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

Abstract

We analyse the restoration of the Slavnov–Taylor (ST) identities for pure massless Yang–Mills theory in the Landau gauge within the Bogolubov–Parasiuk–Hepp–Zimmermann–Lowenstein (BPHZL) renormalization scheme. The Zimmermann–Lowenstein IR regulator M(s − 1) is introduced via a suitable Becchi–Rouet–Stora–Tyutin (BRST) doublet, thus preserving the nilpotency of the BRST differential. We explicitly obtain the most general form of the action-like part of the symmetric regularized action IΓs, s <1 obeying the ST identities and all other relevant symmetries of the model, to all orders in the loop expansion, and show that non-symmetric counterterms arise in IΓs starting from the second order in the loop expansion, unless a special choice of normalization conditions is done. We give a cohomological characterization of the fulfilment of BPHZL IR power-counting criterion, guaranteeing the existence of the physical limit s → 1. The technique analysed in this paper is needed in the study of the restoration of the ST identities for those models, such as the minimal supersymmetric standard model (MSSM), where massless particles are present and no invariant regularization scheme is known to preserve all the relevant ST identities of the theory.