Nonlocal Regularization and Spontaneously Broken Abelian Gauge Theories for an Arbitrary Gauge Parameter

TL;DR

This paper investigates nonlocal regularization in spontaneously broken abelian gauge theories within the R_xi gauge, analyzing gauge parameter dependence of physical observables and the implications for Ward-Takahashi identities and S-matrix independence.

Contribution

It extends nonlocal regularization methods to broken abelian gauge theories with arbitrary gauge parameters, examining gauge dependence and WT identities.

Findings

Physical observable shows xi-dependence at order O[g^{2}].

Modified nonlocal regularization maintains S-matrix xi-independence.

Discussion of WT identities in the context of nonlocal regularization.

Abstract

We study the non-local regularization for the case of a spontaneously broken abelian gauge theory in the R_xi gauge with an arbitrary gauge parameter xi. We consider a simple abelian-Higgs model with chiral couplings as an example. We show that if we apply the nonlocal regularization procedure [to construct a nonlocal theory with finite mass parameter ] to the spontaneously broken R_xi gauge Lagrangian, using the quadratic forms as appearing in this Lagrangian, we find that a physical observable in this model, an analogue of the muon anomalous magnetic moment, evaluated to order O[g^{2}] does indeed show xi-dependence.We then apply the modified form of nonlocal regularization that was recently advanced and studied for the unbroken non-abelian gauge theories and discuss the resulting WT identities and xi-independence of the S-matrix elements.