The MHV Lagrangian for a spontaneously broken gauge theory

Starting from the standard Lagrangian for a SU(2) x U(1) gauge theory plus a Higgs field we derive the corresponding maximal helicity violating (MHV) Lagrangian. From this MHV Lagrangian one deduces simple diagrammatic rules for the calculation of multi-particle scattering amplitudes. We arrive at the MHV Lagrangian by a canonical change of the field variables in the light-cone gauge. We comment on the modifications which occur in a spontaneously broken gauge theory as compared to a pure (unbroken) Yang-Mills theory.