Gluon propagator in linear covariant Rξ gauges

Abstract

Explicit analytical expressions are derived for the gluon propagator in a generic linear covariant R ξ gauge, by a screened massive expansion for the exact Faddeev-Popov Lagrangian of pure Yang-Mills theory. At one-loop, if the gauge invariance of the pole structure is enforced, the gluon dressing function is entirely and uniquely determined, without any free parameter or external input. The gluon propagator is found finite in the IR for any ξ, with a slight decrease of its limit value when going from the Landau gauge (ξ ¼ 0) toward the Feynman gauge (ξ ¼ 1). An excellent agreement is found with the lattice in the range 0 < ξ < 0.5 where the data are available.

Calculation of the nonperturbative strong coupling from first principles

“…As discussed in Ref. [51], one important merit of the screened massive expansion arises from the apparent drawback of having split the action in two parts that are not BRST invariant. The exact constraints arising from BRST invariance cannot be satisfied exactly at any finite order of the expansion, but they must be satisfied by the exact result.…”

“…Without any phenomenological parameter left, the optimized expansion is highly predictive, as shown in Ref. [51] where the optimal gluon propagator was determined by the Nielsen identities.…”

Yang-Mills ghost propagator in linear covariant gauges

“…While a qualitative [1][2][3][4] and even quantitative [5,6] agreement has been reached for the gluon propagator at ξ > 0, the behavior of the ghost propagator G(p) has not been clearly established yet. There are strong analytical arguments for a suppression of the ghost dressing function p 2 G(p) in the IR [2,3,7] but there is no quantitative information on the entity of the suppression and on the scale at which it should be observed.…”

“…where s = p 2 /m 2 (ξ) and m(ξ) is a gauge-dependent mass parameter which was determined in Ref. [6] by requiring that the poles of the gluon propagator are gauge parameter independent, as imposed by Nielsen identities. A very accurate interpolation of the curve m(ξ) in the range 0 < ξ < 1 was determined in [6]…”

“…By a comparison with the lattice units of Ref. [19], the value m 0 = 0.656 GeV was extracted [6]. The adimensional function G(s) gives the finite part of the self energy in the Landau gauge and its explicit analytical expression has been reported in several papers [9][10][11]13] G(s) = (1 + s) 2 (2s − 1) 12s 2 ln(1 + s) − s 6 ln(s) + 1 + 2s 12s .…”