Wing Sheung Chan

24 The Standard Model and lepton flavour violation 1.4. Lepton-flavour-violating Z → `τ decays Hopefully by now, a compelling argument has been made that lepton flavour violation is an interesting BSM phenomenon and searches for it are important for finding or constraining New Physics. But with that comes the natural question of where and how to search for lepton flavour violation. BSM models predict various possible LFV processes and physicists have designed and run experiments to search for many of them. These searches are sensitive to different BSM models, mass scales and lepton flavours, and complement each other. Ultimately, it is the interplay of these searches that teaches us about potential BSM physics. Table 1.9 summarises some of the search channels and their current most stringent limits. While all of the searches are important in their own ways, this thesis focuses particularly on the Z → `τ decays (here and from now on, ` will be used to denote a light lepton, i.e. e or µ , but not a τ lepton). These decays are interesting for a number of reasons. LFV Z decays are interesting both theoretically and experimentally. Theoretically, the massiveness of the Z boson relative to leptons or hadrons would make its decays much more sensitive to BSM physics at a higher energy scale. Assuming that LFV Z decays are induced by loops involving undiscovered particles that are much heavier than the Z rest mass m Z , it can be shown that the effective LFV coupling (branching fraction) would be proportional to m 2 Z ( m 4 Z ), whereas in τ → µµµ it would be proportional to the much smaller m 2 τ ( m 4 τ ) [61] . Experimentally, Z decays are interesting because of the abundance of Z bosons produced at the Large Hadron Collider. The Z boson production cross section in pp collisions at √ s = 13 TeV times the single-charged-lepton-flavour branching fraction has been measured to be 1 . 91 nb [62] . This means that roughly eight billion Z bosons have been produced in the second operational run of the Large Hadron Collider for the ATLAS detector. Such an abundance is essential in providing the necessary statistical power for rare decay searches. The massiveness of the Z boson is also an experimental advantage. While the Large Hadron Collider produces a lot of hadrons and τ leptons, for ATLAS and CMS, their momenta are often too low for meaningful analysis. The high mass of the Z boson, however, ensures that its decay products are boosted in the laboratory frame of reference. This allows for a much higher trigger and reconstruction efficiency compared to hadrons or τ decays searches. The Z boson has three possible LFV two-lepton decay modes, namely eµ , eτ and µτ . There is no necessary correlation between these decay modes. The eµ decay mode generally receives much less attention than the other two. This is mainly because in most models, the precise results from low-energy µ → eγ experiments have already set an indirect limit on B ( Z → eµ ) that is much more stringent than a direct search at the Large Hadron Collider can possibly achieve. Using Effective Field Theory, the limit on B ( µ → eγ ) can be translated into an indirect limit of B ( Z → eµ ) . 10 − 10 [61] . Nevertheless, direct searches of Z → eµ should still be appreciated as concrete confirmation of the µ → eγ indirect limit. In this thesis, however, focus is given to the other two decay modes which have a τ lepton in the final state. With the sensitivities of existing LFV τ decay searches, there is currently no stringent indirect limit on B ( Z → `τ ) . This makes the search for Z → `τ