Wing Sheung Chan

The Standard Model and lepton flavour violation 19 Evidence against lepton flavour universality In the SM, the three generations of leptons have exactly the same behaviours and properties except for their masses (or in other words, their interactions with the Higgs field). This is known as lepton flavour universality (LFU). In recent decades, multiple experiments have shown clues that point to the possibility of the violation of LFU. The most intriguing ones are the anomalies in semi-leptonic B -meson decays: deviations of the values of R ( D ∗ ) = B ( B 0 → D ∗ 0 τ − ¯ ν ) / B ( B 0 → D ∗ 0 µ − ¯ ν ) and R ( K ∗ ) = B ( B 0 → K ∗ 0 µ + µ − ) / B ( B 0 → K ∗ 0 τ + τ − ) measured by the BaBar, Belle and LHCb experiments [29– 34] from the SM-predicted values. The combined measurement for R ( D ∗ ) has a discrepancy of 3 . 08 σ with the SM prediction [35] . These are sometimes referred to as the B - anomalies. Although these deviations are not statistically significant enough to conclusively rule out LFU, they do hint at a possible flaw in the SM and a direction for us to look for New Physics. These problems have motivated the construction of many beyond-the-Standard-Model theories. Some of them will be discussed in the following section. 1.3. Lepton flavour violation in BSM theories Neutrino mixing implies that the lepton family numbers could not be conserved quantities. However, when only point interactions of charged leptons are concerned, lepton family numbers are approximately conserved. Violation of this approximate conservation is termed (charged) lepton flavour violation. Examples of lepton-flavour-violating (LFV) processes include µ → eγ , τ → µµµ , and the processes that are in the spotlight of this thesis: Z → eτ and Z → µτ . The transition amplitudes of these processes are heavily suppressed by a factor of m 2 ν /m 2 W when they are solely induced by neutrino mixing in the SM. As a result, LFV decays typically have an expected branching fraction 1 × 10 − 50 [36, 37] . Such a vanishingly small branching fraction is beyond reach of any experiments, even in the distant future. This makes any observation of LFV processes an unambiguous signal of BSM physics. There are many interesting BSM theories that can give rise to much more sizable amplitudes for LFV processes. These theories are often motivated by unsolved problems in physics, such as those listed in Section 1.2.6. Searches of LFV processes could help us constrain these theories and potentially point us in the right direction of solving these problems. In this section, the main ideas and motivations of a handful of popular (histori- cally or currently) types of models will be discussed: heavy neutrinos, supersymmetry and extended Higgs sector. 1.3.1. Heavy neutrinos and the seesaw mechanism As mentioned earlier, experiments have confirmed that neutrinos indeed have finite rest masses. Nonetheless, the origin of their masses is still unknown. In QFT, fermions can