good agreement. Soit is perfectly normal to have that amount of 0 filter efficiency runs. And from thisperspective the filter has been working fine. Fig. 4.6 can be seen as a superposition26of stretched2 binomial distributions with small n’s, coming from the smaller runs,and of more Gaussian like distributions coming from the larger runs with largern’s.4.3 Study of the Muon RejectionIn this section the possibility of muons in the signal region will be studied. Themuon acceptance will therefore be defined as the number of muons passing dividedby the total number of muons.rx =knAs stated before the identification of muons relies on 4 constituents. In order tostudy the muon acceptance of three of these constituents a muon sample is derivedby requiring a hit in the MUV3. For the RICH there is also a sample of pionsavailable, so for that case the pion acceptance can also be studied. The pion samplewas derived by feeding the information from the LKr, the MUV1 and MUV2 intoa boosted decision tree (BDT). Then a cut is placed on the output of that BDT.4.3.1 RICHSec. 3.3.1 describes how from the data acquired from the RICH a likelihood canbe assigned to the particles of them being a muon(-1) or a pion(1) respectively. Bycutting on this likelihood a distinction between muons and pions can be made.2The distribution is stretched along the x-axis, as the binomial distributed k is multiplied by 1/nto obtain the filter efficiency.27Figure 4.7: Distribution of the RICH likelihood for a pion and a muon sam-ple.A plot of the RICH likelihood distribution of the muon and pion sample isshown in Fig. 4.7. One can see that for the muon sample most of the events arecloser to the left(-1) while the pions are closer to the right(1). One possible cutat 0.75 is also shown. Everything to the left of this cut is rejected and thereforenot part of the signal region. From the events to the right to the cut the muon(pion) acceptance can be calculated by dividing through the total number of muons(pions) in the sample.28Figure 4.8: Muon acceptance of the RICH for different likelihood cuts forbinned momenta.The acceptance of muons in the signal region in terms of bins of the momentumis shown in Fig. 4.8. As expected the muon acceptance rises for larger momen-tums. This can be understood from looking at Fig. 3.3. The band correspondingto the pions and the muons in the radius-momentum plane gets closer as the mo-mentum increases. It gets therefore harder to distinguish between them. The effecton tightening, by demanding a higher likelihood, and lowering, by demanding asmaller likelihood, the likelihood requirement can also be studied.29Figure 4.9: Pion acceptance of the RICH for different likelihood cuts forbinned momenta.The acceptance of pions in the signal region is shown in Fig. 4.9. As the mo-mentum increases the acceptance decreases, this is again due to the more difficultdistinction for higher momenta. The pion acceptance drops for lower values ofmomenta. This is because the RICH has a minimal radius at what it can detectCherenkov radiation. Therefore low momentum pions, that send out Cherenkovradiation at a smaller angle, can not be identified by the RICH.From the graphs it can be seen that it is a trade off between muon rejectionand pion acceptance. By rejecting more muons we automatically also reject morepions. In the end a likelihood requirement of 0.75 was chosen which results in amuon acceptance over the whole momentum region ofrRICH = 6.11+0.22−0.21×10−3 @99%CLand a pion acceptance ofaRICH = 0.875±0.0027 @99%CL304.3.2 Calo PIDThe analysis of the muon acceptance is completed in a similar way, as from theLKr, MUV2 and MUV3 data a likelihood (the Calo PID) can be derived as well(ref. to Sec. 3.3.2). So by cutting on that likelihood the muon acceptance of theCalo PID can be calculated. For this a pion sample was not available.Figure 4.10: Muon acceptance of the Calo PID for different likelihood cutsfor binned momenta.Fig. 4.10 shows the muon acceptance in terms of binned momenta. It can beseen that the acceptance is relatively constant over the whole momentum region. Alikelihood requirement of 0.9 was chosen for the analysis which results in a muonacceptance ofrCaloPID = 8.39+0.32−0.31×10−4 @99%CL4.3.3 Missing Mass RequirementThe missing mass requirement for the signal region is defined as 0.014GeV 2 <m2miss < 0.022GeV2. With this an additional contribution to the muon rejection is31being made. Fig 4.11 shows the missing mass contribution for the pion as well asthe muon sample.Figure 4.11: Missing mass distribution of the pion and muon sample andthe missing mass requirement of the signal region with correspondingmuon acceptance.Three decay channels can be identified in the missing mass spectrum. TheK+ → µ+ + νµ lies to the left, then there is the peak of K+ → pi+ + pi0 that weare interested in and K+ → pi+ +pi+ +pi− further to the right. One can see thatonly a small fraction of the muon sample leaks into the signal region. This smallshoulder of the K+→ µ++νµ is due to the radiative component of said decay. Oris a result of a miss-reconstruction of the tracks by assigning the wrong kaon to thewrong decay. That fraction of the decay results in a muon acceptance in the signalregion ofrmms = 5.66+2.41−1.85×10−6 @99%CLOne can see that this is by far the most effective way in excluding muons fromthe signal region. As there is also the K+ → pi+ + pi+ + pi− decay in the pionsample there is no point in examining the pion acceptance for the missing mass32requirement. As we are only interested of the fraction of the K+→ pi++pi0 decaywhich is being lost. But as can be seen from the graph, most of that decay is withinthe missing mass window. As there are only a few muons remaining after themissing mass requirement a momentum binned analysis, as done for the Calo PIDand the RICH, can not be conducted. To get an idea of the momentum dependenceof the missing mass requirement one can study the mmiss-momentum distributionof the muons shown in Fig. 4.12.Figure 4.12: Missing mass vs momentum for the muon sample.It can be observed that with increasing momentum the missing mass also in-creases. Therefore there is a higher probability for high momentum muons to endup in the signal region. Hence rmms is expected to rise with larger momenta.4.3.4 Muon Veto DetectorsSince the muon sample was generated from requiring hits in the MUV3 the muonacceptance of the muon veto detectors can not be determined from the sample.Therefore the muon acceptance is taken from [7]. Fig. 4.13 shows the muon iden-tification efficiency of the MUV3.33Figure 4.13: Muon identification of the MUV3 detector for different mo-menta by E. Cortina Gil et al. [7] licensed by CC BY 3.0.Over all momenta this results in a muon identification efficiency of 99.5 %.The muon acceptance is thereforerMUV3 = 5×10−34.3.5 Combined Muon AcceptanceFor the actual analysis all these constituents will be applied simultaneously. Byassuming that they are all independent and therefore orthogonal they can simplybe multiplied in order to get the combined muon acceptance.rcombined = rmms ∗ rRICH ∗ rCaloPID ∗ rMUV3 ≈ 10−13The muon sample provided, with around 8× 105 muons, was not large enough todo any sort of hypothesis testing or analysis of correlations. So the question onhow independent those 4 constituents truly are remains unanswered. Especially as34the missing mass requirement, the Calo PID and the RICH all use the momentummeasurement of the charged particle, there are some correlations to be expected.One can get a feeling of the magnitude of these correlations for the Calo PID andthe RICH by applying both likelihood cut simultaneously. Doing so results in amuon acceptance ofrCaloPID+RICH = 9.06+11.98−6.14 ×10−6 @99%CLSo for these two the assumption of the correlation being small or uncorrelated doesnot seem too far fetched. As for the missing mass requirement no such statementcan be made as requiring both the missing mass requirement as well as one of theother constituents does not leave enough muons to derive a sensible acceptance.But an argument can be made by looking at the dependence of the acceptance onmomentum. For the Calo PID the acceptance is relatively flat over the momentumrange of the analysis. As for the missing mass requirement and the RICH themuon acceptance rises for larger momenta. This could be a indication of a possiblecorrelation between the RICH and the missing mass requirement.But even if there is some minor correlation between the rejection criteria, theacceptance of muons will still be orders of magnitude away from the expectedsingle event sensitivity, expected to be around 10−9 at best. Therefore a muoncontamination of the signal region can be ruled out.35Chapter 5ConclusionThe goal of the pi0 → νν¯ analysis is to study the rare decay of a pion into neu-trino and antineutrino and possibly put a new upper limit on the branching ratio ofthis decay. As this decay is forbidden if neutrinos are massless new insights couldbe obtained on neutrino masses based on a direct measurement of the branchingratio. A K+→ pi+pi0 sample can be extracted from NA62’s 2016 data set. Fromthere on the further decay of the pi0 can be studied. From the number of observedpi0 particles an upper limit on the pi0 → νν¯ branching ratio can be derived sinceneutrinos are possible candidates of those non observable particles. NA62 uses atrigger and a filter in order to store only the decays of interest and therefore savestorage. So those decays have to be scaled back by the combined trigger and filterefficiency. After some variations in the beginning (runs 6300-6350) the trigger effi-ciency maintains a value of around 0.1. Those changes in the beginning were prob-ably caused by a change in the definition of the trigger. Consulting the logs revealedthat NA62 was still applying some changes to the calorimetric trigger at that time.In the combined trigger and filter efficiency those runs don’t seem to have a higherefficiency. Even though the trigger efficiency will not be used in the main analysisit is still an essential part of the experiment that needs to be studied. The combinedtrigger and filter efficiency was found to be f = 1.507+0.117−0.108×10−4 @99%CL forall runs combined. A Monte Carlo simulation was conducted in order to confirmthat the combined trigger and filter efficiency follows a binomial distribution withp = 1.507× 10−4. And therefore verify that the filter was working at least most36of the time. A study of a possible muon contamination of the signal region wasconducted. The combined muon acceptance of the RICH, Calo PID, missing massrequirement of the signal region and the MUV was found to be ≈ 10−13 assumingthat those constituents are independent. Minor correlations between these compo-nents could not be ruled out. But even with minor correlations the muon acceptancewould still be orders of magnitude away from the expected single event sensitivityof 10−9 at best. Therefore a muon contamination of the signal region can be ruledout.37Bibliography[1] Super Proton Synchrotron marks its 25th birthday. CERN Courier, 41(6):24–26, Jul 2001. URL http://cds.cern.ch/record/1733215.[2] Artamonov et al. Study of the decay K+→ pi+νν in the momentum region140 < Ppi < 199 MeV/c. Phys. Rev. D, 79:092004, May 2009.doi:10.1103/PhysRevD.79.092004. URLhttps://link.aps.org/doi/10.1103/PhysRevD.79.092004.[3] R. Barate et al. An Upper limit on the tau-neutrino mass from three-prongand five-prong tau decays. Eur. Phys. J., C2:395–406, 1998.doi:10.1007/s100520050149.[4] G. E. P. Box, W. G. Hunter, J. S. Hunter, and W. G. Hunter. Statistics forExperimenters: An Introduction to Design, Data Analysis, and ModelBuilding. John Wiley & Sons, June 1978. ISBN 0471093157. URLhttp://www.worldcat.org/isbn/0471093157.[5] A. Ceccucci et al. Proposal to measure the rare decay K+→ pi+νν¯ at theCERN SPS. Technical Report CERN-SPSC-2005-013. SPSC-P-326, CERN,Geneva, Apr 2005. URL https://cds.cern.ch/record/832885.[6] C. J. CLOPPER and E. S. PEARSON. THE USE OF CONFIDENCE ORFIDUCIAL LIMITS ILLUSTRATED IN THE CASE OF THE BINOMIAL.Biometrika, 26(4):404–413, 12 1934. ISSN 0006-3444.doi:10.1093/biomet/26.4.404. URL https://doi.org/10.1093/biomet/26.4.404.[7] E. Cortina Gil et al. The Beam and detector of the NA62 experiment atCERN. JINST, 12(05):P05025, 2017.doi:10.1088/1748-0221/12/05/P05025.[8] Y. Fukuda et al. Evidence for oscillation of atmospheric neutrinos. Phys.Rev. Lett., 81:1562–1567, 1998. doi:10.1103/PhysRevLett.81.1562.38[9] D. J. Griffiths. Introduction to elementary particles; 2nd rev. version.Physics textbook. Wiley, New York, NY, 2008. URLhttps://cds.cern.ch/record/111880.[10] C. Lefvre. The CERN accelerator complex. Complexe des acclrateurs duCERN. Dec 2008. URL https://cds.cern.ch/record/1260465.[11] D. Meschede. Gerthsen Physik. Springer-Lehrbuch. Springer BerlinHeidelberg, 2015. ISBN 9783662459775. URLhttps://books.google.ca/books?id=qW7dBgAAQBAJ.[12] U. Mueller, J. Engelfried, S. Gerassimov, K. Martens, R. Michaels, H.-W.Siebert, and G. Wlder. Particle identification with the rich detector inexperiment wa89 at cern. Nuclear Instruments and Methods in PhysicsResearch Section A: Accelerators, Spectrometers, Detectors and AssociatedEquipment, 343(1):279 – 283, 1994. ISSN 0168-9002.doi:https://doi.org/10.1016/0168-9002(94)90565-7. URLhttp://www.sciencedirect.com/science/article/pii/0168900294905657.[13] C. Patrignani et al. Review of Particle Physics. Chin. Phys., C40(10):100001, 2016. doi:10.1088/1674-1137/40/10/100001.[14] A. V. Artamonov et al. Upper limit on the branching ratio for the decaypi0→ νν¯ . Physical Review D, 72:91102, 10 2005.doi:10.1103/PhysRevD.72.091102.[15] J. W. von Goethe. Johann Wolfgang Goethe ’Faust’, Der Tragdie Erster Teil.Erluterungen und Dokumente. Reclam, Ditzingen, 2001.39Appendix ASupporting MaterialsA.1 Trigger EfficiencySome cases for which suspicious values for the trigger efficiency or χ2ν were ob-tained will be discussed. An example where a suspicious value for the trigger effi-ciency was obtained is shown in Fig. A.1, it can be seen that there are clearly tworegions in can be seen in the distribution of trigger efficiency/burst. This might bedue to a malfunction of one of the detectors. Therefore more KPi2 were acceptedthan designated. This run was excluded from the analysis.40Figure A.1: Trigger efficiency per burst for run 6725A less drastic case of the same issue can be seen in Fig. A.2. Here only afew of the burst have a different trigger efficiency. That this is not an effect oflow statistics can be seen from Fig. A.3, these higher values of trigger efficienciesalso occur for larger bursts. As this run doesn’t appear to be problematic for thecombined trigger and filter efficiency it was kept in the analysis. The additionalKPi2 passing the trigger were most likely caught by the filter.41Figure A.2: Trigger efficiency per burst and Gaussian fit for run 6356Figure A.3: Trigger efficiency per burst vs the number of KPi2 per burst forrun 635642A interesting case is run 6668, shown in Fig. A.4 here the distribution is nota Gaussian distribution. This is not an effect of low statistics, as can be seen fromFig. A.5. A malfunction of the detectors or the analysis software might have causedthis.Figure A.4: Trigger efficiency per burst and Gaussian fit for run 635643Figure A.5: Trigger efficiency per burst vs the number of KPi2 per burst forrun 6668In Fig. 4.4 two outliers can be seen apart from the runs in the beginning, thoseare shown in Fig. A.4 and A.5. They appear to be Gaussian like. The large χ2ν infor run 6483 might just be an effect of the degrees of freedom. A malfunction ofthe detectors or the analysis software might be the cause for these outliers.44Figure A.6: Trigger efficiency per burst and Gaussian fit for run 6483Figure A.7: Trigger efficiency per burst and Gaussian fit for run 658945A.2 Filter EfficiencyThe filter efficiencies not shown in the main part of the thesis are shown in Fig.A.8 and A.9.Figure A.8: Filter efficiencies for the runs 6380 to 6540. The error bars cor-respond to 99% CL pearson.46Figure A.9: Filter efficiencies for the runs 6540 to 6700. The error bars cor-respond to 99% CL pearson.47(a) n = 2331 (b) n = 8929(c) n = 16377 (d) n = 55310(e) n = 91611 (f) n = 231678Figure A.10: Monte Carlo simulation of the distribution of filter efficienciesf = k/n, where k is assumed to follow a binomial distribution, withprobability p = 1.507× 10−4 and n is the number of trials. 10000samples were produced for each run.48

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