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Michel electrons analysis in the fine-grained detectors for T2K Kim, Jiae 2011-12-09

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Michel Electrons Analysis in the Fine-Grained Detectors for T2K by Jiae Kim B.Sc., The Yonsei University, 2008 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES (Physics) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) December 2011 c Jiae Kim 2011Abstract Over the decades, neutrino physics has advanced remarkably. Con rmation of neutrino oscillation is one of the important results. It indicates that neutrinos have non-zero mass and  avor mixing. T2K is an experiment designed to observe neutrino oscillations. It is an accelerator-based experiment with a baseline of 295 km across Japan from Tokai to Kamioka. The accelerator and the near detector are at Tokai and the far detector is at Kamioka. The near detector characterizes neutrino interactions in the absence of oscillation e ects. Fine-Grained Detectors (FGDs) are a part of the near detector, which provide target mass and track particles emerging from neutrino interactions occurring in the detector. The primary neutrino interaction channel mode of interest is the charged- current quasi-elastic (CCQE) interaction. In CCQE interactions, a charged- lepton and a proton are in the  nal state. The neutrino energy is recon- structed and its  avor is identi ed by the charged lepton. Other, non-CCQE neutrino interactions have another particles in the  nal state such as pions. The pions may stop in an FGD and decay to produce muons, which in turn stop and decay to produce electrons. The electrons from muon decay at rest are called Michel electrons. Michel electrons are a powerful tool to distinguish CCQE and non-CCQE interactions. This thesis describes the studies of Michel electron activity in the near de- tector using cosmic rays. In Monte Carlo simulation studies, the Michel elec- tron detection e ciency is 0.642 0.012, whereas in data, it is 0.593 0.003. The di erence of the data and the Monte Carlo is 0.087 0.012. iiTable of Contents Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi 1 Neutrino Physics . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 In the Standard Model . . . . . . . . . . . . . . . . . . . . . 3 1.2.1 Neutrino Mass . . . . . . . . . . . . . . . . . . . . . . 3 1.2.2 Neutrino Interactions . . . . . . . . . . . . . . . . . . 4 1.3 Neutrino Oscillation . . . . . . . . . . . . . . . . . . . . . . . 7 1.3.1 Evidence of the Neutrino Oscillation . . . . . . . . . . 7 1.3.2 Oscillation Probability . . . . . . . . . . . . . . . . . 11 1.3.3 A Review of Experiments . . . . . . . . . . . . . . . . 14 2 T2K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.1 Measurement Theory . . . . . . . . . . . . . . . . . . . . . . 19 2.1.1 O -Axis Con guration . . . . . . . . . . . . . . . . . 20 2.2 Beamline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.3 The Super-Kamiokande Detector . . . . . . . . . . . . . . . . 25 2.4 The Near Detectors . . . . . . . . . . . . . . . . . . . . . . . 27 2.4.1 The INGRID Detector . . . . . . . . . . . . . . . . . 29 2.4.2 ND280 . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.5 FGD Detail . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2.5.1 Water Module . . . . . . . . . . . . . . . . . . . . . . 39 2.5.2 Scintillator Module . . . . . . . . . . . . . . . . . . . 39 2.5.3 Electronics . . . . . . . . . . . . . . . . . . . . . . . . 43 iiiTable of Contents 3 ND280 Software . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.1 Overviews of ND280 Software . . . . . . . . . . . . . . . . . 47 3.2 Monte Carlo Simulation . . . . . . . . . . . . . . . . . . . . . 48 3.3 oaEvent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 3.4 Example Event Displays . . . . . . . . . . . . . . . . . . . . 50 3.5 FGD Software Packages . . . . . . . . . . . . . . . . . . . . . 51 3.5.1 FGD Time Binning . . . . . . . . . . . . . . . . . . . 53 3.5.2 FGD Reconstruction . . . . . . . . . . . . . . . . . . 54 4 Cosmic Muon Studies . . . . . . . . . . . . . . . . . . . . . . . 56 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 4.1.1 Michel Electron Tagging . . . . . . . . . . . . . . . . 56 4.1.2 Cosmic Rays . . . . . . . . . . . . . . . . . . . . . . . 57 4.2 Data Set Description . . . . . . . . . . . . . . . . . . . . . . 58 4.3 Direction Convention . . . . . . . . . . . . . . . . . . . . . . 58 4.4 Example Cosmic Event . . . . . . . . . . . . . . . . . . . . . 59 4.5 Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . 61 4.5.1 Select a Clean Sample of Stopping Muons . . . . . . 61 4.5.2 Select  with a Michel Electron . . . . . . . . . . . . 78 4.6  Lifetime Plots . . . . . . . . . . . . . . . . . . . . . . . . . 78 4.7 Summary of Selection Cuts . . . . . . . . . . . . . . . . . . . 79 4.8 Data and MC Simulation Comparison . . . . . . . . . . . . . 81 4.9 Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 4.10 Implications for the Neutrino Interactions . . . . . . . . . . . 85 4.10.1 The Inclusive CC Selection . . . . . . . . . . . . . . . 87 4.10.2 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 88 5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 ivList of Tables 1.1 List of the CC and NC neutrino interactions . . . . . . . . . . 5 1.2 The estimated solar neutrino  uxes and cross sections for the reaction 37Cl( ; e ) 37Ar. . . . . . . . . . . . . . . . . . . . . 7 1.3 List of neutrino experiments. L is distance between the  beam and the far detector, called baseline. . . . . . . . . . . . 15 1.4 Measured solar neutrino parameters. . . . . . . . . . . . . . . 16 1.5 Measured atmospheric neutrino parameters. . . . . . . . . . . 16 1.6  13 measurements . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.1 List of electronics . . . . . . . . . . . . . . . . . . . . . . . . . 46 4.1 FGD1 true edge, the  ducial volume of FGD1 and the posi- tion of the red box . . . . . . . . . . . . . . . . . . . . . . . . 63 4.2   lifetime and capture rates in di erent materials . . . . . . 79 4.3 The numbers of events passing single cut. The fraction takes a ratio of the number of events passing a cut to the number events passing the previous cut. . . . . . . . . . . . . . . . . . 82 4.4 The inclusive CC   selection result . . . . . . . . . . . . . . 88 vList of Figures 1.1 CC and NC Feynman diagrams at tree level. . . . . . . . . . 5 1.2 Cross sections for di erent neutrino interactions . . . . . . . . 6 1.3 Solar neutrino  ux at various energy range for di erent reactions 9 1.4 Solar neutrino result . . . . . . . . . . . . . . . . . . . . . . . 10 1.5 Two di erent mass hierarchy . . . . . . . . . . . . . . . . . . 13 1.6 Allowed neutrino mass and mixing region for di erent neu- trino experiments. . . . . . . . . . . . . . . . . . . . . . . . . 17 2.1 Overview of the T2K experiment across Japan. . . . . . . . . 18 2.2 Neutrino  ux for three di erent o -axis angles and corre- sponding oscillation probability. . . . . . . . . . . . . . . . . . 21 2.3 Map of J-PARC facilities. . . . . . . . . . . . . . . . . . . . . 22 2.4 History of protons on target . . . . . . . . . . . . . . . . . . . 23 2.5 The neutrino  uxes at ND280 for di erent parent decay modes 24 2.6 Simpli ed schematic of the T2K beamline . . . . . . . . . . . 25 2.7 Outline of the Super-Kamiokande detectors . . . . . . . . . . 26 2.8 SK event reconstruction . . . . . . . . . . . . . . . . . . . . . 27 2.9 Example event displays at SK . . . . . . . . . . . . . . . . . . 28 2.10 The outline of installation of all near detectors . . . . . . . . 29 2.11 The overview of INGRID . . . . . . . . . . . . . . . . . . . . 30 2.12 A single INGRID module . . . . . . . . . . . . . . . . . . . . 31 2.13 All elements in ND280 . . . . . . . . . . . . . . . . . . . . . . 32 2.14 A single TPC . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.15 Cross section of a single scintillator bar for FGDs . . . . . . . 34 2.16 A photo of an FGD . . . . . . . . . . . . . . . . . . . . . . . . 35 2.17 The scintillator bars for P0D . . . . . . . . . . . . . . . . . . 36 2.18 Sliced view of a SMRD slab . . . . . . . . . . . . . . . . . . . 37 2.19 Wave-length shifting  ber . . . . . . . . . . . . . . . . . . . . 40 2.20 A photo of the MPPCs with the WLS  bers . . . . . . . . . . 41 2.21 The MPPC sensitivity as a function of wavelength . . . . . . 42 2.22 The MPPC gain . . . . . . . . . . . . . . . . . . . . . . . . . 42 viList of Figures 2.23 FGD Electronics . . . . . . . . . . . . . . . . . . . . . . . . . 44 3.1 The ND280 Software . . . . . . . . . . . . . . . . . . . . . . . 47 3.2 Sand muons going through all subdetectors. . . . . . . . . . . 51 3.3 Cosmic track reconstructed across all detectors . . . . . . . . 51 3.4 Neutrino event in P0D sending single negative track into TPC1/FGD1/TPC2. . . . . . . . . . . . . . . . . . . . . . . . 52 3.5 Clean CC interaction in FGD1 . . . . . . . . . . . . . . . . . 52 3.6 An example waveform of an FGD MPPC . . . . . . . . . . . 53 3.7 Time binning schematic . . . . . . . . . . . . . . . . . . . . . 54 4.1 Charge distribution of all delayed time bins . . . . . . . . . . 57 4.2 The topology of the FGD cosmic trigger primitives . . . . . . 59 4.3 A going-through cosmic ray. . . . . . . . . . . . . . . . . . . . 60 4.4 A going-through cosmic ray with a large angle . . . . . . . . 60 4.5 A stopping cosmic ray in FGD1 . . . . . . . . . . . . . . . . . 61 4.6 Stopping selection geometry . . . . . . . . . . . . . . . . . . . 62 4.7 The distribution of the minimum z position of the  rst time bin in the FGD  ducial volume . . . . . . . . . . . . . . . . . 64 4.8 Example cosmic tracks . . . . . . . . . . . . . . . . . . . . . . 65 4.9 Charge distribution of the  rst delayed time bin for all stop- ping tracks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 4.10 TPC2 momentum distribution after the geometry cut. . . . . 66 4.11 Charge distribution of the  rst delayed time bin after TPC2 quality cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 4.12 CT versus momentum distribution . . . . . . . . . . . . . . . 68 4.13 Momentum distribution of the stopping events . . . . . . . . 69 4.14 Muon pull of the stopping events . . . . . . . . . . . . . . . . 70 4.15 Electron pull of the stopping events . . . . . . . . . . . . . . . 70 4.16 Muon pull versus electron pull for the stopping events of the MC simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . 71 4.17 Muon pull versus electron pull for the stopping events of data. 72 4.18 Pull versus Pulle for the stopping tracks with momentum lower than 120 MeV/c . . . . . . . . . . . . . . . . . . . . . . 72 4.19 Pull versus Pulle for the stopping tracks with momentum higher than 120 MeV/c . . . . . . . . . . . . . . . . . . . . . 73 4.20 De nition of the track length in FGD1 . . . . . . . . . . . . . 74 4.21 Track length in FGD1 versus momentum in the MC simulation 75 4.22 Track length in FGD1 versus momentum in the data . . . . . 75 viiList of Figures 4.23 After the track length cut, muon pull of the stopping events for the MC simulation (blue triangles) and the data (black circles). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 4.24 After the track length cut, electron pull of the stopping events for the MC simulation (blue triangles) and the data (black circles). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 4.25 After the track length cut, muon pull versus electron pull for the stopping events of the MC simulation. . . . . . . . . . . . 77 4.26 After the track length cut, muon pull versus electron pull for the stopping events of data. . . . . . . . . . . . . . . . . . . . 78 4.27 Bin time di erence for stopping  with a Michel electron (the MC simulation) . . . . . . . . . . . . . . . . . . . . . . . . . . 80 4.28 Bin time di erence for stopping  with a Michel electron (the data) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 4.29 The distributions of the minimum z position of the  rst time bin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 4.30 The fractional number of events after the geometry cut . . . . 83 4.31 The fractional number of events after the TPC cut . . . . . . 84 4.32 The fractional number of events after the muon selection cuts 85 4.33 The  nal e ciency and the corresponding z distribution . . . 86 4.34 Momentum distribution of the highest momentum tracks for negative (left) and positive (right) tracks . . . . . . . . . . . . 87 4.35 An example of CCQE interactions with two tracks . . . . . . 89 viiiChapter 1 Neutrino Physics 1.1 History The neutrino, named by Enrico Fermi, means \a little neutral object" [1]. This subatomic fundamental particle was postulated theoretically  rst by Pauli as one of solutions to missing energy in beta decays. At  rst, the beta decay process was thought to be the decay of a nucleus to another nucleus by emitting a single electron: N(Z;A)! N 0 (Z + 1; A) + e (1.1) where N and N 0 are two di erent nuclei. By the energy conservation law, the released electron energy would have a single energy equal to Ee = m2N  m 2 N 0 +m2e 2mN (1.2) The electron energy should be  xed when the three masses are speci ed. But the observed spectrum was continuous, not constant, and not even discrete [2]. To make the decay satisfy the conservation laws and solve this spectrum problem, there should exist another undetected particle. In 1956, the hypothesis was con rmed and the existence of neutrinos was proved by Reines and Cowan. It was one of six neutrinos and anti-neutrinos, the electron anti-neutrino ( e) [3]. They used the inverse beta decay in their experiment:  e + p! e + + n (1.3) The anti-neutrinos in the initial state were nuclear  ssion products that occurred in the nuclear detector. The detector had a target of water and CdCl2. These anti-neutrino interactions were detected by identifying pho- tons from the annihilation of the emitted positrons and a delayed photon from the capture of the neutrons. 11.1. History Since then, physicists tried to explain why some reactions occur, while others do not. For example,  ! e +  had never been observed. Feinberg pointed out that the branching ratio ( ! e+  )=( ! e+  +  ) should be of order 10 4, unless the neutrinos associated with muons are di erent from those associated with electrons [4]. However, the limit on the branching ratio was much less than this, indicating that there is something wrong. This is called the two-neutrino hypothesis, and it was tested in 1962 by L. Lederman, M. Schwartz and J. Steinberger. They inserted a target in a proton beam to produce charged pions. The pions decay to muons and neutrinos in  ight:  + !  + +  (1.4)   !   +  (1.5) Using about 1014 anti-neutrinos from   decay, the physicists investi- gated two reactions:  + p+ !  + + n (1.6)  + p+ ! e+ + n (1.7) If only one type of neutrino exists, the two reactions should happen equally. But they did not detect electrons. The absence of electron events suggested the existence of another type of neutrino, the muon neutrino (  ) [5]. In the 1970s, the existence of the third lepton  was con rmed and physicists inferred the existence of its associated neutrino, named the tau neutrino (  ). This last neutrino was observed  nally in 2000 by DONUT experiment [6]. Now, the lepton families have three charged leptons, three charged anti-leptons, three neutrinos, and three anti-neutrinos. As the name suggests, neutrinos are extremely light. Until fairly re- cently, it was assumed that the neutrinos are massless. However, a series of recent experiments have shown that neutrinos have non-zero mass. The  rst indication of neutrino mass starts from the solar neutrino problem. The neutrinos produced in the Sun are electron neutrinos. But the  ux of  e from the Sun observed on Earth was less than it was predicted to be. In 1968, one physicist, B. Pontecorvo, had a new theory. He said that the electron neutrinos produced in Sun converted in traveling to Earth to a di erent species [7]. Now we call this \neutrino oscillation". 21.2. In the Standard Model Neutrino oscillation is a consequence of the non-zero neutrino masses and neutrino mixing. The  avor eigenstates , which are  e,   and   , are superpositions of the mass eigenstates, which are energy eigenstates. This causes  avor mixing. This is described in more detail in Section 1.3.2. 1.2 In the Standard Model In the Standard Model, there are three types of neutrino. They do not have charge, so they cannot feel the electromagnetic  eld. They do not have color, so they cannot feel the strong  eld either. They only interact via the weak interactions. In the weak interactions, only left-handed neutrinos can be coupled to the weak interaction gauge bosons. While other fermions can be both right-handed and left-handed via other interactions, neutrinos only can interact as left-handed particles [8]. 1.2.1 Neutrino Mass The Standard Model Lagrangian consists of three parts: LSM = Lkinetic +LHiggs +LY ukawa (1.8) LY ukawa is the interaction of the Higgs scalar  elds to the Dirac fermion  elds. Generally, the Yukawa couplings are not diagonal. Since the discus- sion is focused only on the lepton sector, consider the lepton component of the Yukawa couplings:  LY ukawa = Y l ijE Li lRj + h:c: (1.9) where L=R denote left-handed and right-handed and i/j denote di erent mass eigenstates. In the language of  eld theory, leptons are expressed by a doublet con- taining the left handed charged lepton and its corresponding neutrino and a singlet containing the right handed component of the charged lepton: EL =  lL  L ! ; lR Here Y in Equation 1.9 is a non-diagonal coe cient matrix and  is the Higgs  eld. After spontaneous symmetry breaking when the Higgs  eld obtains a vacuum expectation value v, the Higgs  eld is rewritten as 31.2. In the Standard Model  = 1 p 2 (v + h(x)) (1.10) where v is a constant and h(x) describes the  uctuations of the  eld about the vacuum expectation value. Then, the Yukawa couplings break into one with and one without couplings to h(x):  LY ukawa = vY l ijlLilRj + h:c:+ (couplings to h(x)) = (ml)ijlLilRj + h:c:+ (couplings to h(x)) (1.11) It is assumed that there are no right-handed neutrinos, since they would not interact in the Standard Model. A mass term requires left and right- handed components of the  led. Therefore, there are no neutrino mass terms. This is the reason why neutrinos are considered massless in the Stan- dard Model. Generally, the mass matrix is non-diagonal. But it is easy to diagonalize the matrix by introducing transformation matrices, VlL and V y lR. Since right-handed neutrinos are not included in this theory, we have the freedom of choosing the transformation matrix V for neutrinos such that Vl = V y . That means the couplings of leptons and weak interaction gauge bosons are isolated for each  avor after transformations. This is why  avor mixing is forbidden in lepton sector when the neutrino is massless. Despite the masslessness of neutrinos in the Standard Model, the mass of neutrinos have been questioned since Fermi developed his theory of neutri- nos. Several experiments have attempted to measure the mass of neutrinos directly via beta decays, pion decays, and tau lepton decays. However, they did not  nd any evidence of neutrino mass. Another way to probe neutrino mass is to search for neutrino oscillations. In 1957, B. Pontecorvo proposed the possibility of oscillations between neutrinos and anti-neutrinos [9]. 1.2.2 Neutrino Interactions Since neutrinos have no charge, they cannot be seen via electromagnetic in- teractions used in current detector technologies. Generally, electromagnetic interactions are required to detect particles. They can only be inferred by seeing other particles which emerge from neutrino interactions that interact electromagnetically or strongly. Neutrino interactions only occur through weak gauge bosons. There are two types of weak interactions, Charged- Current (CC) interactions and Neutral-Current (NC) interactions. The ba- sic Feynman diagrams at tree level are shown in Figure 1.1. 41.2. In the Standard Model Figure 1.1: CC and NC Feynman diagrams at tree level. Channels CC quasi-elastic  + n! l + p CC resonant pion  + n! l + n+  + CC coherent pion  +A! l +A+  + NC resonant pion  + n!  + n+  0 NC coherent pion  +A!  +A+  0 Table 1.1: List of the CC and NC neutrino interactions. The top channels are CC interactions in which a charged lepton emerges. The bottom ones are NC interactions in which a neutrino emerges. A denotes a nucleus. The outgoing charged leptons from CC channels must have the same  avor as the incoming neutrinos. That is, the  avor of the incoming  can be identi ed by the outgoing charged lepton. In the same manner, the  avor of outgoing neutrinos and incoming neutrinos in NC interactions must be identical. Then, in the CC channels, the  avor of the neutrino can be inferred by charged lepton. For example, if   is detected in the  nal state, the incoming neutrino is a   . However, in the NC channels, we cannot know the neutrino  avors because there is no charged lepton in the  nal state. Some example interactions for both CC and NC channels are shown in Table 1.1. The examples in the table are channels that are typically observed in the T2K experiment, where the neutrino  ux is peaked at 0.6 GeV. Figure 1.2 shows the neutrino interaction cross sections as a function of neutrino energy [10]. At around 0.6 GeV, the cross section of charged- current quasi-elastic (CCQE) interactions is the highest among CC interac- 51.2. In the Standard Model Figure 1.2: Cross sections for di erent neutrino interactions at various en- ergy range [10]. tions. CCQE interactions are the main signal in T2K neutrino oscillation measurement. They are chosen because the neutrino energy E can be well reconstructed by two-body kinematics. In CCQE ( + n! l + p ), the en- ergy of the neutrino can be approximately calculated using the energy and direction of the  nal state lepton by Erec  m2p  (mn  ml) 2 2(mn  El + q E2l  m 2 l cos  l) (1.12) where n denotes the neutron, p denotes the proton, and l denotes the charged lepton after the interaction. A smaller number of single pion interactions occur as well. In these cases, since there are three particles in the  nal state, the assumed kinematics is incorrect. Thus, the neutrino energy cannot be well estimated via this formula. The hardest cases are the neutral current channels. Since there is no outgoing charged lepton, we will not know the neutrino  avors. 61.3. Neutrino Oscillation Neutrino Sources Cross Section Neutrino Flux at Earth (cm2) (cm 2sec 1) H + H + e ! D +  1:72 10 45 1:7 108 7Be decay 2:9 10 46 3:9 109 8B decay 1:35 10 42 1:3 107 13N decay 2:1 10 46 1:0 109 16O decay 7:8 10 46 1:0 109 Table 1.2: The estimated solar neutrino  uxes and cross sections for the reaction 37Cl( ; e ) 37Ar. 1.3 Neutrino Oscillation 1.3.1 Evidence of the Neutrino Oscillation In the 1960s, J. N. Bahcall did most of the calculations detailing the produc- tion and spectra of neutrinos produced in solar fusion processes [11]. Table 1.2 shows cross sections and  ux for several sources. At around the same time, R. Davis and colleagues detected solar neutrinos and measured their  ux based on the neutrino capture reaction 37Cl( ; e )37Ar. They concluded that the neutrino  ux from 8B decay in the Sun was equal to or less than 2 106 cm 2sec 1 [12], while Bahcall’s prediction was (1:3 0:6) 107 [13]. This was the beginning of the solar neutrino problem. Solar Neutrino Problem The Sun is a source of neutrinos via fusion processes such as [14] p+ p! 2H + e+ +  e (1.13) p+ e +! 2H +  e (1.14) Figure 1.3 shows the neutrino  ux at the Earth for di erent reactions pro- ducing neutrinos [15]. The Homestake experiment was the  rst to observe the solar neutrino  ux at the Earth form the Sun [16]. They observed the solar neutrinos from the decay 8B!8 Be + e+ +  e (1.15) 71.3. Neutrino Oscillation and compared the result to the prediction that was made by Bahcall in the Standard Solar Model. The SSM is a theoretical framework for understand- ing the physics of the Sun. The model treats the Sun as a spherical bulb with four basic assumptions [17]:  The Sun is in hydrostatic equilibrium. In other words, gravity and pressure in the Sun are locally balanced.  Energy in the Sun is transferred via radiation, conduction, convection, and neutrino losses.  The only energy sources are thermonuclear reactions.  The Sun was initially homogeneous in its distribution. The measured neutrino  ux traveling to the Earth was less than the prediction by the model. This is the solar neutrino problem [18]. After the Homestake experiment, the Kamiokande experiment, using a large water  Cerenkov detector, published a result consistent with the Home- stake experiment [19]. The solar neutrino problem was  nally solved by SNO and Super Kamiokande (higher statistics than Kamiokande) [20]. Whereas the Homestake experiment used radiochemical detectors, SNO and Super Kamiokande used water  Cerenkov detectors. SNO used heavy water (D2O) that allowed sensitivity of NC processes whereas SK used normal water (H2O). SNO observed 8B neutrinos via three di erent interaction channels: CC interactions, NC interactions and elastic scatterings  e + d! e  + p+ p (1.16)   + d!   + p+ n (1.17)   + e  !   + e  (1.18) where d denotes a deuteron. Figure 1.4 is solar  ux result from SNO [21]. Without oscillations, all measured neutrinos would be electron neutrinos. However, by measuring the neutrino  ux via CC, NC and elastic scattering channels SNO found that there was a de cit of electron neutrinos that ap- peared as other neutrino  avors. In the  e transition to   or   , the result from NC channels are independent of neutrino oscillation, so it agrees with the 8B solar neutrino  ux predicted by the SSM [15]. The initial CC result 81.3. Neutrino Oscillation Figure 1.3: Solar neutrino  ux at various energy range for di erent inter- actions [15]. The horizontal axis is the  e  ux and the vertical axis is the   (  )  ux. The dotted lines are limits from the SSM prediction. The col- ored bands represent the measured  uxes via di erent interactions at 68% C.L. and the solid-lined contours are the 68%, 95% and 99% joint probability for  e and   ( ). from SNO combined with the result from the Super-Kamiokande provided evidence for neutrino oscillation of solar neutrinos [22]. Atmospheric Neutrino Problem Primary cosmic rays entering the Earth’s atmosphere are mostly made of protons (up to 90 %). When they enter the atmosphere, hadronic interac- tions produce hadrons such as pions and kaons which then decay to produce neutrinos. The pions decay into  and   , then subsequently the  decay into e,  e, and   . These neutrinos are called atmospheric neutrinos. Since the dominant interaction producing neutrinos is the decay chain  + !  + +   and subsequently  + ! e+ +   +  e [23], atmospheric neutrinos are electron and muon neutrinos, but mostly   : 91.3. Neutrino Oscillation Figure 1.4: Solar neutrino result. The x axis is the  ux of  e and the y axis is the  ux of   or   from SNO measurements. The red band is from the SNO CC result. The blue is from the SNO NC result and the light green is from the SNO elastic scattering result. The dark green band is from the Super-Kamiokande elastic scattering result. The bands represent the 1 error. The sum of the neutrino  uxes is consistent with the SSM expectation (dashed line) [21].  + !  + +    + ! e+ +   +  e (1.19)   !   +     ! e +   +  e (1.20) While the muon neutrinos and anti-neutrinos are produced during both pion and muon decays, the electron neutrinos are produced only in muon decays. Hence, the amount of   ;   is approximately twice as much as  e. 101.3. Neutrino Oscillation Since cosmic rays come from everywhere, the ratio of    ux and  e  ux would be isotropic without oscillations. But an anisotropic  ux of   was observed by Super-Kamiokande experiment. It is caused by the transition of   to   . (i.e. neutrino oscillation) 1.3.2 Oscillation Probability In 1962, Z. Maki, M. Nakagawa, and S. Sakata formulated a theory for neu- trino  avor oscillation [24], and in 1968, Pontecorvo also developed a theory of neutrino oscillations to explain the solar neutrino problem [7]. If neutri- nos have non-zero and non-degenerate mass and their  avor eigenstates are not identical to their mass eigenstates, then the neutrinos can change their  avor [25]. The neutrino  avor states, j  i, can be written by as a linear combination of mass eigenstates, j ii; i = 1; 2; 3: j  i = X U  ij ii (1.21) where U is a unitary matrix. This mixing matrix is referred to as the PMNS matrix [24], similar to the CKM matrix in the quark sector [26]. There are many ways to parametrize the PMNS matrix. Usually, it is written in the following form: U = 0 B @ c12c13 s12c13 s13e i  s12c23  c12s23s13ei c12c23  s12s23s13ei s23c13 s12s23 c23c13 1 C A where cij = cos  ij ; sij = sin  ij . To see how neutrinos oscillate, we would like to study the time evolu- tion of a neutrino  avor eigenstate. Assume that a neutrino is in a  avor eigenstate, j  i, at t = 0. Then we apply the time evolution operator to the state. Mass eigenstates are also energy eigenstates, so they have a simple time dependence. This gives j  (t)i = e  iHtj  (0)i = X U  ie  i(Eit piL)j i(0)i (1.22) where Ei and pi are the energy and momentum of j ii. The mass eigenstates can be expressed by the  avor eigenstates using the inverse relation: 111.3. Neutrino Oscillation j ii = X Ui j  i (1.23) Substituting Equation 1.23 into Equation 1.22, we get j  (t)i = X Ui e  i(Eit piL)U  ij  i (1.24) Since neutrino masses cannot exceed the upper limit of 1 eV [27] and the typical value of neutrino energies is MeV or greater, they travel close to the speed of light and are relativistic. This allows us to approximate t  L. Moreover, neutrino masses are small enough so that E = q p2i +m 2 i  pi +m2i =2pi. Then, Equation 1.24 can be rewritten as j  (L)i = X Ui e  i(pi+m2i =2pi pi)LU  ij  i = X Ui e  im2iL=2piU  ij  i (1.25) Lastly, we assume the energy are all same, Ei = E: j  (L)i = X U  ie  im2iL=2E j ii = X Ui e  im2iL=2EU  ij  i (1.26) From Equation 1.26, we can get the amplitude of   !   and the probability for the transition from   to   Amp(t) = h  j  (t)i = X Ui e  im2iL=2EU  i (1.27) Prob(  !   ) = jAmp(t)j 2 = j X Ui e  im2iL=2EU  ij 2 (1.28) Following from Equation 1.28, the transition probability from the  avor  to the  avor  after L is P (  !   ) =     4 X Re(U  iU iU jU   j) sin 2  m 2 ijL 4E  2 X i>j Im(U  iU iU jU   j) sin 2  m 2 ijL 2E (1.29) where  m2ij = m 2 i  m 2 j . For oscillation between anti-neutrinos, the prob- ability is similar but with a plus sign for the last term. So far, a total of 7 parameters have been found, three mixing angles, three neutrino masses, 121.3. Neutrino Oscillation and single CP phase. But, by the condition of  m212 +  m 2 13 +  m 2 23 = 0, only two of three masses are actually independent. That is, the total inde- pendent parameters in neutrino oscillations in the case of 3  avors and mass eigenstates is six. The  rst conclusive evidence that neutrinos do oscillate and therefore have to have mass, comes from the Super Kamiokande experiment [28]. They observed a zenith-angle dependence of the rate of muon neutrinos produced in the atmosphere by cosmic rays relative to expectation. Afterwards, the atmospheric neutrino oscillation was con rmed by K2K [29]. The solar neutrino oscillation was con rmed by SNO, the Super Kamiokande, and KamLAND [30]. The results from the experiments are j m231j = 2:40 10  3eV2; m221 = 7:65 10 5eV2 (1.30) j m221j  j m 2 31j (1.31) More detail about these experiments will be discussed in Section 1.3.3. The sign of the solar mass di erence is known. But the sign of the atmospheric mass di erence is unknown. Two ways of arranging the masses, normal (m1 < m2 < m3) and inverted (m3 < m1 < m2) hierarchy, are possible as shown in Figure 1.5. Figure 1.5: Two di erent mass hierarchies. The left is normal hierarchy, and the right is inverted.  1,  2 and  3 are mass eigenstates and colors represent  avor eigenstates. Yellow is  e, red is   and blue is   . If the normal hierarchy is correct, m3 is larger than m1 so that m231 > 0. However, if the inverted hierarchy is correct,  m231 < 0. The neutrino 131.3. Neutrino Oscillation oscillation probability in matter is di erent to the probability in vacuum and the mass hierarchies a ect the oscillation probability in the matter [31]. 1.3.3 A Review of Experiments In the Standard Model, which has three neutrinos, the neutrino mixing is determined by six independent parameters; three mixing angles, one CP vi- olation parameter, and two mass di erence squares. Over the last decade, many experiments have been performed to measure the parameters and understand neutrino oscillations. Currently, we know two mixing angles,  12;  23, limits on  13, the mass splitting,  m221, and the absolute value of the other mass splitting j m232j.  12 and  m 2 21 are solar neutrino param- eters and are sometimes called  sol and  m2sol. Likewise,  23 and  m 2 32 are atmospheric neutrino parameters, and are sometimes called  atm and  m2atm. But, we do not know yet the CP violation parameter,  , the sign of  m2atm, and the last mixing angle  13. Many experiments around the world are investigating neutrino oscillations to improve our knowledge. Neutrino experiments can be categorized by four neutrino sources and two mass di erence regions. The four neutrino sources are solar, atmo- spheric, accelerator, and reactor. Table 1.3 is a summary of recent experiments. Some are no longer in operation, while others are still active and some are under construction. Figure 1.6 also summarizes mass and mixing sensitivity regions of several experiments. SNO, Super-K, Kamiokande, KamLAND and other experiments using solar or reactor neutrinos have produced measurements of  m221;  12. The best- t parameters are  m221 = 7:59 +0:20  0:21  10  5eV2 and tan2  12 = 0:457+0:040 0:029 [10]. Table 1.4 summarizes these results [32]. Meanwhile, Super-K, a large water  Cerenkov detector, measured  m232 and  23. The allowed mass region is between 1:9 10 3 and 3:0 10 3eV2 and sin2 2 23 > 0:90. The K2K experiment in the 1.3 GeV energy range, con rmed these measurements. The best- t parameters are j m232j = 2:8  10  3eV2 and sin2 2 23 = 1:00. MINOS also measured the parameters in atmospheric re- gion. Their best- t values are j m232j = 2:43 10  3eV2 at sin2 2 23 > 0:90. Table 1.5 lists of some important results of atmospheric neutrino parame- ters [33]. 1Daya Bay has two near detectors. These baselines are the distances between a far detector and the two near detectors. 141.3. Neutrino Oscillation Experiment Sources Flavor Detector E L SNO solar   ;e;  Cerenkov 3.5MeV  108km Super-K atmospheric/   ;e;  Cerenkov  1GeV  104km solar KamLAND reactor  e Scintillator 3 MeV 180km CHOOZ reactor  e Scintillator 3 MeV 1 km Double reactor  e Scintillator 3 MeV 1.05 km CHOOZ Daya Bay reactor  e  Cerenkov 3 MeV 1.6 km/ 1.9 km 1 RENO reactor  e Scintillator 3 MeV 1.4 km OPERA accelerator   Scintillator 17 GeV 730 km MINOS accelerator  e;   Scintillator  5GeV 735km MiniBooNE accelerator  e;    Cerenkov 800MeV 540m K2K accelerator   Scintillator, 1GeV 250km  Cerenkov T2K accelerator   Scintillator, 1GeV 300km  Cerenkov Table 1.3: List of neutrino experiments. L is distance between the  beam and the far detector, called baseline. A new generation of neutrino experiments have focused on the mea- surement of the last mixing angle,  13. It can be measured directly us- ing  e oscillation. In the   appearance oscillation, the dominant term is 2 sin2  23 sin2 2 13 and sin2  23 is close to 1. So the measurements on  13 are in terms of 2 sin2  23 sin2 2 13 in the case of   !  e appearance. The  rst experiments searching for  e disappearance was CHOOZ. The experiment was a short baseline (1 km) reactor neutrino experiment and the neutrino energy was around 3 MeV. Since CHOOZ did not see evidence of neutrino oscillations, it set an upper limit of sin2  13 < 0:15. K2K was another experiment looking for  13. However, it used accel- erator with accelerator neutrino beam. The experiment searched for  e appearance signals in   beam. They also set a limit the measurement, sin2 2 13 < 0:26. The summary is on Table 1.6. Recently, MINOS and T2K published new results on  13. The MINOS re- 1The mass region is allowed at sin2 2 23 = 1:00 268% C.L. 151.3. Neutrino Oscillation Data j m221j (eV 2) tan2 2 21 Global 5:89+2:13 2:16  10  5 0:457+0:038 0:041 Global + KamLAND 7:59+0:20 0:21  10  5 0:457+0:040 0:029 Table 1.4: Measured solar neutrino parameters. The  rst row is global- t parameters, and the second row is combined result of global- t and Kam- LAND [32]. Data  m232 (eV 2) sin2 2 23 Super-K 1:9 10 3 <  m2 < 3:0 10 3 > 0:90 K2K 1:9 10 3 <  m2 < 3:5 10 3 1 1:00 MINOS j m2j = (2:43 0:13) 10 3 2 > 0:90 Table 1.5: Measured atmospheric neutrino parameters (90% C.L.) [33]. sults are 2 sin2  23 sin2 2 13 = 0:041 +0:047  0:031 or 2 sin 2  23 sin2 2 13 = 0:079 +0:071  0:053 for normal and inverted mass hierarchy respectively with j m232j = 2:32  10 3 eV2 [34],  23 = 0:785 0:100 [35]. They further report the upper limit on  13, 2 sin2  23 sin2 2 13 < 0:12(0:20) at 90% C.L. for normal(inverted) hierarchy [36]. Meanwhile, T2K  nd 0:03(0:04) < sin2 2 13 < 0:28(0:34) at 90% C.L. for normal(inverted) mass hierarchy with sin2 2 23 = 1:0 and j m223j = 2:4  10  3 eV2 [37]. Because the result depends on the mass hierarchies they publish two di erent results based on normal or inverted hierarchy. Data  13 limit (90% C.L.) CHOOZ sin2 2 13 < 0:15 K2K sin2 2 13 < 0:26 Table 1.6:  13 measurements [33]. 161.3. Neutrino Oscillation Figure 1.6: Allowed neutrino mass and mixing region for di erent neutrino experiments. This  gure is taken from 17Chapter 2 T2K Figure 2.1: Overview of the T2K experiment across Japan. T2K is a \long-baseline"neutrino oscillation experiment from Tokai to Kamioka in Japan. The experiment uses a high intensity proton beam to produce the neutrino beam using the J-PARC accelerator facilities in Tokai. Accelerated protons interact on a target to produce pions. The produced pions decay to  and   in  ight. The neutrinos are measured at the near detector (ND280), located 280 m away from the beam. Measurements at the near detector provide understanding of the neutrino beam and interaction properties in the absence of neutrino oscillation e ects. After that, the neutrino beam travels 295 km to the far detector, the Super-Kamionkande detector (SK) at Kamioka. The neutrinos from the J-PARC beam are mostly muon neutrinos, which typically oscillate to   at SK. However, we cannot identify the   at SK, because it is kinematically forbidden to produce the tau leptons via charged weak interactions. The reason for this is that the tau mass is much larger than our mean neutrino energy, 0.6 GeV. Therefore,   !   oscillations are measured by   disappearance. The measured neutrino events at SK are expected to be reduced by   !   oscillations. Within   disappearance, we make a more precise measurement of the mixing angle  23 and  m232. This is one goal of T2K. On the other hand, if   !  e oscillations occur, more  e are detected at SK. This  e appearance is used to measure the last mixing angle  13. This is the other goal of the experiment. 182.1. Measurement Theory 2.1 Measurement Theory The neutrino transition probabilities of  e appearance and   disappearance in vacuum are P (  !  e)  sin 2 2 13 sin 2  23 sin 2 (  m231L 4E ) (2.1) P (  !   )  1 sin 2 2 23 sin 2 (  m231L 4E ) (2.2) where L is the neutrino path length and E is the neutrino energy. The probability depends on two mixing angles, one of the three mass-squared di erences, and L=E . Reactor- and accelerator-based experiments with a  xed, well-known baseline can make precise measurements of  m2. The neutrino energy can be tuned to choose the L=E that maximizes the oscil- lation probability. For T2K, L is 295 km, which is the distance between Tokai and Kamioka. This is the reason why T2K is called a long-baseline experiment. The dis- tribution of E from the neutrino beam peaks around 0.6 GeV to maximize P (  !  e) and minimize P (  !   ). N obsSK is the number of observed events at SK, and NexpSK is the number of expected events at SK. More precisely, the number of neutrino events at SK is as a function of the reconstructed neutrino energy. It is given as NexpSK (E rec  ;  m 2;  ) = R dE MSK(Erec ; E ) P (E ;  m 2;  ) SK(E ) (E ) SK(E ) where  SK is the neutrino  ux,  is the neutrino cross section,  is the neutrino detection e ciency and M is the detector response function rep- resenting the probability to observe E as Erec , the reconstructed neutrino energy [38]. The estimation of  SK ;  ;  and M is necessary. Since the T2K neutrino beam is originally generated from pion and kaon decays, the cross sections of the pion and kaon production are key parameters to estimate  SK . The estimation is done using a beam Monte Carlo simulation called JNUBEAM that uses NA61/SHINE measurements for the pion production cross section [39]. The neutrino energy has to be inferred by the kinematics of the par- ticles detected in the neutrino interaction. The neutrino energy in CCQE 192.1. Measurement Theory interactions ( l + n ! l + p) is calculated by the lepton momentum pl and scattering angle  l with respect to the beam direction: Erec = (mn  V )El + (m2p  m 2 l )=2 (mn  V ) 2=2 (mn  V ) El + pl cos  l (2.3) where V is the average nuclear potential of oxygen [38]. At SK, events are identi ed by  Cerenkov rings. More description about  Cerenkov radiation will be given in Section 2.3. In CCQE interactions, the proton is usually below  Cerenkov thresh- old [40], and thus there is typically only one  Cerenkov ring from the out- going lepton. In other interactions, typically multiple rings are detected because they have more than one charged particle in the  nal state. There- fore, CCQE and non-CCQE interactions can be distinguished by counting the number of rings. However,  + from non-CCQE interactions and  + produced from the  + can be below  Cerenkov threshold. But, in this case, an electron is produced in the muon decay, so we can also use the electrons to distinguish CCQE and non-CCQE interactions. The signal events for the   disappearance are clear single ring events, called  - like events, in CCQE interactions. One of the main backgrounds is from charged-current single  production (CC1 +). In the  nal state of CC1 + interactions,  and  are produced. If the  Cerenkov ring from the pion is not observed, or the Michel electron is not observed, then the CC1 + is mistaken as a single  -like ring. Likewise, the signal events for the  e appearance are fuzzy single ring events, called e - like events, in CCQE interactions. One of backgrounds for  e appearance is the  e contamination in the neutrino beam from muon decays ( + !  +  and  + ! e+   e) and K =K0 decays. The fraction of  e contamination in the   beam is about 1%. The other main background is NC single  0 production (NC1 0). When  0 decays, two gamma rays are produced. The photons convert into e+e pairs and produce e - like rings in the detector. If these two rings from the two photons overlap or one of two rings is missed, the event will look like an electron event. 2.1.1 O -Axis Con guration T2K is the  rst experiment that uses o -axis con guration. The o -axis angle is the angle between the neutrino beam and the detectors. Figure 2.2 shows the neutrino energy  ux for di erent angles and the corresponding probability[31]. For on-axis angle, the neutrino energy has a 202.1. Measurement Theory Figure 2.2: Neutrino  ux for three di erent o -axis angles and correspond- ing oscillation probability. peak at 2 GeV. Going further o -axis angle, the peak energy of the neutrinos becomes lower. At the 2.5 degrees o -axis, the peak of the  ux is at  0:6 GeV, and here, the oscillation probability is maximized. In addition, the tail in neutrino energy distribution is shortened so that the number of high energy non-CCQE and NC interactions are reduced. Therefore, T2K sets the o -axis angle at 2.5 degrees. 212.2. Beamline Figure 2.3: Map of J-PARC facilities. 2.2 Beamline The T2K primary beamline transports protons extracted from the Main Ring (MR) at J-PARC, Japan. The proton beam is accelerated in three steps through a series of accelerators. First, it is the LINAC where the protons are accelerated to 181 MeV. Second, the boosted protons are fed to the 3 GeV synchrotron, called RCS. The beam increases in energy to 3 GeV. Finally, some of the 3 GeV proton beam enters the MR, and is accelerated up to 30 GeV [41]. The overall facility is shown in Figure 2.3. The extracted beam from the MR is delivered to the target, where a large number of pions and some kaons are produced by interactions. The target itself is a thin carbon rod,  90 cm long. The phase 1 goal of T2K is to accumulate 8:33 1021 protons on target (POT), but as of December 2011 we have 1:43 1020 POT. Figure 2.4 shows the history of POT and the protons-per-pulse [42]. The secondary particles (predominantly pions) from proton interactions are focused by the magnet horns and passed to the decay pipe. More specif- ically, the pions are focused to the beam direction by the magnet horns. The dominant processes in the decay volume are 222.2. Beamline Figure 2.4: History of protons on target (POT). Solid line is the integrated number of delivered protons from the beginning of the experiment. The scale is in the left axis. Red dots are the number of protons per beam pulse, and the scale is in the right axis [42].  + !  + +   K+ !  + +   K+ !  + +   +  0 K+ ! e+ +  e +  0  + ! e+ +  e +   Figure 2.5 shows the neutrino energy  ux at ND280 for di erent parent decay modes. The   is mostly from  + decays and most of the  e is from kaon and muon decays. At the end of the decay pipe, the muon  ux monitor (MUMON) sits to measure the properties of the muons penetrating the beam dump, including the pro le center and intensity to ensure that the beam axis is correct [38]. Two kinds of near detectors are 280 m away as described in Section 2.4, one on the beam axis (on-axis) and one o -axis. The o -axis neutrino beam will be observed at the far detector. Figure 2.6 shows overall schematic [43]. 232.2. Beamline Figure 2.5: The neutrino  uxes at ND280 for di erent parent decay modes. The left column is of   (top) and  e (bottom). The right column is of   (top) and  e (bottom). These  gures are taken from 242.3. The Super-Kamiokande Detector Figure 2.6: Simpli ed schematic of T2K beamline. Primary proton enters the target station and produce secondary pions and kaons. The particles decay into charged leptons and neutrinos in the decay pipe. The neutrinos are observed by ND280 and SK. 2.3 The Super-Kamiokande Detector The Super-Kamiokande detector (SK) is the far detector for T2K. It is the world’s largest contained water  Cerenkov detector, located 1000 m under a mountain [44]. Figure 2.7 shows the outline of SK. It is 39.3 m in diameter and 41.4 m in height,  lled with 50,000 tones of ultra-pure water. About 13,000 photomultipliers are installed on the detector walls. It is divided into two sections, the inner-detector (ID) and the outer-detector (OD). The ID is used to detect and reconstruct events, while the OD is a veto for back- ground events such as cosmic muons or other interactions in the surrounding material [45].  Cerenkov radiation is electromagnetic radiation which is produced when charged particles, such as electrons, pass through a medium faster than the speed of light in that medium [46]. The radiation is detected by photomulti- plier tubes (PMTs), which are very sensitive photosensors with high gain of 107 (at a supply voltage from 1700 to 2000 V), low noise rate of 3 kHz, and good time resolution of 2 ns [47]. These properties allow PMTs to detect a large fraction of single photon signals. Figure 2.8 provides an illustration of  Cerenkov radiation. The left shows 252.3. The Super-Kamiokande Detector Figure 2.7: Outline of the Super-Kamiokande detectors. This  gure is taken from . a light cone of a neutrino-nucleus CCQE interaction, in which a muon is pro- duced, emitting  Cherenkov radiation. The recoil proton is below  Cerenkov threshold, so it does not produce a ring. The right  gure shows a lengthwise section of the cone. The emitted radiation from charged particles constructs a wavefront in the shape of a cone with an angle related to the speed of the particle in the medium [48]. Therefore, its cross section is a ring. The angle of the cone is expressed as cos  = c vn( ) = 1  n( ) (2.4) where c is the speed of light, v is the speed of light in medium and n is the refractive index of medium. n depends on wavelength of light  . Muons and electrons are distinguished by looking at how well-de ned the edge of the ring is. Particles with heavy mass will not radiate signi cantly in the water, so that they create a well-de ned ring. In other words, massive particles such as muons make sharp rings. However, light particles such as electrons will lose energy radiatively and scatter, so that secondary particles are released. They make fuzzy rings. As a result, a ring from a muon has a 262.4. The Near Detectors Figure 2.8: The left  gure shows  Cerenkov light in a cone shape. It is nucleus scattering, which is the relevant for  1 GeV neutrinos. The right  gure shows lengthwise section of a light cone. The angle  is determined by speed, travel time, and refractive index of the medium. These  gures are taken from much sharper edge than an electron ring. The top  gure in Figure 2.9 is an example of a  - like event. The bottom  gure is an e - like event. 2.4 The Near Detectors The near detector complex consists of two detectors. One is the on-axis detector, INGRID, measuring the neutrino beam pro le. The other one is the o -axis detector, ND280, that measures the interaction rates, neutrino energy spectrum, and interaction kinematics of the o -axis neutrino beam directed towards SK. ND280 consists of several detectors enclosed within a dipole magnet, which provides a magnetic  eld. Figure 2.10 shows how both ND280 and INGRID are installed together within the near detector complex. 272.4. The Near Detectors Figure 2.9: Example  - like event at SK on the top and e - like event on the bottom. These  gures are taken from http://www-sk.icrr.u- 282.4. The Near Detectors Figure 2.10: The outline of installation of all near detectors, located 280 m away from the decay pipe. This  gure is taken from 2.4.1 The INGRID Detector INGRID, the Interactive Neutrino GRID, sits on-axis with respect to the beam line, 280 m from the beam target. The detector is designed to measure the on-axis neutrino  ux and beam pro le. The main purpose is to estimate systematic uncertainties related to the beam  ux [49]. INGRID is a cross-shaped detector, made of 16 identical modules as shown in Figure 2.11. Each module is composed of alternating layers of iron and active scintillator. This is surrounded by veto scintillator planes to reject background events occurring outside the detector. Figure 2.12 shows a single INGRID module. 292.4. The Near Detectors Figure 2.11: The overview of the INGRID detector. 14 identical modules are arranged as a cross and 2 additional separate modules located outside of the main cross. This  gure is taken from . 2.4.2 ND280 T2K uses an o -axis beam con guration so that the oscillation is maximum at the far detector around the T2K neutrino energy range. Since the neutrino  ux seen by the far detector is o -axis, it is important to also have a near detector o -axis to understand the neutrino beam and interaction properties. The main goal of ND280 is understanding these properties. The central tracking system of ND280 consists of three time projection chambers (TPCs) and two  ne-grained detectors (FGDs). The  0 detector (P0D) is used to understand  0 production channels, which are key back- grounds to the  e appearance measurement. The electromagnetic calorime- ter (ECal) and the side muon range detector (SMRD) surround both the tracker and the P0D. The ECal is designed to detect photons, and the SMRD measures the range of charged particles exiting the tracker. 302.4. The Near Detectors Figure 2.12: A single INGRID module. The module consists of a sandwich structure of nine iron plates and 11 tracking scintillator planes surrounded by veto scintillator planes. This  gure is taken from . All of the tracker, P0D, ECal, and the SMRD are surrounded by the magnet. The magnet provides a horizontal uniform 0.2T magnetic  eld perpendicular to the beam direction. Because of the magnetic  eld, particles have curved trajectories in the detectors, so that the momentum and sign can be measured by the curvature of the particles. Figure 2.13 shows the overall con guration of ND280. Time Projection Chamber A Time Projection Chamber (TPC) is a gas- lled detector. Figure 2.14 shows a single TPC. Along its width, a TPC is divided by a central high- voltage cathode plane, which makes a uniform electric  eld between the cathode and the end planes. When particles pass through the TPC volume, they produce ionization in the gas. The electrons from the ionization drift to the end plates, where the MicroMegas (MM) modules lie. Each end plate has 12 MicroMegas modules and each module contains 1728 pads [51]. The MM detect free electrons ionized in the gas that drift to the an- ode. Because high momentum leptons from CCQE interactions are mostly forward-going, they will be curved in the y direction in the applied magnetic  led. In the yz plane, the trajectory of the particle is determined directly by the MicroMegas detectors, depending on which pad observes charge. x- 312.4. The Near Detectors Figure 2.13: All elements in ND280. P0D, FGDs, TPCs, and DsEcal are held inside a stainless steel frame, called the basket. BrEcal and P0DEcal are attached directly to the magnet. The magnet encloses all of the detectors. This  gure is taken from . position information is recovered by looking at the time taken for the drift electrons to reach the MicroMegas modules. A time is needed to set the ab- solute drift time, so a good initial time coming from the scintillator detectors like the FGDs is required. A TPC is  lled with a gas mixture of Ar, CF4, and C4H10. The ratio of gases is chosen to maximize the drift velocity of electrons. The drift velocity in the gas mixture is  77 mm/ s and the maximum drift distance from central cathode to MicroMegas is 897 mm [50]. This reduces the time to readout the detector. The TPC is a slow detector in the sense that it must wait for all the ionization to drift to the readout planes. The faster this happens, the faster the detector can start taking data again [52]. Since the density of this mixture is low, relatively few interactions are expected in the TPCs. Rather, most neutrino interactions occur in the FGDs, which have a large target mass. T2K uses three identical TPCs for tracking. The primary purpose of the TPCs is to measure muon momenta in CCQE interactions and to identify particles using the measured energy loss in the gas, dE/dx [53]. 322.4. The Near Detectors Figure 2.14: An TPC is a double-box. The inner box is actually  lled with gas mixture. Electronics are attached to the front of the inner box [50]. The most upstream TPC (TPC1) is located between the P0D and the upstream FGD (FGD1). The second TPC (TPC2) is between the two FGDs. This measures forward going particles from FGD1 and backward-going parti- cles from the downstream FGD (FGD2). The last TPC, placed after FGD2, measures the momentum of particles produced in FGD2 and going forward. 332.4. The Near Detectors Figure 2.15: A single scintillator bar for FGDs. The scintillator part has rounded corners and is coated by TiO2. At the center, there is a hole for a WLS  ber [54]. Fine-Grained Detector The Fine-Grained Detectors are the other part of the tracker system of ND280. They are placed between the three TPCs. The two FGDs have the same size, but di erent internal structure. In each FGD, scintillator bars are arranged in layers along the x or y axis alternatively, perpendicular to the beam direction. This structure gives 3D tracking by alternating measurements of x and y as the track travels in the z-direction. Figure 2.16 shows a part of an FGD and how all components are installed. Figure 2.15 shows an FGD scintillator bar. Each bar is coated with TiO2 to reduce optical cross-talk which would make noise in other channels [54]. A wavelength shifting (WLS)  ber passes through the center of each bar. One end of the  ber is mirrored and the other end is coupled to a Multi-Pixel Photon Counter (MPPC). When a charged particle hits a bar, the attached MPPC measures the emitted light. FGD1 has 30 layers of scintillator bars. FGD2 has fewer layers and instead has water layers between the scintillator layers. This allows the determination of neutrino cross sections on water by comparing the rates in the two detectors. The FGDs provide target mass for neutrino interactions in the tracker, 342.4. The Near Detectors Figure 2.16: A photo of an FGD showing layered structure of scintilla- tors and the MPPCs with the WLS  bers. This is installed vertically so that the plane faces the neutrino beam. This photo is taken from but also play the role of tracking particles emerging from the interaction ver- tex. The tracking system measures the  e and   rate and the neutrino en- ergy spectrum through CC interactions and provides the unoscillated muon and electron neutrino event rates and energy spectrum for the oscillation analysis. There will be more detail about the FGDs later.  0 Detector The pi-zero detector (P0D) is used to understand  0 production, which is one of the dominant backgrounds for the  e appearance analysis. The  0 detector measures  0 cross section on water for processes such as, 352.4. The Near Detectors Figure 2.17: The scintillator bars for P0D are triangular to improve po- sition detection. The water cell is removable. This  gure is taken from .   + n!   + p+  0 (2.5)   + p!   +  +  + ! p+  0 (2.6) where n denotes a neutron and p denotes a proton. This allows us to under- stand one of the important backgrounds, NC1 0 interactions, and predict the expected number of  0 events at SK [55]. The P0D consists of active scintillator layers, brass and lead layers to induce photon conversions, and target water layers. The water layers are removable, so that data can be taken with water in and with water out. Active layers are built of triangular scintillator bars with a  ber coupled to an MPPC. Figure 2.17 shows the P0D bars. Because of the triangular bars, particle positions can be reconstructed with good resolution if more than two layers of bars are hit. The two types of inactive layers are targets and radiators. Targets are water cells providing oxygen target mass. Radiator layers are made of two di erent materials, lead and brass. These are using to contain decay photons from  0. Since the radiation length of lead is shorter than brass, lead will absorb more of the particles from the photon shower, reducing the information available for reconstruc- tion. Because of this reason, lead radiator layers are used as a radiator on the outer layers of the P0D. Otherwise, in the inner layer, brass is used as radiator rather than lead so that it can give better energy resolution [56]. 362.4. The Near Detectors Electromagnetic Calorimeter The ECals are installed to detect photons. While the TPCs already measure the particle momenta, the ECals cover a larger area and detect neutral particles which are invisible in the TPCs. The ECals consist of three sections: The Barrel ECal (BrEcal) surround- ing the tracker, the P0D ECal surrounding the P0D and the Downstream ECal which is placed downstream of TPC3. Each ECal is a combination of lead and scintillator. Each scintillator layer is orientated perpendicular to its neighboring layer. The BrEcal consists of modules on each side, top, and bottom of the tracker. Each BrEcal module has 31 layers of scintillator bars. The dimensions of the top and bottom modules are 150 50 420 cm3. The side modules have di erent dimensions, 50 230 420 cm3. The P0D ECal consists of 6 layers of scintillator bars and has similar dimensions to the BrEcal. The top and bottom modules of the P0D Ecal have dimensions, 140 50 230 cm3. The side module dimensions are 50 230 260 cm3. The DsEcal has 34 scintillator layers and dimensions of 200 200 50 cm3 [55]. The lead layers are  4 mm in thinckness. Figure 2.18: Sliced view of a SMRD slab. This  gure is taken from . Side Muon Range Detector The Side Muon Range Detector (SMRD) allows us to detect particles that exit the central tracker region. For example, a muon emitted at large angles with respect to the beam direction might not pass through the TPCs or just leave a short track in the TPCs. The SMRD is designed to detect these muons with high e ciency. 372.5. FGD Detail The SMRD consists of scintillator slabs. An individual SMRD slab is similar to an FGD scintillator bar, but is wider and is coupled to the  ber in a di erent way. The slab is embedded with s-bent wavelength shifting  bers. Figure 2.18 shows a sliced view of a SMRD slab. The s-bent  ber collects light evenly over the broad surface. Whereas the other detectors are placed in the inner volume enclosed by the magnet, the Side Muon Range Detector is installed between the steel yokes of the magnet. Therefore the size of the SMRD is determined by the magnet structure.The magnet yoke is split into C-shaped segments on either side of the detector. A single C-like segment consists of 18 iron layers made from 50 mm steel. Each layer is separated by an air gap of 17 mm thick and its dimensions are 90 70 cm2 [57]. The SMRD modules are held in this air gap [58]. This sub-detector has two purposes. The  rst is to measure the muon momentum leaving the inner detectors. The muon momentum is measured by how far the muon penetrates into the iron of the magnet. By seeing how many layers of the SMRD are hit, the range can be measured. 2.5 FGD Detail The FGDs serve as target mass for the tracking system and provides tracking of particles emanating from neutrino interactions in the FGDs. These FGD tracks are combined with the TPCs to provide complete tracking information for the interaction. Target materials are mainly carbon and hydrogen from scintillator bars, small amounts of TiO2 from scintillator coating, and water. The FGD2 contains scintillator bars and water modules, while FGD1 is made of only scintillator bars. By comparing interaction rates in the two FGDs, the cross section of neutrino interactions on water can be estimated. Since the far detector is a water  Cerenkov detector, it is important to measure cross section on water target. In addition, determining the type of interactions occurring inside the volume is crucial. Hence, the FGDs must also have good tracking perfor- mance of particle detection. The most useful interactions for measuring neutrino oscillations are CCQE, so this means that it is important to dis- tinguish CCQE and non-CCQE interactions. If non-CCQE interactions are mistaken for CCQE interactions, it leads to a wrong estimation of the neu- trino energy spectrum since the important assumption is the mass of the recoiling hadron in reconstructing the energy. Most non-CCQE interactions are associated with pions produced with a muon and nucleon. Therefore, 382.5. FGD Detail we should detect pions and reconstruct proton trajectories as accurately as possible. Though the inner structure of the two FGDs are a little bit di erent, basically they have same geometry and electronics architecture. Each FGD measures 280 240 36:5 cm3. Its depth along the beam direction is rela- tively thin so that most of charged lepton produced inside FGDs can pene- trate into the TPCs, which can then provide a measurement of the particle momentum. Each scintillator module hangs inside a light-tight box made of aluminum. When charged particles pass through the scintillator bars, they produce light. The MPPC converts the light into an electrical signal. Since the FGD electronics are designed to provide both timing and charge measurements, they rely on digitizing the photosensor waveform to extract time and charge. Every single scintillator bar has a MPPC, and this MPPC is attached to a photosensor daughter board. FGD1 contains 5760 MPPCs and associated daughter boards, and FGD2 contains 2688 MPPCs and boards. 16 of the boards and photosensors are together on a photosensor bus board. No one can access the electronics boards during data running, so it is important to build a robust slow control system which is able to monitor and control the condition of the boards. Furthermore, the temperature must be carefully controlled in order to ensure proper operation of the photosensors. The bias voltage of each pho- tosensor must also be set individually in order to obtain an uniform detector response. Thus, a slow control system must be built to monitor the elec- tronics and photosensor as well as to control the photosensor bias voltage. 2.5.1 Water Module The water modules in FGD2 are a series of layers of water in polycarbonate vessels. The ends of each vessel are sealed by epoxy. Since the detectors have lots of water-sensitive electronics, it is important to make sure the water never leaks out. A negative pressure system using a vacuum pump provides water leak protection in the case of minor leaks in the module. The water pressure is kept below atmospheric pressure by the system. 2.5.2 Scintillator Module The scintillator produces the light that is detected by the MPPC. The scin- tillation light is produced when the charged particles ionize the molecules 392.5. FGD Detail in the material. The basic building block of a scintillator module is a scintillator layer. The layer consists of 192 scintillator bars alternating between x and y in the xy plane. One X layer and one Y layer are glued together and form a single XY module. The dimensions of each module are 186:4 186:4 2:2025 cm3. A scintillator bar contains a  ber in its central hole. The  ber is not glued to the bar, but coupled to the bar through the air gap. One end of a  ber is mirrored to re ect light back along the  ber and improve light collection e ciency. The other end is coupled to a Multi-Pixel Photon Counter to measure light and its timing. The FGD1 has 15 XY modules, 30 layers in total. The FGD2 has 7 XY modules, alternating with water modules. Figure 2.19: Wave-length shifting  ber comparing single cladding and dou- ble cladding  bers [54]. Wavelength Shifting Fiber Light from scintillator bars travels through a  ber inside the bar. This  ber is a double-clad wavelength shifting  ber(WLS). Figure 2.19 is the cross section of the  ber. Double cladding improves capture and transmission of light in the  ber. The produced light in the scintillator is in the UV range, 100  400 nm, while the MPPC is sensitive at the range of green light,  500 nm. For this 402.5. FGD Detail reason, we use WLS  bers. Its peak absorption wavelength is  430 nm, and subsequent emission spectrum is peaked at 476nm. Figure 2.21 shows the detection e ciency of the MPPC as a function of wavelength. Figure 2.20: A photo of the MPPCs with the WLS  bers. This photo is taken from Multi-Pixel Photon Counter For choosing proper photosensors for the FGDs, a number of requirements were considered. The sensors should be compact and robust. They should also have high gain with low voltage and high detection e ciency. Moreover, since the photosensors will be used inside a magnet, they must be insensitive to magnetic  eld. The MPPCs satisfy these features, so T2K selected them. The MPPC is a pixellated avalanche photodiode that operates in Geiger mode with 1:3 mm2 sensitive area, so it has single photon sensitivity. An avalanche photodiode (APD) is a semiconductor electronic device which converts light to electricity. It can amplify the resulting photocurrent when a reverse voltage is applied. If the APD is operated in a reverse voltage above its breakdown voltage, a very high gain( 105) is obtained. This is called \Geiger mode". Figure 2.20 shows the MPPC with the WLS  bers. Each pixel of the MPPC works independently in Geiger mode, and all the pixels are connected in parallel. Since a single incident photon will  re 412.5. FGD Detail Figure 2.21: The MPPC sensitivity as a function of wavelength. The  gure is taken from Figure 2.22: The MPPC gain as a function of the reverse volt- age (left) and temperature (right). The  gures are taken from 422.5. FGD Detail a single pixel, the number of  red pixels are proportional to the number of incident photons. This device counts the number of photons. But when the number of incident photons is more than the number of pixels in an MPPC, the device is saturated. In other words, the number of  red pixels are not proportional to the number of the photons any more. So the device becomes non-linear at higher light levels. The gain depends on the operating voltage and the ambient temperature. Figure 2.22 shows the relations. In the left plot, the gain linearly changes with varying reverse voltage. In the right plot, the gain decreases with increasing temperature at  xed reverse voltage. It is important to measure the temperature and operation voltage during data-taking to calibrate the MPPCs. The MPPC measurement has three main sources of uncertainties; cross- talk, dark noise, and after-pulsing. Cross-talk is when 1 pixel  res an ad- jacent pixel in the same MPPC resulting in more than one pixel  red by a single photon. Dark noise is from avalanches induced by thermal excita- tion without an optical signal. Lastly, after-pulsing is caused by a second avalanche from the same photon. 2.5.3 Electronics As mentioned earlier, each FGD is covered by a dark box. The front-end electronic system, back planes, and the mini-crates are attached around the outside of the dark box. The back-end electronics, which monitor and control the overall system of the FGDs and give connection between the FGDs and the database, are located outside of the magnet. The photosensors are very sensitive to temperature. However, the nec- essary electronic components continuously emit signi cant heat. It is thus important to locate the readout electronics outside of the dark box. More- over, cooling water circulates around the dark box to cool the electronics. Only the scintillator bars,  bers, photosensors, and the passive electronic components are housed within the dark box, thus providing thermal isola- tion. Figure 2.23 shows the overall installation of the electronics. Photosensor Connection Two types of boards are used to provide electrical connectivity to the pho- tosensors; the photosensor daughter boards (PDB) and the photosensor bus boards (PBB). 432.5. FGD Detail Figure 2.23: FGD Electronics. Only photosensor daughter boards and bus boards are in the dark box. Mini-crates including Light Pulsar Boards, Crate Master Boards, and Front End Boards are outside of the dark box. All of them connects to Data Concentrator Cards and the slow control system [54]. The PDBs connect individually to the MPPCs and 16 of these are col- lected on a PBB. The PBBs provide electrical connection between PDB and monitoring/controlling systems. Each PBB has two temperature sensors, and they are monitored by the slow control system. It also has 16 LEDs to  ash the  ber to calibrate the measurements. The PBBs are connected to the Front-End Board(FEB) located outside the dark box with cables. Front End Electronics There are two main purposes of the Front-End Electronics. First, they amplify and digitize the signals from the photosensors. Second, they also control the photosensor bias voltages and monitor currents and tempera- tures. Each scintillator bar has a photosensor and a LED. The LED is used to calibrate the waveform measured at a photosensor. So the FGD electronics is designed to read out and collect data from photosensors and to control 442.5. FGD Detail measuring components like the LEDs. There are three types of boards for di erent uses. A Front-End Board (FEB) generates photosensor bias voltages and digitizes the analog wave- forms coming from the sensors. A FEB handles 64 MPPC channels. FEBs must provide stable and  exible bias voltage for the photosensors, because the gain and noise rates of the sensors are highly sensitive to the applied voltage and vary from sensor-to-sensor. A Crate Master Board (CMB) controls communication between the front-end and the back-end electronics. CMBs handle communication with the back-end electronics. The CMB receives clock and trigger signals from the Data Concentrator Card (DCC) and distributes them to the FEBs. The CMB also receives the data from the FEBs and compresses the data. Only important data such as carge and time of a large pulse are stored by the online pulse- nding algorithm. The compressed data are transfered to the DCC. A Light Pulser Board (LPB) controls the duration and intensity of LED pulses and provides electrical pulses to  ash the LEDs. The LPB controls the LEDs which are used for photosensor calibration and  nding dead chan- nels. If CMBs receive a light calibration trigger from DCCs, the LPBs  ash the LEDs. The LEDs provide a method for identifying dead channels and calibration the MPPCs. A mini-crate houses all of these boards: 15 PBBs(one per XY module), 1 CMB, 1 LPB, and 4 FEBs for FGD1. The mini-crates in FGD2 are the same, except that only 2 FEBs are required. Back End Electronics The back-end electronics are located outside of the magnet and are con- nected to the front-end electronics by a combination of electrical and opti- cal cables. This system monitors the condition of inner electronics elements, control power and  ow of data, and also packages the data for storage. The Data Concentrator Cards (DCC) make the connection between the front-end electronics and the data acquisition (DAQ) server. The DAQ is responsible for collecting the data taken from the detector electronics. One DCC covers 4 mini-crates, so 12 DCCs are needed in total. While the data are compressed on CMBs, further compression is done on the DCCs. The back-end electronics also include the slow control system, which in- teracts with detector components to set and monitor detector parameters. All of the boards in the mini-crates are connected to a slow control system link. The system controls power and bias voltages, and monitors tempera- 452.5. FGD Detail FGD1 FGD2 XY modules 15 7 Layers 30 14 Channels 5760 2688 Photosensor Bus Board 360 168 Front End Boards 96 48 Crate Master Boards 24 24 Light Pulser Boards 24 24 Mini-Crates 24 24 Data Concentrator Cards 6 6 Table 2.1: List of electronics ture and current. The slow control system also provides an alarm system when speci ed limits are exceeded and presents a uni ed interface to the users. A summary of the full electronics is shown in Table 2.1. 46Chapter 3 ND280 Software 3.1 Overviews of ND280 Software The ND280 Software is a set of software packages which are closely as- sociated with each other. The packages handle all aspects of the o ine handling of ND280 data, including data handling, calibration, reconstruc- tion and analysis output, as well as the Monte Carlo simulation (MC) of the detector. It also contains classes, called oaEvent, to store the information from the various stages of processing. The MC simulation consists of several parts. JNUBEAM simulates the neutrino beam. The beam  ux determined by this stage. The neutrino interactions based on the simulated  ux is then generated using the two external particle generators, NEUT [59] and GENIE [60] with the geome- try from nd280mc, which is the ND280 simulation package. This provides the  nal state particles for each interaction. nd280mc handles the particle tracking and generation of hits through the detector geometry and material. nd280mc relies on the external particle generation and tracking framework Geant4 [61]. Based on the  ux and the geometry, it simulates how outgo- ing particles from the interactions propagate through ND280 and what the energy deposits are. The generated events are propagated to the electron- ics simulation package, elecSim, to generate the simulated electric response, which then are passed through the rest of the ND280 Software chain in the same way as the real data. Further details will be described in Section 3.2. Unlike the MC simulation, real data is output in a di erent format by the MIDAS-based data acquisition. Thus an additional step is needed to Figure 3.1: The ND280 Software 473.2. Monte Carlo Simulation decode this data into the oaEvent format that can be processed by the ND280 software. Figure 3.1 shows a simple schematic for the ND280 software process. For the data, the  rst step is to \unpack data". At this step, raw data are converted to oaEvent-based classes and which are stored in the ND280 ROOT  les. oaEvent depends on the ROOT framework and de nes the ROOT  le structure for ND280 data. The second step is \oaCalib". At this step, calibration constants for each sub-detector are calculated and then applied to calibrate charge, time, and other observed variables. The next step is \oaRecon". Reconstruction is  nding tracks, vertices, and clusters based on the measured hits. The package receives the calibrated hits and reconstructs the neutrino interactions over all detectors, from the P0D to the DsECal. Each detector has its own reconstruction package. Then the global reconstruction (oaRecon) combines the results from the individual reconstruction to form reconstructed objects that span all of ND280. The last step is \oaAnalysis", which makes simple ROOT trees from which the user can perform analysis using ROOT macros. Since this thesis focuses on the FGDs, we will have more description of the FGD software than other detectors. This will be described in Section 3.5. 3.2 Monte Carlo Simulation Currently, we have two stages of detector simulation. One is nd280mc for detector simulation, and the other one is elecSim for electronics simulation. Geant4 is used as the platform for nd280mc [61]. It provides a way to take into account complicated detector geometry. It also tracks the particles through geometry, accounting for things like energy loss and deposition in the materials, and hadronic interactions. It generates hits, which are energy depositions in the active elements of the detector. The hits are stored in a class called TG4Hits and are translated into the detector response via elecSim. elecSim is the second stage of the detector simulation. It generates elec- tronic responses for sub detectors by modeling detection components. The  rst step simulates the scintillator bars and the WLS  bers. These are simulated considering the average light yield of the scintillator and the at- tenuation length of light in the WLS  bers. For the scintillator, the output of this step is the predicted number of photons and their times at the MPPC. The next step is the MPPC response simulation. The simulation takes ac- 483.3. oaEvent count of photon detection e ciency, cross-talk and dark noise. The MPPCs are treated as a grid of pixels, and each pixel releases a charge if a photon is incident on the pixel. The noise caused by cross-talk or after-pulsing e ects are also simulated to make the simulation more realistic. The output is a list of charges and times of the simulated hits. elecSim also simulates the TPC response. TPC elecSim calculates the number of ionization electrons created in the TPCs as a charged track tra- verses the gas volume. Then, it simulates electron drift and di usion, which is how the electrons move towards the MicroMegas planes, and the electric responses in the MicroMegas planes. 3.3 oaEvent The fundamental structure for ND280 data is provided by the package oaEvent. The package strongly depends on ROOT, which is a program- ming package o ered by CERN for particle physicists. oaEvent de nes the data format of ND280 output  les based on ROOT, and handles writing, opening and reading of  les. The ROOT  les made by oaEvent record in- formation in several classes that mirror the way in which the information is produced in order to facilitate access to the information that is stored. For example, the ROOT  les save raw data, simulated data, and reconstructed data separated into di erent classes for which oaEvent provides methods to set, access and modify these data structures. An individual measurement of charge and time is stored as a single hit, with hits from di erent sub-detectors stored separately in di erent lists. oaEvent has three main data classes: MC truth classes, raw data classes, and reconstructed data classes. MC truth classes store information such as the true primary vertices or true particle trajectories. In ND280 terminology, the term \trajectory"is used to distinguish the true path of the particle from its reconstructed coun- terpart, which is called a \track". Subclasses within the vertex and trajec- tory classes store pertinent information such as the position, momentum, charge and particle type. The raw data classes are handled by two sub packages, oaRawEvent and oaUnpack. These packages decode the MIDAS banks, which contain the raw data, into the oaEvent format which is readable by the other ND280 software packages. oaEvent also contains the reconstruction classes, which store reconstruc- tion information. The classes are split into several categories: TReconBase, 493.4. Example Event Displays TReconCluster, TReconShower, TReconTrack, TReconPID and TRecon- Vertex. TReconBase objects have lists of reconstructed hits called nodes. The nodes are points on the reconstructed tracks, while the hits in gen- eral have their own de nition of position. TReconCluster, TReconShower, TReconTrack, TReconPID and TReconVertex are di erent types of recon- structed objects. All these classes are derived from the base class TRecon- Base. A TReconCluster object is a collection of hits in space that represents a blob of energy deposition. A TReconVertex object is also a collection of hits, but is di erent from a cluster in that hits in a vertex are at the same point in space. If a vertex is associated with a neutrino interaction, this is a primary vertex. If a particle coming from a primary vertex make an interaction such as decay, a vertex associated with the interaction is called a secondary vertex. A TReconTrack object is a collection of clusters or hits, which de nes a path of particles. It contains information such as position, direction, charge and curvature. If a track is identi ed with a particle type, it becomes a TReconPID. A TReconShower object is a path with a null curvature. It might represent electromagnetic shower, for example. 3.4 Example Event Displays In the following, event displays for various di erent event types are shown. Figure 3.2 shows a sand muon event passing through all sub detectors from P0D to the DsECal. Sand muons are muons entering the detector that are produced by neutrino interactions in the sand surrounding the detector hall. In the  gure, the left-most region in brown represents P0D, after that 3 TPCs and 2 FGDs. The right-most box is the DsECal. One can see that each sub-detector contains a single track corresponding to the muon, and that the tracks recorded in each detector match to form a single track across all the detectors. Figure 3.3 depicts a cosmic event coming from the upper left in the P0D. It also shows one clear reconstructed global track. Figure 3.4 and Figure 3.5 show neutrino interactions occurring in the P0D and FGD1 respectively. Interaction in FGD1 can be separated from interactions in the upstream P0D by rejecting events with any tracks in the P0D or TPC1. 503.5. FGD Software Packages Figure 3.2: Sand muons going through all subdetectors. Figure 3.3: Cosmic track reconstructed across all detectors 3.5 FGD Software Packages The FGD data analysis is separated into two stages. The  rst stage uses raw MIDAS data as input  les. The raw data contains waveforms resulting from digitizing the activity in the MPPCs as recorded in a switched capacitor array (SCA). Figure 3.6 shows an example waveform [62]. A set of routines performs pulse- nding and  tting on the waveforms. For each pulse, a raw pulse height is measured from a digitized MPPC waveform, that is related to the energy deposit on the scintillators. After that, charge and time are extracted based on the pulse heights and positions in the wave form. These tasks are performed in fgdRawData, which is responsible for decoding the raw data,  nding pulses in waveforms,  tting the pulses, and extracting charge/time from the pulses. The information is then available for further analysis. 513.5. FGD Software Packages Figure 3.4: Neutrino event in P0D sending single negative track into TPC1/FGD1/TPC2. Figure 3.5: Clean CC interaction in FGD1 The pulse heights are normalized in units of the average pulse height from a single MPPC avalanche, which depends on the operation voltage and temperature of the MPPC. The voltage and temperature can vary during data-taking. We measured how the height changes by varying the MPPC voltage at a  xed temperature. During data-taking, the temperature is measured by the sensors located on the PDB. The measured temperature is used to calibrate the MPPC, because the gain of the MPPC depends on a 523.5. FGD Software Packages Figure 3.6: An example waveform of an FGD MPPC. The red region is used to measure the pixel  res from optical sources and the blue is used to measure background from dark noise [62]. temperature. The times extracted from the  tted pulse are corrected for the skew in various clock domains and the di erent cable lengths. The time and charge information is converted into the oaEvent/THit class and stored in a ROOT  le. 3.5.1 FGD Time Binning A FGD time bin is a cluster of hits from tracks which are passing through the detector at the same time. The time binning algorithm sorts the hits in time and compares the times between the two neighboring hits, starting from the  rst hit. A pre- xed parameter used by the algorithm is the maximum time gap, which is 100 ns by default. If the time di erence is less than 100 ns, the two hits are put together in a bin. If the time di erence is larger than 100 ns, the later hit is put into the next bin. This algorithm is shown in Figure 3.7. The main purpose of the time binning is tagging Michel electrons and to separate neutrino interactions in di erent bunches. When a muon stops in the detector, it decays to an electron and neutrinos:   ! e +  e +   (3.1)  + ! e+ +  e +   (3.2) 533.5. FGD Software Packages Figure 3.7: Time binning schematic. Time runs along the horizontal axis. Black points represent times of individual hits and red circles encompass hits which are placed into the same time bin. The decay electrons are called Michel electrons. Since the muon lifetime ( 2:2  s) is much longer than the  xed time gap, the Michel electrons form isolated time bins. This is used for CCQE selection. In Chapter 4, the Michel electron detection e ciency using cosmic data is discussed. We will see how often the Michel electron is found by the FGD time binning method. 3.5.2 FGD Reconstruction Particles traversing through the FGDs with some energy and direction are represented as a set of hits which record point-like information along its path based on the position of the bars which are hit. In the data, we cannot know any true information of particles. Instead, we have methods to reconstruct the path, energy, or direction based on the hit information. The reconstruction algorithm  nds 2D tracks in the xz or yz planes  rst by matching reconstructed hits, then 3D tracks are found by matching the 2D tracks. The FGD reconstruction has two goals;  nding hits in the FGDs which match to tracks reconstructed in the TPCs such as muon tracks, and  nding short isolated tracks that start and stop in FGDs such as proton tracks. Since the FGD reconstruction strongly depends on the TPC reconstruc- tion, they share a uni ed algorithm. Before doing the FGD reconstruction, the TPC reconstruction must be done  rst. Once TPC tracks are recon- structed, the tracks are extended into FGDs and matched hits identi ed using the Kalman  lter. Hits which were not used in the FGD-TPC matching process are saved and reconstructed separately. This algorithm identi es short tracks which start and stop in an FGD and therefore are not matched to TPC tracks. A standalone hit clustering algorithm, called a Cellular Automaton, is used 543.5. FGD Software Packages for isolated reconstruction. The method creates segments, which are sets of hits in adjacent layers. If the segments in di erent layers form a quasi- straight line, they are connected together. The sets of connected segments form tracks [63]. FGD reconstruction has several types of objects. Cluster is a collection of hits in space, represents a blob of energy. Vertex is also a collection of hits, but a di erence to Cluster is that hits in a vertex are at the same point in space. If all particles are emerging from a vertex, it could be a primary vertex. If at least one particle enters a vertex and some particles are emerging from it, it could be a secondary vertex. Track is a collection of clusters or hits, which de nes a path of particles. It contains information of position, direction, charge, and curvature. Shower is a path with null curvature. It might represent electromagnetic shower for example. The FGD tracks are split into a few categories.  ttedFgdTpcTracks are TPC-FGD matched tracks. xyFgdTracks, yzFgdTracks, and  tted- FgdTracks are the tracks from the FGD isolated reconstruction in 2D and 3D respectively. These kinds of tracks are fully contained in an FGD. 55Chapter 4 Cosmic Muon Studies 4.1 Introduction 4.1.1 Michel Electron Tagging The neutrino interactions via CC channels can be identi ed by the primary charged lepton in the  nal state, since NC interactions have a primary neu- trino instead of a charged lepton. In CC interactions, we are primarily interested in CCQE interactions because the neutrino energy reconstruction is possible by two-body kinematics. So it is important to distinguish CCQE and non-CCQE interactions. Michel electron tagging is a powerful method for this purpose. For   CC interactions, both CCQE and non-CCQE have muons in the  nal state. We call these primary  . The primary  usually have high enough momentum to exit the FGDs. However, CC1 +, which are the majority of non-CCQE interactions, have additional  + produced via the  resonance. They share energy with the nucleon produced in the decay of the  . Thus the pion typically has less momentum than the muons from CCQE. The pions with low momentum often stop in an FGD and decay to muons. We call these muons secondary  . The secondary  also stop shortly, usually in the same FGD where the pions stop, and decay to Michel electrons. For this reason, the Michel electron tagging can be used to discard non-CCQE interactions. The Michel electron tagging is made by the identi cation of a delayed time bin following the  rst time bin associated to the stopping muon itself. But the problem is that other particles can also make delayed time bins as well. Therefore, other criteria are required to distinguish Michel electrons and non-Michel electrons bins. Figure 4.1 shows the total deposited charge distribution in all delayed time bins for di erent interaction channels in simulated neutrino interactions. Most CCQE (red) interactions have lower charge deposit, while CC resonant pion (light green) and CC DIS (blue) interactions have a noticeable bump with higher charge deposit. It is clear from the plot that eliminating events with delayed time bins having charge 564.1. Introduction Figure 4.1: Charge distribution of all delayed time bins for di erent inter- action channels. deposit higher than 200 PEU (pixel equivalent units, i.e. the number of  red pixels of the MPPCs) will reduce CC1 + without removing CCQE. In conclusion, an event is vetoed as a non-CCQE event if it has more than one delayed time bin and the bin with the highest charge has greater than 200 PEU. However, we may fail to identify a Michel electron, even if there is a Michel electron decay. This is what we are interested in this thesis will be studied using cosmic data. We will look at the Michel electron detection e ciency. The e ciency is de ned as E ciency = Number of stopping  with an identi ed Michel electron Number of all stopping  (4.1) 4.1.2 Cosmic Rays Cosmic rays consist of energetic particles produced in outer space. The composition of cosmic rays depends on which part of the energy spectrum is observed. But, generally, almost 90% of the incoming cosmic rays to the 574.2. Data Set Description Earth are protons. When the protons enter the Earth, they interact with molecules in the atmosphere and produce lighter particles, typically mesons such as pions and kaons. The resulting pions decay to muons in  ight. So cosmic rays produce many muons and can provide a large sample of stopping muons in the FGDs. It allows us to understand how often a Michel electron is found by the FGD time binning method when a cosmic muon stops in FGD1. 4.2 Data Set Description For the analysis, we use cosmic events recorded by the detector at Tokai in 2010. During the data taking, cosmic events are triggered by the external Cosmic Trigger Modules (CTM). ND280 have two CTMs. The FGD cosmic trigger is one of them. We have two FGDs and each FGD has 24 trigger primitives to the FGD CTM. It is organized as a 6 6 matrix as shown in Figure 4.2 [64]. The trigger in its current con guration requires a coincidence between hits in the two FGDs. The CTM generates a trigger that provides cosmic rays that pass deposit energy in both FGDs [65]. The Monte Carlo simulation of cosmic rays is done by the external sim- ulation package called Corsika. Corsika is a computer software package for the simulation of air showers induced by the incoming cosmic rays [66]. The total numbers of events are 82,042 of the MC simulation and 7,697,733 of the data. Note that the MC simulation has much smaller statistics than the data. 4.3 Direction Convention In ND280, the beam direction is along +z axis. Tracks traveling along the beam direction are called forward-going tracks, while tracks in the opposite direction are called backward-going tracks. The scintillator layers in FGD1 are numbered starting from the left with respect to the beam direction. So the left end (upstream) layer is  rst and the right end (downstream) layer is last. In a ND280 event display (See Figure 4.3), the beam direction (+z) is from left to right. The left-most box is TPC1, the next box is FGD1 and the right-most box is TPC3. 584.4. Example Cosmic Event Figure 4.2: The projective tower structure of the FGD cosmic trigger prim- itives [64]. 4.4 Example Cosmic Event While most cosmic rays pass through the whole tracker, some muons stop in one of the FGDs and produce secondary particles such as Michel electrons. Some muons with more vertical trajectories enter the tracker at a large angle and clip the corner of an FGD without stopping. Figure 4.3 shows a through-going event. It spans TPC2, TPC3 and all the FGDs to the P0D. Another through-going event is in Figure 4.4, but with a large angle. Because the ray enters the detector quite vertically, it clips the corners of FGD1 and FGD2. 594.4. Example Cosmic Event Figure 4.3: A going-through cosmic ray. Figure 4.4: A going-through cosmic ray with a large angle. 604.5. Event Selection Figure 4.5: A stopping cosmic ray in FGD1. Then it produces a secondary particle in FGD1. A stopping track is shown in Figure 4.5. The muon stops in FGD1 and produces a secondary particle, a Michel electron. The secondary track is the small blue one at the end of the primary track in FGD1. This kind of event is the type we are interested in. In the following section, we will describe how to select the stopping events. 4.5 Event Selection 4.5.1 Select a Clean Sample of Stopping Muons Select stopping particles Since cosmic rays contain not only muons but also other particles such as electrons, it is important to select a clean sample of stopping muons. This is the control sample to test the Michel electron detection. The sample is de ned through two steps, stopping particles selection and non-muon elimination. The  rst step is to select tracks stopping in FGD1. Basically, this is done by considering the position of the stopping point. Using time bins, the stopping point is determined by the upstream-most hit with respect to the 614.5. Event Selection Figure 4.6: FGD1 on the yz plane. The gray box is the actual FGD1 detector of active layers not including the dark box. The dotted black box is  ducial volume. The solid box, the smallest one, is the de ned box with the reduced downstream z position compared to the  ducial volume. The upstream-most hit of the  rst time bin with the minimum z position must be in the solid box. The boundary in the xz plane is also made in the same manner. beam direction of the  rst time bin. The  rst bin is associated to the track of a cosmic particle entering the detector. The outermost hits are the hits having the minimum z or the maximum z in a bin. That is, each bin has two outermost hits; one with the minimum z and the other with the maximum z. Because the cosmic events are required to go through both FGDs by the FGD cosmic trigger, the tracks that stop in FGD1 are necessarily going in  z with respect to the beam direction. So we use the outermost hit having the minimum z in the  rst bin to designate the stopping point of the cosmic tracks. Figure 4.6 shows the detailed geometry of how tracks which do not stop in FGD1 are vetoed. The dotted box is the FGD1  ducial volume. The  ducial volume is the e ective detection area. It is smaller than the true FGD1 volume. Table 4.1 summarizes the position of the  ducial volume 624.5. Event Selection and the true edge of FGD1. The solid red box in Figure 4.6 is the allowed region. If the upstream-most hit is in the de ned box, it is considered a stopping track. Figure 4.7 shows the minimum z distribution of the  rst time bins in FGD1  ducial volume. The MC (blue triangles) has relatively more tracks stopping in the last several layers. This is believed to be due to a mis-modeling of the FGD trigger in the MC simulation. It is not expected that this discrepancy will a ect the analysis results. So the downstream z should be further upstream than the  ducial volume to make sure the MC simulation and the data are consistent. This discrepancy is currently not understood and will be investigated in the future. In addition, there is a strange peak at the 7th layer ( 190 mm) in the data. This results from a noisy channel in the layer. Some events have only one or two hits in FGD1 and one of the hits is produced the noisy layer. These events are not from actual cosmic events and are not simulated in the MC simulation. The discrepancy will be removed after the event selection cuts. The x or y boundaries are also required based on the plane of the outer- most hit. If the hit is in a xz plane, the y cut does not matter. Otherwise, if the hit is in a yz plane, the x cut does not matter. The cuts remove clipping tracks as shown in the left  gure of Figure 4.8. Even if the minimum z position of the track is within the allowed region, the track does not satisfy the cuts on x or y. FGD1 FGD1 edge (mm)  ducial volume (mm) allowed region (mm) minX -932.17 -874.51 -874.51 maxX 932.17 874.51 874.51 minY -877.17 -819.51 -819.51 maxY 987.17 929.51 929.51 minZ 115.95 136.875 136.875 maxZ 447.05 446.955 350.00 Table 4.1: FGD1 true edge, the  ducial volume cuts and the position of the red box in Figure 4.6. Sometimes, a forward-going track stops in FGD1 and does not have hits on the  rst several layers, as shown in the right  gure of Figure 4.8. In this case, the track is misidenti ed as a backward-going stopping track. So we also require there is a track in TPC2 (between FGD1 and FGD2) but not 634.5. Event Selection Figure 4.7: The distribution of the minimum z position of the  rst time bin in FGD1  ducial volume of the data (black circles) and the MC simulation (blue triangles). Each bin corresponds to each layer. On the last layer, there are events in the MC simulation, but it is too small to appear in the plot. 644.5. Event Selection Figure 4.8: The left is a track that clipped the corner of FGD1. It forms a time bin that looks like a stopping track in FGD1. The right is a forward- going and stopping track. This stops in FGD1, but we do not need this kind of event. in TPC1. Figure 4.9 shows the charge distribution of the  rst delayed time bin for all stopping tracks having more than one delayed time bin. There is a discrepancy near zero charge between the MC simulation and the data, indicating that there are more stopping tracks with low charge in the  rst delayed bin. The very low charge indicates that the delayed bin has only few hits, which may be a form of noise such as after-pulsing of the MPPCs or a broken piece of the  rst time bin that are not simulated in the MC simulation. The data also has large tail with high charge deposit which are not shown in the MC simulation either. The discrepancy is removed after adding other cuts on the TPC2 track. TPC2 track should have enough number of hits to maker sure the track is fully contained in TPC2 and low enough momentum to make sure the tracks are allowed to stop in FGD1.  Number of hits > 60  Momentum < 300 MeV/c Since there are 72 columns in the MicroMegas, we expect a track passing through TPC2 from beginning to end to typically have  72 hits. The 654.5. Event Selection Figure 4.9: Charge distribution of the  rst delayed time bin for all stopping tracks. In the data, there is a large peak near zero. The data is black circles and the MC simulation is blue triangles. Figure 4.10: TPC2 momentum distribution after the geometry cut. 664.5. Event Selection momentum cut was chosen to be as loose as possible to avoid biasing the sample. Figure 4.10 shows the TPC2 momentum distribution after the geometry cut. Most events have momentum less than 200 MeV/c. We chose the cut on 300 MeV/c which is further than 200 MeV/c, so that we do not lose too many events by the cut. Figure 4.11: Charge distribution of the  rst delayed time bin for all stopping tracks after TPC2 quality cuts of the MC simulation (blue triangles) and the data (black circles). Figure 4.11 is the charge distribution after TPC2 quality cuts. The discrepancy is removed, indicating that the cuts reduce the noise in the data. Select stopping  The selected events contain all kinds of stopping particles (i.e. muons and other particles). The next step is to improve muon purity in the events. This is particle identi cation and can be done by TPC pulls based on the energy loss of a particle in TPCs. The pull for a track is de ned via CT . CT denotes the truncated mean of dE/dx, which means discarding the low and high ends of dE/dx distribution. The truncated mean is less sensitive to large  uctuations in the energy loss. It is de ned as 674.5. Event Selection Pull = CmeasT  C exp; Tq  2CmeasT +  2Cexp; T (4.2) where  denotes a particle type, Cexp; T is the expected value of a particle of type  , CmeasT is the corresponding value measured by the TPCs, and  is the standard deviation of the CT distribution. The CT is scaled by the expected variations in the measurement so that its value can be interpreted as the number of standard deviations the measured CT is from the expectation for a given particle hypothesis. Figure 4.12: CT versus momentum distribution. The blue triangles are the measured CT values for electrons, and the red circles are for muons. The lines are the predicted values. The muon line and electron line cross at 120 MeV/c [67]. If Pull is close to zero, the reconstructed object has dE/dx consistent with the particle  . If Pull has a large positive value, the measured CT is larger than the expected CT relative to the expected uncertainty. Otherwise, if Pull has a large negative value, the reconstructed object has much lower measured CT than the expected CT . The latter two cases cannot satisfy the  particle hypothesis. 684.5. Event Selection Figure 4.13: Momentum distribution of the stopping events of the MC simulation (blue triangles) and the data (black circles). The peak is at around 150 MeV/c close to where the  line and e line cross in Figure 4.12. In principle, the TPC pulls can be used to identify particle type by accepting or excluding the particle hypothesis. For example, to select  and reject e, the electron hypothesis is excluded and the  hypothesis is accepted. In other words, events with Pull close to zero will be accepted, while events Pulle close to zero will be excluded. The Pull and Pulle distribution of the stopping events are shown in Figure 4.14 and Figure 4.15. Pull is peaked at zero. However, Pulle dis- tribution has two peaks, one centered at zero and one at slightly negative values. Figure 4.12 shows the mean CT versus momentum for  and e below 300 MeV/c. The markers are measurements of CT from M11 beam test at TRIUMF and the lines are predicted behavior from a model called PAI [68]. The line which follows the triangular markers, which is quite  at, is the expected electron CT from this model. The  line is the curve plot which follows the circular markers. They cross at 120 MeV/c. Figure 4.13 shows the momentum distribution of the TPC2 track for the sample of stopping muons we are using. As we will see later, in the  gure, the left peak (50 MeV/c) corresponds to electrons, while the right peak (150 MeV/c) corresponds to muons. Usually, the cosmic electrons have less momentum 694.5. Event Selection Figure 4.14: Muon pull of the stopping events for the MC simulation (blue triangles) and the data (black circles). Figure 4.15: Electron pull of the stopping events for the MC simulation (blue triangles) and the data (black circles). 704.5. Event Selection than the cosmic muons [69]. The higher momentum corresponding to muons is peaked at 150 MeV/c which is the momentum where the lines cross in Figure 4.12. So it is di cult to separate muons and electrons using CT at this momentum. The next few paragraphs and plots illustrate the di culty in using CT to select muons and reject electrons. Figure 4.16: Muon pull versus electron pull for the stopping events of the MC simulation. Figure 4.16 and 4.17 show Pull versus Pulle plots of the stopping tracks for the MC simulation and the data, respectively. The highest density region is centered at zero Pull . But the stopping tracks also include electron-like events (the low density vertical band centered at zero Pulle). If we reject the band, we also lose some events which are likely muons. In Figure 4.12, CT of muons is larger than that of electrons at momentum higher than 120 MeV/c. If the measured CT is close to the predicted value on the muon line, Pull has a small value near zero, while Pulle is negative. Figure 4.18 shows the pull distribution of the events with momentum lower than 120 MeV/c for the data. These low momentum events are mostly electron-like (red dashed box). But some of them with large positive Pulle might be low momentum muons (black dotted box). Figure 4.19 shows the pull distribution of the events with momentum higher than 120 MeV/c for the data. For the events, the distribution is roughly linear. This is because of the fact that Pull and Pulle are both 714.5. Event Selection Figure 4.17: Muon pull versus electron pull for the stopping events of data. Figure 4.18: Pull versus Pulle for the stopping tracks with momentum lower than 120 MeV/c, which is the intersection point in Figure 4.12 (the data). The events in the dashed red box are electron-like, while the events in the dotted black box are muon-like. 724.5. Event Selection Figure 4.19: Pull versus Pulle for the stopping tracks with momentum higher than 120 MeV/c, which is the intersection point in Figure 4.12 (the data). roughly  at when the momentum is above 120 MeV/c. As discussed previously, the behavior Pulle and Pull in the momentum region of the sample we are using is not much di erent. That is, it is hard to use Pulle to remove electron contamination. Instead of the TPC pulls, we also consider the relation between track length in FGD1 and momentum coming from the TPC2 track. We assume that the track enters from the downstream, so that the track length estimation is based the upstream-most hit in z and the track angle. Figure 4.20 explains how this is done. We used the downstream z of the  ducial volume of FGD1 rather than the maximum z position of the  rst time bin, because we already know where the track is coming from and what the maximum z position should be. We expect typically a muon track is shorter than a electron track at the same momentum because it has higher mass. Figure 4.21 and 4.22 clearly shows two separated dense bands for both the MC simulation and data, respectively. The right band is from  . To only select  , we put two boundaries on either side of the  band. The left line passes the two points (90 MeV/c , 100 mm) and (150 MeV/c , 400 mm). The right line passes the two points (160 MeV/c , 100 mm) and (220 MeV/c , 400 mm). The equations of the lines are 734.5. Event Selection Figure 4.20: The  is a polar angle with respect to the direction of TPC2 track. The z position di erence is calculated by subtracting of the down- stream edge of FGD1 and the minimum z position of the  rst time bin. (d 100 mm) = (400 mm 100 mm) (150 MeV/c 90 MeV/c) (p 90 MeV/c) (4.3) (d 100 mm) = (400 mm 100 mm) (220 MeV/c 160 MeV/c) (p 160 MeV/c) (4.4) where d is the track length in mm and p is the momentum in MeV/c. 744.5. Event Selection Figure 4.21: Track length in FGD1 versus momentum in the MC simulation. Muon candidates are selected between the red dashed lines. Figure 4.22: Track length in FGD1 versus momentum in the data. Muon candidates are selected between the red dashed lines. 754.5. Event Selection The Pull distribution after the track length cut is shown in Figure 4.23. The bump below zero is gone. (See Figure 4.14) and only muon-like events are left. Meanwhile, Figure 4.24 shows Pulle distribution after the cut. The peak at zero corresponding to electrons is removed, but the other peak corresponding to muons remains. Figure 4.23: After the track length cut, muon pull of the stopping events for the MC simulation (blue triangles) and the data (black circles). To be more clear, looking at Figure 4.25 and Figure 4.26, the track length cut successfully removes the tail in Pull and the peak in Pulle which correspond to tracks that are not  . But, the data still has a tail where Pull and Pulle have similar values. To reduce these events, an additional cut requiring jPull j < 2:0 is made. 764.5. Event Selection Figure 4.24: After the track length cut, electron pull of the stopping events for the MC simulation (blue triangles) and the data (black circles). Figure 4.25: After the track length cut, muon pull versus electron pull for the stopping events of the MC simulation. 774.6.  Lifetime Plots Figure 4.26: After the track length cut, muon pull versus electron pull for the stopping events of data. 4.5.2 Select  with a Michel Electron Now we have a clean sample of the stopping  selected from the cosmic events. Finally, to see how many Michel electrons are tagged by the FGD time binning method, we apply the Michel electron cut in the same way as in the   analysis. We identify muons which  have more than one delayed time bin  the highest charge time bin has a charge higher than 200 PEU 4.6  Lifetime Plots The time di erence distribution is expected to be exponentially decaying. The function to  t the distribution of the time di erence is de ned as f( T) = p0 + p1  e   T=p2 (4.5) where  T is the reconstructed time di erence of the  rst bin and the delayed bin with the highest charge. The p0, p1, and p2 would be determined using a  t to the data. p0 accounts for any remaining background such as cosmic 784.7. Summary of Selection Cuts rays within the same event that is  at in this time di erence. p1 depends on the size of samples and p2 represents the mean lifetime of muons. A time bin has the minimum/maximum time of hits within the time bin and the bin time is de ned as the average of the two times: BinT = minT + maxT 2 (4.6) The   lifetime in carbon is 2.02  s [70]. In the B- eld perpendicu- lar to the beam direction, the backward-going positive particles are bent downwards and leave the detector before stopping in FGD1. Hence, most  stopping in FGD1 are negative. Sometimes the   might be captured by a nucleus. In these cases, there is no Michel electron, thus the   lifetime is shorter than the normal  lifetime of 2:2  s. Since the capture process does not produce a Michel electron, the Michel electron cut does not actually fail to identify a Michel electron. As the result, the Michel electron detection e ciency will include the capture rate as part of the ine ciency in these cases. Element Mean lifetime(ns) Total capture rate(s 1) C 2020 20 44 10 103 O 1812 12 98 3 103 Table 4.2:   lifetime and capture rates in di erent materials [70]. The   lifetime of the MC simulation, measured by the stopping  with a Michel electron, is in Figure 4.27. The  tted value of the lifetime is 2.22 0.17 s. While the MC simulation has low statistics, it is consistent with the expected lifetime. For the data, the lifetime is 2.05 0.03 s, con- sistent with the actual muon lifetime. 4.7 Summary of Selection Cuts To understand the Michel electron detection e ciency, it is necessary to  rst have a pure sample of stopping muons. The  rst two cuts, geometry and TPC2 quality, are to veto non-stopping particles. The next two cuts, track length and Pull , remove electrons, which are not expected to produce Michel electrons. The last cut is the current Michel electron cut used in the current   CCQE selection. Up to the fourth cut, the stopping muon 794.7. Summary of Selection Cuts Figure 4.27: Bin time di erence for stopping  with a Michel electron (the MC simulation). Fit with Equation 4.5. purity is improved. Afterwards, only the muons with a Michel electron are identi ed by the Michel electron cut. 1. Select stopping events  Geometry The outermost hit of the  rst bin have to be in the box de ned in Figure 4.6  TPC2 Quality No TPC1 track and 1 TPC2 track Number of hits in TPC2 track > 60 Momentum of TPC2 track < 300 MeV/c 2. Select  in the stopping events  5( mmMeV/c)(p  160 MeV/c) + 100 mm < d < 5( mm MeV/c)(p  90 MeV/c) + 100 mm 804.8. Data and MC Simulation Comparison Figure 4.28: Bin time di erence for stopping  with a Michel electron (the data). Fit with Equation 4.5.  jPull j < 2:0 3. Select  with a Michel electron in the stopping  events  Charge deposit in one of the delayed time bins should be larger than 200 PEU 4.8 Data and MC Simulation Comparison Now we look at how many events survive after each cut with the MC sim- ulation compared to the data. The numbers of events passing each cut are summarized in Table 4.3. In this section, the fractional number of events is de ned relative to the events passing the previous cut: Fractional number of event = number of events passing the cut number of events passing the previous cuts (4.7) 814.8. Data and MC Simulation Comparison MC data Events Fraction Events Fraction Total Events 82,042 7,697,733 Geometry 15,941 0.194 801,432 0.104 TPC2 quality 3,339 0.209 96,487 0.120 Length in FGD1 1,909 0.572 50,396 0.522 Pull Muon 1,636 0.865 43,618 0.866 Charge Sum 1,051 0.642 25,865 0.593 Table 4.3: The numbers of events passing single cut. The fraction takes a ratio of the number of events passing a cut to the number events passing the previous cut. Figure 4.29: The distributions of the minimum z position of the  rst time bin of the MC simulation (blue triangles) and the data (black circles). Figure 4.29 shows the distributions of the minimum z position of the  rst time bin for all total cosmic events. Almost 60% events are at 110 mm for both the MC simulation (blue triangles) and the data (black circles). These are through-going events. By applying the geometry cut, the through-going events are rejected. The fraction of events surviving the cut as a function of the minimum z 824.8. Data and MC Simulation Comparison position is shown in Figure 4.30. This ratio shows how the cuts a ect the data and the MC simulation. The events stopping at the last couple of layers are also removed by the reduced downstream z cut. Figure 4.30: The fractional number of events after the geometry cut as a function of the minimum z position of the  rst time bin for the MC simulation (blue triangles) and the data (black circles). After the TPC2 quality cut, the fractional number of events of the MC simulation and the data do not agree as shown in Figure 4.31. Fewer events in the data pass the TPC2 cut compared to the MC simulation, so there is a background present in the data that is not present in the MC simulation which increases the denominator. This is consistent with the result that the MC simulation/the data discrepancy on the charge distribution has been eliminated by the cut. The data also has worse resolution so the fractional number of events in the data may be worse. Figure 4.32 shows the fractional number of events after applying the muon selection cuts, which are the track length cut and the pull muon cut. Now the fractional number of events looks more similar. But it seems that the fractional number of events is higher for the MC simulation for longer tracks. As shown in Figure 4.26, there are more contamination in the data after the geometry cut, the TPC cut, and the track length cut, while there are not in the MC simulation. Therefore, less events in the data pass the pull muon cut. This causes the lower fractional number of events in the 834.9. Result Figure 4.31: The fractional number of events after the TPC cut as a function of the minimum z position of the  rst time bin for the MC simulation (blue triangles) and the data (black circles). data. Finally, the top of Figure 4.33 shows the fractional number of events after the Michel electron cut, which is the Michel electron detection e ciency in FGD1. 4.9 Result The bottom plot in Figure 4.33 shows the minimum z position distribution of the  rst time bin of the MC simulation (blue triangles) and the data (black solid line). The minimum z of FGD1  ducial volume is 136.875 mm and the maximum z is 446.955 mm. The top plot is the e ciency as a function of the minimum z position. Over most of the z range, the MC simulation (blue triangles) and the data (black circles) agree reasonably well. The total numbers of cosmic events are 82,042 for the MC simulation and 7,697,733 for the data. In the MC simulation, 1,636 stopping  were identi ed, of which 1,051 events passed the Michel electron cut, resulting in an e ciency of 0.642 0.012. Meanwhile, in the data, 43,618 stopping  were identi ed, of which 25,865 events are left. The e ciency is 0.593 0.003 (See Table 4.3). 844.10. Implications for the Neutrino Interactions Figure 4.32: The fractional number of events after the muon selection cuts, the track length and pull muon, as a function of the minimum z position of the  rst time bin for the MC simulation (blue triangles) and the data (black circles). The data e ciency is lower than the MC simulation e ciency and the di erence is 0.087 0.012. The di erence is calculated as Di erence = (MC E ciency) (data E ciency) data E ciency (4.8) 4.10 Implications for the Neutrino Interactions Michel electron studies using time-bin analysis in the neutrino beam are di cult because the beam data has background in which there are delayed time bins not due to Michel electrons. So we used cosmic events. Cosmic muons have a well known behavior in the detector and are abundant compared to the neutrino interactions, allowing a high statistics study. The purpose of the study is to estimate how often a Michel electron is found when  stops in FGD1 and how di erent the detection e ciency is in the data and the MC simulation. Using the result, we can infer how many events the Michel electron cut will remove in real beam data compared to the beam MC. 854.10. Implications for the Neutrino Interactions Figure 4.33: The top  gure is the  nal e ciency as a function of the mini- mum z position of the  rst time bin. The bottom  gure is the corresponding z distribution of the  nally selected events. The numbers of events are nor- malized to 1. Blue indicates the MC simulation and black is the data. 864.10. Implications for the Neutrino Interactions 4.10.1 The Inclusive CC Selection The majority of neutrino interactions are CC interactions. The   analysis starts from the inclusive   CC selection. Since the incoming   are trans- formed to   via W+ boson, the   CC interactions can be identi ed by the outgoing   . That is, the main idea to select inclusive CC events is identify   -like particles with high momentum in the FGD  ducial volume. The CC selection cuts are  the highest momentum track in the event should be negative  the highest momentum track in the event is required to have muon PID The muon PID cut is based on the PID likelihood, which is de ned as Likelihood = Prob( ) Prob( ) + Prob( ) + Prob(p) + Prob(e) (4.9) The PID is based on the TPC dE/dx. To be a muon track, the track has to be satisfy Likelihood > 0:05. Figure 4.34: Momentum distribution of the highest momentum tracks for negative (left) and positive (right) tracks [71]. Muons are in red and protons are in black. Figure 4.34 shows the momentum distributions of the highest momentum tracks for negative and positive tracks [71]. As shows in the left  gure in red, the negative tracks with the highest momentum are mostly muons. The inclusive CC selection selects 88.83% of all   CC interactions in Run 1 (from Jan. 2010 to Jun. 2010) and 88.99% in Run 2 (from Nov. 2010) according to the MC simulation. The result is shown in Table 4.4. 874.10. Implications for the Neutrino Interactions Run 1 Run 2 CC 88.83% 88.99% NC 2:93 0:31% 2:75 0:31% interactions in 7:55 0:77% 7:57 0:49% non-Fiducial anti-neutrino 0:69 0:24% 0:75 0:16% interactions Table 4.4: The inclusive CC   selection result [72]. After the inclusive CC selection, the next step is to separate CCQE and non-CCQE interactions in the inclusive CC samples. In general, CCQE interactions produce a negative muon and a proton in the  nal state, while CC1 + have an additional pion. The pion usually has less momentum than a muon from CCQE, so it often stops and decays to a muon in an FGD. The muon typically stops and decays to an electron. Using these characteristics, further cuts are used to select CCQE from the events passing the inclusive CC cuts [71].  not more than 2 tracks in the event  one negative track  no Michel electrons Figure 4.35 shows an example of CCQE interactions with two global tracks. After CCQE selection, the CCQE e ciency and purity are 38.9% and 71.5% respectively. 4.10.2 Conclusion In the MC simulation, after the inclusive CC   selection, 1,706 events are left. The current Michel electron cut removes 85 events. According to the study, the e ciency in the data is 8.7% lower than the MC simulation, so we expect 77 events will be removed in the data. The change of 8 out of 1,706 events is a 0.5% systematic error. The numbers in the MC simulation are normalized to the data POT. 884.10. Implications for the Neutrino Interactions Figure 4.35: An example of CCQE interactions with two tracks [72]. 89Chapter 5 Conclusion In this thesis the e ciency of Michel electron detection has been discussed. Cosmic rays provide a large sample of muons with which to test the Michel electron identi cation e ciency. If a muon stops in FGD1 and decays, there is a Michel electron. The Michel electron can be identi ed by the FGD time binning algorithm. Since muons in FGD1 are most after negatively charged, sometimes a stopping muon does not produce a Michel electron by the cap- ture process. This process is well understood so it should be accurately reproduced by the MC simulation. By identifying a clean sample of muons stopping in FGD1 and determining how often a Michel electron is detected, one can measure the e ciency for the Michel electron reconstruction. Because cosmic rays have non-muon particles as well, it is necessary to identify a clean muon samples  rst. The stopping tracks are identi ed by the location of the downstream-most hit. The downstream-most hit must be in the allowed region, which is de ned as the FGD1  ducial volume with more stringent downstream z cut. We require that there is a track in TPC2, but that there is no track in TPC1. The TPC2 track should have more than 60 hits, and momentum lower than 300 MeV/c. To reduce non-muon contamination in the selected stopping sample, par- ticle identi cation using the TPC2 pull, which is based on dE/dx measure- ments, and the track length are used. We require the cut on the muon pull, jPull j < 2:0. Meanwhile, the track length cut is also required. Since electrons travel further in FGD1 before stopping than muons at the same momentum, we can distinguish electron and muons based on track length in FGD1 and momentum relation. With these cuts, we obtain a clean sample of stopping muons that are selected independently of the Michel electron cut. Finally, the Michel electron requirement is applied to the sample to see how many muons have Michel electrons and how well the MC simulation and the data agree. 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