SEARCH FOR τ → 3μ  WITH τ - LEPTONS PRODUCED IN D AND B DECAYS USING FULL RUN II DATA AND THE EFFECT OF GEM DETECTOR FOR RUN III WITH RESPECT TO THE BACKGROUND AT CMS

A study of the decay of τ → 3μ using full LHC Run II data with a special  consideration on  B and D decays, and an update of the detector with Gas Electron Multiplier (GEM) detectors  of the Compact Muon Solenoid (CMS) experiment at the Large Hadron Collider (LHC) is presented. The Standard Model (SM) of particle physics describes the known particles and  their interactions with great success. Charged lepton flavour-violating decays like, τ → 3μ decays are not predicted in the SM. Even in the extended SM with massive neutrinos, it is highly suppressed. This makes it a sensitive channel to search for new physics Beyond the Standard Model. An important part of this work is the development and validation of Gas Electron Multiplier (GEM) detectors at CMS, in particular GE1/1 chambers. A robust production and qualitycontrol process was set in place, providing a template for the subsequent GEM projects. Long-term leakage current tests showed that the chambers can tolerate high voltage with fewer than one trip per chamber per hour, and only one chamber out of the full production failed the gas leak test. Tests of efficiency, gain  and uniformity showed that the detectors meet their design goals; non-uniformities found during efficiency measurements were traced to readout non-planarity, and planarity verification was introduced during component inspection. Proper grounding schemes were also found to be important for controlling noise rates, allowing the chambers to be operated at thresholds as low as 8 fC under laboratory conditions, with further improvement expected under CMS conditions. Overall, the GE1/1 detectors demonstrated reliable, long-term performance and met their design expectations. The thesis also develops a simulation framework using ANSYS, Garfield++, GEANT4, and FLUKA to study GEM detector performance and backgrounds. These simulations reproduced earlier results, confirmed detector efficiency at nominal geometry, and matched well with slice test measurements. Although such simulations are time-consuming, CERN’s grid computing system made the process fast and efficient, and the framework can be extended to other detector at LHC. Using 33.2 fb⁻¹ of 2016 CMS data, an upper limit on B(τ → 3μ) of 8.0×10⁻⁸ at 90% CL was set. The 2017 and 2018 CMS Run II dataset, accounting for 97.7 fb⁻¹ at a centre-of-mass energy of 13 TeV, was then analysed for the τ → 3μ decay in the heavy-flavour channel, carried out as part of this work, finding no evidence of the decay and setting observed (expected) upper limits of 3.4(3.6)×10⁻⁸ at 90% CL. Combining this with the 2016 dataset and the W boson channel,analysed independently, gave the final observed (expected) limits of 2.9(2.4)×10⁻⁸ at 90% CL. This thesis demonstrates how advanceddetector technology, reliable simulations, and precise data analysis work together to push the sensitivity of rare decay searches. The results provide an important benchmark and a foundation for future searches at CMS during Run III and the High-Luminosity LHC, where the upgraded GEM detectors will play a central role in exploring new physics.