chapter  6
8 Pages

Electroweak Unification II

The starting point is the theory based on the symmetry SU(2)L ⊗ U(1)Y illustrated earlier in section 4.3, in its exactly symmetric version, i.e. without ad hoc mass terms for the vector and electron fields. The Lagrangian follows from the classification under SU(2)L⊗U(1)Y of the lepton fields given in (4.15) that we repeat for convenience:

l =

( (νe)L eL

) Y=−1

; (eR)Y=−2 . (6.1)

The corresponding Yang-Mills Lagrangian is therefore:

LeW = l¯iγµDµl + e¯RiγµDµeR − 1 4 [WµνW

µν +BµνB µν ] . (6.2)

Covariant derivatives and field tensors are given by:

Dµl = [∂µ + igWµ · τ 2 + ig′(−1

2 )Bµ]l ;

DµeR = [∂µ + ig ′(−1)Bµ]eR ;

W iµν = ∂νW i µ − ∂µW iν + g ǫjikW jµW kν ;

Bµν = ∂νBµ − ∂µBν . (6.3)

At this stage, the theory describes fermions and vector fields, all massless.