Wing Sheung Chan

The Standard Model and lepton flavour violation 13 Z boson and the neutral-current interaction The remaining component of the weak isospin gauge field W 3 and the weak hypercharge gauge field B both lead to neutral-current interactions. As a result, the physical neutral- current fields, A µ and Z µ , can be a linear combination of the W 3 and B fields: A µ Z µ ! = cos θ w sin θ w − sin θ w cos θ w ! B µ W 3 µ ! , (1.15) where the parameter θ w is known as the weak mixing angle. The Higgs mechanism predicts that if A is to be the massless physical photon field, then θ w is related to the weak isospin and weak hypercharge coupings by tan θ w = g 0 g , (1.16) and the electromagnetic charge Q is related to the third component of weak isospin and the weak hypercharge by Q = T 3 + Y 2 . (1.17) For the Z field, the coupling becomes g Z = g cos θ w . (1.18) The interaction Lagrangian terms in the electroweak sector can now be written as L EW , int = − eQ ¯ ψγ µ A µ ψ − g 2 √ 2 ¯Ψ γ µ 1 − γ 5 τ + W + µ + τ − W − µ Ψ − g 2 cos θ w ¯ ψγ µ C V − C A γ 5 ψ, (1.19) where C V and C A are the vector and axial vector couplings related to the weak isospin and the electric charge of the fermions by C V = T 3 − 2 Q sin 2 θ w , (1.20) C A = T 3 . (1.21) Table 1.6 shows the Feynman rules [18] that represent the possible interactions expressed in Equation (1.19) .