Study of the nonlocal gauge invariant mass operator $\mathrm{Tr} \int d^4x F_{\mu\nu} (D^2)^{-1} F_{\mu\nu}$ in the maximal Abelian gauge

TL;DR

This paper investigates a nonlocal gauge invariant mass operator in Yang-Mills theories within the maximal Abelian gauge, demonstrating its renormalizability through a local formulation and algebraic renormalization techniques.

Contribution

It introduces a local formulation of a nonlocal mass operator in Yang-Mills theories and proves its renormalizability to all orders of perturbation theory.

Findings

Successful local reformulation of the nonlocal operator

Proof of all-order perturbative renormalizability

Framework for analyzing gauge invariant mass operators

Abstract

The nonlocal gauge invariant mass operator $\mathrm{Tr} \int d^{4}x F_{\mu\nu} (D^2)^{-1} F_{\mu\nu}$ is investigated in Yang-Mills theories in the maximal Abelian gauge. By means of the introduction of auxiliary fields a local action is achieved, enabling us to use the algebraic renormalization in order to prove the renormalizability of the resulting local model to all orders of perturbation theory.