Higher-order non-symmetric counterterms in pure Yang-Mills theory

TL;DR

This paper investigates the restoration of Slavnov-Taylor identities in massless Yang-Mills theory using BPHZL renormalization, providing a general form of the symmetric action and conditions for IR regulator removal.

Contribution

It offers a comprehensive analysis of the most general symmetric regularized action satisfying ST identities in pure Yang-Mills theory to all loop orders.

Findings

Derived the general form of the symmetric regularized action.

Provided a cohomological criterion for IR regulator removal.

Applicable to models with massless particles like MSSM.

Abstract

We analyze the restoration of the Slavnov-Taylor (ST) identities for pure massless Yang-Mills theory in the Landau gauge within the BPHZL renormalization scheme with IR regulator. We obtain the most general form of the action-like part of the symmetric regularized action, obeying the relevant ST identities and all other relevant symmetries of the model, to all orders in the loop expansion. We also give a cohomological characterization of the fulfillment of BPHZL IR power-counting criterion, guaranteeing the existence of the limit where the IR regulator goes to zero. The technique analyzed in this paper is needed in the study of the restoration of the ST identities for those models, like the MSSM, where massless particles are present and no invariant regularization scheme is known to preserve the full set of ST identities of the theory.