Wing Sheung Chan

The Standard Model and lepton flavour violation 11 The gluon is an electrically neutral massless gauge boson that mediates the strong force. Gluons interact only with particles that carry colour charges, which include all the quarks as well as gluons themselves. Gluons and quarks are constituents of hadrons. In such context, they are both referred to as partons. The theory that describes the strong interaction in the Standard Model is called quantum chromodynamics (QCD). The Higgs boson The last elementary particle to be introduced is the Higgs boson ( H ), a neutral spin-0 boson. It is neither a matter particle or a force carrier, and is the only scalar particle in the SM. The existence of the Higgs boson has been conjectured more than half a century ago [10– 15] . It was discovered by the ATLAS and CMS experiments in 2012 [16] , which completed the search for all elementary particles in the SM. The discovered Higgs boson has a rest mass of (125 . 1 ± 0 . 2) GeV and has been observed to behave as the SM predicted so far. The discovery is a direct evidence of the Higgs mechanism, the mechanism that naturally explains why elementary fermions and the W and Z bosons appear to have rest masses, despite the lack of an explicit mass term in the SM Lagrangian. The Higgs field interacts with the SM fermions via the Yukawa coupling, which is hypothesised to be proportional to the observed fermion masses. At an energy below the electroweak scale ( ≈ 250 GeV ), the Higgs field acquires a vacuum expectation value, spontaneously breaking the weak isospin and weak hypercharge SU(2) ⊗ SU(1) symmetry and giving the otherwise massless elementary particles their apparent masses. In the SM, the Higgs boson mass is a measured parameter. The SM provides no explanation to the observed value. Naturally, one could expect the Higgs boson mass to be comparable to the Planck mas s † due to quantum corrections. The fact that the observed Higgs boson mass is so much smaller than the Planck mass thus poses a fine-tuning problem, which is known as the hierarchy problem in particle physics. 1.2.3. The electroweak theory The reader might have noticed that even though we claimed that the photons, the W and the Z bosons are the fundamental force carriers in the SM, there are no corresponding gauge fields explicitly written in Equation (1.9) . This is because these physical gauge fields are only results of the spontaneous breaking of the SU(2) ⊗ SU(1) symmetry. Since it is not directly relevant to this thesis, we will refrain from going into the details of how the symmetry is broken. However, we can show that, given a broken symmetry, the W and B fields in Equation (1.9) could indeed be recast into the physical photon, W ± and Z fields. This was first shown by Weinberg, Salam and Glashow in the 1960s [2– 4, 17] , and is now known as the GWS theory or the electroweak theory. † The Planck mass is a natural unit of mass defined as p ~ c/G , where G is the gravitational constant. It is roughly equal to 1 . 22 × 10 19 GeV . Physical quantities similar in magnitude to the Planck mass are said to be at the Planck scale.