UV finiteness of 3D Yang-Mills theories with a regulating mass in the Landau gauge

Abstract

We prove that three-dimensional Yang-Mills theories in the Landau gauge supplemented with a infrared regulating, parity preserving mass term are ultraviolet finite to all orders. We also extend this result to the Curci-Ferrari gauge.

Landau gauge gluon and ghost propagators in the refined Gribov-Zwanziger framework in 3 dimensions

“…Moreover, the form of the propagators is only quantitatively influenced by this additional mass m 2 , whereby the main consequences of the mass related to ϕϕ − ωω are preserved (see later) [18]. In the presence of 1 2 m 2 A 2 , all Z-factors are 1, or said otherwise, there are no ultraviolet divergences when computing Green functions [33,34]. Having a look at the relations (B18) and (B19), this also means that any other Z-factor is 1, and hence the Gribov-Zwanziger theory is completely ultraviolet finite, including the vacuum functional, since there is no independent renormalization for it: the potential divergences related to γ 4 are killed by the already available Z-factors, which are themselves trivial, and we already know that there are no divergences related to g 2 J.…”

Exploring the infrared structure of QCD with the Gribov-Zwanziger Lagrangian

“…It is also worth observing that both γ 2 and 1 2 (A a µ ) 2 have the same anomalous dimensions in the Landau gauge [40,41]. Indeed the effect that the Gribov mass has on the condensation of 1 2 (A a µ ) 2 has been examined in [22,42,43]. One final point is that the sign of γ 2 is not fixed in (1).…”

Two loop correction to the Gribov mass gap equation in Landau gauge QCD

“…Given the recent interest in both the Zwanziger approach to incorporating the Gribov problem in a localized renormalizable Lagrangian and in gauges such as linear covariant, [23], and maximal abelian gauge, [24], it would appear plausible that one could extend the one loop mass gap equations in those gauges to two loops as well. Moreover, given that [8,25,26] also examined the Gribov problem using the local composite operator formalism to include the dimension two composite operator 1 2 A a µ A a µ it would be interesting to extend that one loop analysis to see whether the operator condenses and lowers the vacuum energy as it does in the case when the Gribov volume is regarded as infinite. Finally, we note that we believe that this is the first non-trivial loop computation performed with Zwanziger's Lagrangian.…”