On-Shell Electroweak Sector and the Higgs Mechanism

Abstract

We take the first steps towards an entirely on-shell description of the bosonic electroweak sector of the Standard Model. We write down on-shell three particle amplitudes consistent with Poincare' invariance and little group covariance. Tree-level, four particle amplitudes are determined by demanding consistent factorization on all poles and correct UV behaviour. We present expressions for these $2\rightarrow 2$ scattering amplitudes using massive spinor helicity variables. We show that on-shell consistency conditions suffice to derive relations between the masses of the $W^\pm, Z$, the Weinberg angle and the couplings. This provides a completely on-shell description of the Higgs mechanism without any reference to the vacuum expectation value of the Higgs field.