Wing Sheung Chan

22 The Standard Model and lepton flavour violation 1.3.2. Supersymmetry Supersymmetry (SUSY) [41, 42] is a conjectured symmetry that relates fermions and bosons, the two fundamental types of particles. It is an extension to the SM Poincaré symmetry of spacetime. The fundamental idea of SUSY is that for each SM particle, there exists a superpartner, also known as sparticle. The SM particles and their corresponding superpartners carry exactly the same quantum numbers, except for their spins, which are always different by a half-integer. This means that superpartners of fermions are always bosons, and vice versa. If it exists, SUSY could provide an elegant solution to many of the puzzling problems in modern physics. One of which is the hierarchy problem. In a supersymmetric theory, contributions from SM particles and their superpartners to the quantum corrections of the Higgs boson mass can cancel each other. This allows the smallness of the observed Higgs boson mass compared to the Planck scale to be explained without a miraculous fine tuning. With an additional discrete symmetry known as the R-parity, which forbids the decay of the lightest sparticle, SUSY could also provide us with a promising dark matter candidate. Supersymmetric theories typically have many free parameters. Even in the Minimal Supersymmetric Standard Model (MSSM), which only extends the Standard Model minimally by adding the smallest possible number of supersymmetric particles and interactions, has over 100 parameters. The high dimensionality of SUSY models make them very difficult to search for or constrain. The lack of evidence so far has made SUSY much less popular among physicists than it was decades ago. Nonetheless, popularity is no indication of truth, and SUSY still remains a possible candidate of undiscovered BSM physics. Like in the SM, superpartners of leptons, or sleptons ( ˜ ` ), can also have flavour mixing. In some particular models, such as the minimal supergravity model (mSUGRA) with seesaw mechanism, charged slepton flavour mixing can be sizeable [43] . The large flavour mixing can be realised by their additional contributions to the amplitudes of LFV processes. A study has shown that, subject to constraints from existing measurement of neutrino oscillation and ` → ` 0 γ decays, slepton flavour mixing could enhance the branching fraction of LFV Z decays to up to 10 − 8 [44] . 1.3.3. Extended Higgs sector The SM has only one single Higgs doublet. However, that is merely the simplest hypothesis one can assume in order to explain the electroweak symmetry breaking and the mass generation of fermions. There is no reason why Nature cannot be more complex and have multiple Higgs doublets or even multiplets. In fact, there are a number of BSM models that have extended Higgs sectors, which include, for example, the aforementioned MSSM. The most studied model with an extended Higgs sector is probably the Two-Higgs-doublet model (2HDM) [45] , the next simplest case to having only one Higgs doublet. Just by adding an extra Higgs doublet, the 2HDM could already allow many more phenomena than by the SM. This can be appreciated from the fact that there are five physical Higgs boson in the 2HDM, compared to just one in the SM. The five bosons consist of two CP-even