Search of second family related charged vector like leptons at muon colliders

Vector-like leptons (VBLs) are predicted by the E6 Grand Unified Theory and the Flavor Democracy Hypothesis, and they can potentially address issues such as the mass hierarchy in the Standard Model (SM). Muon colliders offer advantages in the detection of VBLs due to their achievable center-of-mass energy, luminosity, and precision. The mass limit for charged VBLs was determined to be 101.2 GeV in LEP experiments. This thesis investigates the detection probabilities of charged VBLs associated with the second SM family leptons at muon colliders with center-of-mass energies of 3-6-10-14 TeV, by calculating the cross sections. It was found that in pair production, masses up to the kinematic limit (1.5-3-5-7 TeV) can be probed, while in single production, second-generation charged VBLs can be investigated up to near the center-of-mass energy for mixing angles greater than 0.0035. If VBLs are detected in single production, the mixing angle will be determined if it is greater than 0.0035. For muon colliders, pair production at center-of-mass energies of 6-10-14 TeV and single production at all investigated energies can probe charged VBL masses significantly beyond the mass limits reached by the LHC.