Wing Sheung Chan

10 The Standard Model and lepton flavour violation Table 1.5.: Properties of gauge bosons [6] . Gauge boson Rest mass [GeV] Electric charge [ e ] Assicoated interaction γ 0 0 Electromagnetic g 0 0 Strong W ± 80 . 379 ± 0 . 012 ± 1 Weak (charged-current) Z 91 . 1876 ± 0 . 0021 0 Weak (neutral-current) Force carriers Another class of elementary particles in the SM is the gauge bosons. They are the force carriers for the electroweak and strong interactions. Leptons and quarks can interact with each other by exchanging gauge bosons. There are four different gauge bosons in the SM: the photon ( γ ), the gluon ( g ), the W and the Z bosons. Some of them have finite rest masses while some of them are massless. All of them have spin one. A summary of their properties [6] are shown in Table 1.5. Photons are neutral massless gauge bosons that mediate the electromagnetic (EM) force. They interact with any particles that carry electric charges, including charged leptons, quarks and the W bosons. The zero rest mass and the lack of charges of the photon implies that EM interaction is a long-range interaction and is observable at macroscopic levels. The theory that describes the interaction between photons and electrically charged particles is called quantum electrodynamics (QED). The first reasonably complete theory of QED was created by Paul Dirac in 1927 [8] . Since then, QED has demonstrated huge success in explaining and predicting experimental results. One particularly remarkable achievement is the excellent agreement of the experimentally measured value of the electron gyromagnetic ratio with the theoretical value calculated from QED. The relative difference between the values is in the order of merely 10 − 12 [9] . The W and Z bosons are the mediators of the weak interactions. They can interact with any fermions in the Standard Model, including neutrinos, which otherwise do not participate in any other fundamental interactions. Both the W and Z bosons are relatively heavy particles. Their high masses limit the range of the weak interaction, which is consistent with the observed short range of the weak nuclear force. The W boson the only charged gauge boson in the SM. It is responsible for the charged-current interactions, which couple left-handed up-type quarks to left-handed down-type quarks, or left-handed charged leptons to left-handed neutrinos. Right-handed fermions do not interact with the W bosons at all. The Z boson is responsible for the neutral-current interactions. In the SM, neutral-current interactions can only transfer momentum from a particle to another, without changing the flavours and charges of the interacting particles. These interactions will be discussed in more details in the next section when the electroweak theory is introduced.