The full gauge fixing parameter independent Higgs boson self-energy

Abstract

The standard model of Glashow-Salam-Weinberg is a non-abelian gauge field theory of electroweak and strong interactions. It involves a Yang-Mills sector in its classical Lagrangian, which on the whole is invariant under a local SU(2) and U(1) gauge tranformation. This gauge invariance property is compromised when one wishes to quantize the theory. Quantization would require gauge fixing terms in the Lagrangian breaking the underlying gauge symmetry. Furthermore, the introduction of terms involving anticommutting Faddeev Popov ghost fields into the Lagrangian is necessary to ensure only physical fields are dealt with in the theory. Both these requirements for quantization complicates matters concerning calculations, for example radiative corrections involving loop diagrams, in the vector and scalar bosons portion of the theory. As in the case of the Higgs boson, its full one-loop self-energy, when calculated from an assumption that the Higgs boson is an asymptotic state of the scattering matrix, while gauge independent on-shell, turns out to depend on the gauge fixing parameter ξ off-shell. This property, among others, is by no means an obstacle in conventional perturbation theory which predict meaningful observables independent of the gauge fixing procedure. However, this is not the case where the conventional perturbation theory breaks down like in the "strongly coupled theory of Quantum Chromodynamics (QCD)" and "in the vicinity of resonances in a weakly coupled theory" like the electroweak interaction in the standard model. The search "for a self-consistent scheme for constructing off-shell Green's functions" resulted in a formalism based on what is called the pinch technique.