Study of the sensitivity of CMS to the lepton flavour violating neutrinoless $\tau$ decay $\tau \to \mu\mu\mu$

The world largest proton-proton collider, the Large Hadron Collider (LHC), which was built up at CERN in the near of Geneva, will start its operation in summer 2009. The total τ lepton production cross-section for the CMS experiment, at a center-of-mass energy of 14 TeV, is about 140 μb. Assuming an integrated luminosity of 10 fb−1 per year, which is expected to be reached in the low luminosity phase of L = 2 × 1033 cm−2 s−1 , about 1012 τ leptons are produced in total. This copious τ production at the LHC provides an excellent potential for the search of neutrinoless and therefore lepton flavour violating τ decays. It is already known since the experimental discovery of neutrino oscillations, that the conservation law of the lepton family number is not strict. The neutrino oscillations have dramatic consequences for the picture of leptons in the Standard Model. The neutrinos become massive particles, the mass eigenstates differ from the flavour eigenstates and a mixing matrix similar to the CKM matrix in the quark sector is introduced. The neutrino mixing also gives rise to neutrinoless τ decays in the Standard Model. However, the τ → μμμ decay is heavily suppressed by the GIM mechanism (Br ∼ 10−50) and therefore not measurable with current experiments. The observation of such a lepton flavour violating τ decay will be an unambiguous sign of new physics beyond the Standard Model. There are a large number of models beyond the Standard Model which give rise to the lepton flavour violating τ → μμμ decay, partially with branching ratios close to the current experimental upper limit of Br(τ → μμμ) < 3.2 · 10−8. The τ → μμμ decay is an alternative option in search of new physics. After a brief introduction of some of these models, the Large Hadron Collider, as well as the CMS experiment, and the Monte Carlo simulation methods used in this thesis are described. Furthermore the reconstruction algorithms and trigger paths, which are required for the study of the τ → μμμ decay, are presented. A possible improvement of the reconstruction of τ → μμμ events using an alternative muon identification, as well as a possible increase of the trigger efficiency using a dedicated τ → μμμ trigger algorithm are pointed out. Moreover a Monte Carlo study of the influence of different models on the reconstruction of τ → μμμ events is presented and also a possible separation of the models is discussed. The results of this study have been achieved in close collaboration with the theory department. In the last part of this thesis, the production of τ leptons in CMS, possible backgrounds of this study, the signal selection and the determination of the sensitivity are described.