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Studies on the Performance of the Simulated Mu3e Detector Studies on the performance of the simulated Mu3e detector Sean Hughes 201111055 First year PhD report Under the supervision of Dr Nikolaos Rompotis At the Faculty of Science and Engineering Department of Physics 2020 Contents 1 Literature review 1 1.1 Muon Physics . .1 1.2 Mu3e Physics . .4 1.3 Concluding remarks . .6 2 Mu3e Detector and Simulation 7 2.1 Mu3e Detector . .7 2.2 Track reconstruction . .8 2.3 Vertex reconstruction and selection . 10 2.4 Concluding remarks . 15 3 Detector performance studies 16 3.1 Improvements to the tile and fibre detector timing resolution . 16 3.2 Fibre timing efficiency . 21 3.3 Tile timing efficiency . 22 3.4 Charge misidentification . 23 3.5 Concluding remarks . 27 4 Summary 28 Bibliography 28 Appendices 31 A 32 A.1 Fit definitions . 32 A.2 Extra figures . 32 i Chapter 1 Literature review This chapter will provide an introduction to both the physical properties of the muon, and the processes that govern its interactions and dominant decay modes. Experimental searches for exotic decay modes of the muon are also summarised, and an outline to their potential physical significance is provided. The physics entailed within the Mu3e experiment is also introduced, describing not only the basic premise of the experimental procedure and the goals of the experiment, but also the unique kinematic qualities of the µ ! eee decay. Descriptions of the several types of background are also provided. 1.1 Muon Physics The Standard Model of elementary Particle Physics (SM) [1] is a description of elementary particles and their interactions, based on gauge theories. The SM Lagrangian is the result of the combination of symmetries of the Electromagnetic, Weak (together described by symmetry breaking in the Electroweak theory), and Strong interactions. Leptons are defined as elementary particles with half-integer spins that do not undergo Strong interactions, and each lepton is associated with a particular `family' of leptons defined by the quantum number `lepton flavour'. Experimentally, three generations of leptons have been observed: electronic, muonic and tauonic leptons. Lepton flavour number is currently a symmetry in the SM Lagrangian, and is therefore a conserved quantity between leptons in the context of the SM. However, lepton flavour violation was first conclusively demonstrated in the form of neutrino oscillations, implying that neutrinos carry mass, at Super- Kamiokande [2], and has been the subject of extensive study in many other experiments. As a 1 (a) Michel decay (b) Radiative Michel decay (c) Internal conversion Figure 1.1: Lowest order Feynman Diagrams for various decay modes of the muon. consequence, therefore, lepton flavour is known to only be an approximate symmetry, and one which must be accounted for in the SM. With the discovery of lepton flavour violation for neutral leptons, it is possible for similar phenomena to occur at some level for charged leptons. An observation of which would imply the need for further additions to the SM. The muon is an elementary particle, with properties defined in table 1.1. Discovered in 1936 in cosmic rays by Anderson and Neddermeyer [3], the first calculation of the energy distribution of electrons from an observed decay mode of the muon was completed by Louis Michel in 1950 [4], who postulated that the muon would decay into an electron and two neutrinos (the decay mode which is now named `Michel decay' of the muon). Three dominant decay modes are experimentally observed: the Michel decay (µ ! eνeνµ), radiative Michel decay (µ ! eγνeνµ) and through internal conversion (µ ! eeeνeνµ). Lowest order Feynman diagrams describing these interactions are shown in figure 1.1, and a summary of the decay modes is presented in table 1.1, with their associated branching fractions. Much rarer decay modes of the muon are believed to exist, but the decays are heavily suppressed in the SM due to the fact that lepton flavour is conserved to a higher suppression. Examples include: muon to electron conversion (detected in µN ! eN, interactions, where N is an atomic nucleus), muon to electron gamma conversion (detected in µN ! eNγ interactions) and µ ! eee. The latter of which is the subject of study within this report, and has a branching fraction less than 1 × 10−50, with the decay mediated by an oscillating neutrino. For a muon that decays at rest, the differential probability of an electron decay product with energy E and momentum ~p in direction θ (polar angle) with respect to the spin of the muon is given by: d2Γ(x; θ) / (3 − 2x)x2 + q P (2x − 1)x2 cos θ; (1.1) dxd cos θ µ µ 2 where x = 2E=Emax, Pµ represents the polarisation of the muon, and qµ represents the charge. Several experiments have utilised the muon as a means to search for physics beyond the SM frame- work. One of the first measurements attempting to observe lepton flavour violating decay modes of the muon involved muon to electron conversion and muon to electron-gamma conversion exper- iments. Two such experiments, both involving atoms of copper, were conducted at the University of Liverpool, constraining the decays µCu ! eCu to a branching fraction of 2.2 ×10−7 [7], and, µCu ! eγCu to 7.5 ×10−6 [8], both at 90% confidence level. These decays have since been con- strained further by more modern, advanced experiments such as MEG (Muon to electron-gamma) and SINDRUM II (muon to electron conversion). As lepton flavour is a quantity currently con- served within families in the SM, an observation of one of these decay modes would be a clear indication that the symmetry is not only broken for neutral leptons, but for charged leptons too. Potential decay modes that are currently explored include: µ ! eγ, µN ! eN, and µ ! eee. Their constraints on the relevant branching fractions are shown in table 1.2. Other experiments include the g − 2 experiment, which aims to measure to a precision of 140 ppb (parts per billion) the anomalous magnetic moment of the muon. The currently available experimental result has a discrepancy with respect to the SM calculation that is about 3 standard deviations. The experiment was first conducted at CERN [12], with results confirming quantum electrodynamics. The latest results from the Brookhaven National Laboratory confirms this 3σ discrepancy with a precision of 0.5 ppb [13]. A new experiment is now being conducted at Fermilab [14]. Property Value Decay mode Branching fraction (%) 2 + + mµ [MeV/c ] 105.6583745(24) µ ! e νeν¯µ ∼ 100 1 + + + − −5 Spin 2 µ ! e e e νeν¯µ (3:4 ± 0:4) × 10 + + −8 Charge +1 µ ! e γνeν¯µ (6:0 ± 0:5) × 10 −6 τµ [s] 2:1969811(22) × 10 Table 1.1: A summary of both the physical properties and parameters that define the muon [5] and prominent decay modes [6]. The branching fraction quoted for the radiative Michel decay (µ ! eγνeνµ) only includes events with electron and photon energies greater than 45 MeV and 40 MeV, respectively. 3 Decay mode Branching fraction (%) 90% CL Reference µ ! eγ < 4:2 × 10−13 [6] µ−N ! e−N µ−Ti ! e−Ti < 6:1 × 10−13 [9] µ−Pb ! e−Pb < 4:6 × 10−11 [10] µ−Au ! e−Au < 7:0 × 10−13 [11] µ ! eee < 1 × 10−12 [6] + + µ ! e ν¯eνµ < 1:2% [6] µ ! eγγ < 7:2 × 10−11 [6] Table 1.2: Constrained branching fractions of active searches for CLFV muon decay modes. 1.2 Mu3e Physics The Mu3e experiment aims to constrain the branching fraction of the charged lepton violating anti- muon decay, µ+ ! e+e+e−, up to a sensitivity of 10−16. This final sensitivity is four magnitudes better than the existing result obtained by the SINDRUM collaboration [15]. The core elements of the experiment include the generation of a slow beam of muons which come to rest on a hollow double-cone target inside a cylindrically symmetric detector. The muons subsequently decay, and their decay products are detected by the Mu3e detector. The Mu3e detector is placed within a magnetic field pointing in the direction of the beampipe. This magnetic field is produced by a solenoidal magnet, and serves the purpose of measuring the charge and momentum of the produced electrons and positrons. The magnetic field has a value of 1T along the direction of the muon beam. The electron and positron decay products will pass through the multiple cylindrical layers of the experiment. The silicon pixel tracker layers will register the hits, and will be used in track reconstruction through triplet construction. Following this, the tracks are then back-propagated towards the target where vertex reconstruction is then conducted. The Mu3e experiment is currently planned to conduct the experiment in two main phases. Phase I of the experiment will use the central station together with two `recurl' stations. These recurl stations are responsible for the detection of recurling particles, and will contain an extra two silicon pixel tracker layers, and will contain within itself the scintillating tile layer, which is used for timing, providing a ∼60 ps timing resolution. The first phase of the experiment will make use of the πE5 proton beamline at the Paul-Scherrer institute (PSI), which currently provides a muon stream of rate 2 × 108 µ+=s, with 27 MeV. This implies for the experiment a sensitivity of 1 in 4 1015 muon decays at 90% CL. Phase II of the experiment will utilise the high intensity muon beam upgrade, which will be providing a muon beam rate of at least 109 µ+=s [16]. This will improve the sensitivity obtained by the experiment to an order of 10−16 at 90% CL.
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