One-loop Self-energy and Counterterms in a Massive Yang-Mills Theory based on the Nonlinearly Realized Gauge Group

TL;DR

This paper computes the one-loop self-energy of vector mesons in a massive Yang-Mills theory with a nonlinear gauge, introducing a subtraction scheme that maintains unitarity and finiteness of amplitudes.

Contribution

It presents a novel subtraction scheme for massive nonlinearly realized SU(2) Yang-Mills theory and explicitly calculates one-loop self-energies and counterterms ensuring consistency.

Findings

Self-energy results are consistent with unitarity.

Counterterms satisfy Slavnov-Taylor and other functional equations.

The scheme ensures finiteness of one-loop amplitudes.

Abstract

In this paper we evaluate the self-energy of the vector mesons at one loop in our recently proposed subtraction scheme for massive nonlinearly realized SU(2) Yang-Mills theory. We check the fulfillment of physical unitarity. The resulting self-mass can be compared with the value obtained in the massive Yang-Mills theory based on the Higgs mechanism, consisting in extra terms due to the presence of the Higgs boson (tadpoles included). Moreover we evaluate all the one-loop counterterms necessary for the next order calculations. By construction they satisfy all the equations of the model (Slavnov-Taylor, local functional equation and Landau gauge equation). They are sufficient to make all the one-loop amplitudes finite through the hierarchy encoded in the local functional equation.