Renormalizability of a quark–gluon model with soft BRST breaking in the infrared region

Abstract

We prove the renormalizability of a quark-gluon model with a soft breaking of the BRST symmetry, which accounts for the modification of the large distance behavior of the quark and gluon correlation functions. The proof is valid to all orders of perturbation theory, by making use of softly broken Ward

Thermodynamics of an exactly solvable confining quark model

“…As discussed above, this model is expected to describe the infrared properties of confined (positivity-violating) quarks, while keeping compatibility with ultraviolet QCD properties. Indeed, the analytical propagator of the model fits well the available lattice data [30] and the model has been proven to be renormalizable [29], reducing to perturbative quarks in the ultraviolet regime. Our goal here is to show not only that soft BRST breaking in the quark sector implies a well-defined macroscopic behaviour, but also that the tree level model is capable of predicting nontrivial features, being in general qualitatively compatible with the effect of nonperturbative interactions as observed in lattice data.…”

“…Following the discussion of [29], let us briefly review how a model with soft breaking of the BRST symmetry can be obtained from an extension of the QCD lagrangian. We start from the gauge-fixed lagrangian density in an euclidean space of dimension 4,…”

“…We choose a normalization such that log Z(0, 0) ≡ 0, i.e., log Z 0 = 0. Finally, notice that although two of the ϕ i are complex, their imaginary parts cancel in (29), so that the final result is real, as it had to be.…”

“…The idea is that confined degrees of freedom are described by an effective action with a BRST-breaking soft term. Interestingly, the breaking of the BRST invariance may have a connection with chiral symmetry breaking, since the currently known formulations of soft BRST breaking in the quark sector always imply chiral symmetry breaking [29,30] and thus dynamical mass generation in the deep infrared seems to be intimately related to BRST breaking [21]. In this sense, one may hope that the investigation of the nonperturbative breaking of the BRST symmetry may shed some light on a long-standing puzzle in the QCD phase structure: the apparent and unexplained link between confinement and chiral symmetry breaking.…”

Gauge anomalies in Lorentz-violating QED

“…At the end of the study the theory is contracted down to the starting action. We emphasize that this method was vastly employed in Yang-Mills theories in order to control a soft BRST symmetry breaking in the Gribov-Zwanzinger scenario [35,36,37,38,39,40], and also in the study of the renormalizability of Lorentz-violating Yang-Mills theory [41]. We shall see that the Lorentz-violating QED is free of gauge anomalies to all orders in perturbation theory by verifying that the solution of the Slavnov-Taylor operator (functional form of the BRST operator) in the nontrivial sector of the cohomology is empty.…”