The Nielsen Identities for the generalized $R_\xi$-gauge

TL;DR

This paper demonstrates the derivation of Nielsen identities for the effective action and potential in the generalized R_xi gauge, confirming their validity at one-loop in the Abelian Higgs model and deriving the Higgs mass identity.

Contribution

It introduces a method to derive Nielsen identities in the generalized R_xi gauge, countering previous conjectures and extending their applicability.

Findings

Nielsen identity for effective action derived in generalized R_xi gauge.

Verification of Nielsen identity for effective potential at one-loop.

Derived identity for the physical Higgs mass in the Abelian Higgs model.

Abstract

We show that it is possible, in opposition to a previous conjecture, to derive a Nielsen identity for the effective action in the case of the generalized $R_\xi $-gauge, where the gauge function explicitly depends on the gauge parameter $\xi $. Also the Nielsen identity for the effective potential is verified to one-loop in the Abelian Higgs model and the corresponding identity for the physical Higgs mass is derived.