Gluon propagator in Feynman gauge by the method of stationary variance

Abstract

The low-energy limit of pure Yang-Mills SU (3) gauge theory is studied in Feynman gauge by the method of stationary variance, a genuine second-order variational method that is suited to deal with the minimal coupling of fermions in gauge theories. In terms of standard irreducible graphs, the stationary equations are written as a set of coupled non-linear integral equations for the gluon and ghost propagators. A physically sensible solution is found for any strength of the coupling. The gluon propagator is finite in the infrared, with a dynamical mass that decreases as a power at high energies. At variance with some recent findings in Feynman gauge, the ghost dressing function does not vanish in the infrared limit and a decoupling scenario emerges as recently reported for the Landau gauge.

Gluon propagator in linear covariant Rξ gauges

“…The mechanism can be understood as the effect of low-energy gluon clouds dressing the current quark, so that the study of the gluon propagator in the IR becomes of paramount importance for a full comprehension of the mass generation [1][2][3][4][5][6][7]. Unfortunately, even in the pure gauge sector, perturbation theory breaks down in the IR and the results of lattice simulations [5,[8][9][10][11][12][13][14][15][16][17][18] are regarded as the only benchmark for the continuum approaches [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38] that have been developed. Among them, a purely analytical method has been proposed in the last years [39][40][41], which is based on a change of the expansion point of ordinary perturbation theory and provides explicit and very accurate expressions for the gluon propagator in the Landau gauge [42].…”

Analytic structure of QCD propagators in Minkowski space

“…Most of the non-perturbative approaches that have been developed so far rely on numerical calculations in the Euclidean space, where synergic studies by lattice simulations [2][3][4][5][6][7][8][9][10], Schwinger-Dyson equations [11][12][13][14][15][16][17][18][19][20][21] and variational methods [22][23][24][25][26][27][28][29][30][31][32] have drawn a clear picture for the propagators of QCD deep in the IR.…”

Dispersion relations for unphysical particles

“…For instance, gluons and quarks are believed to be confined but their color singlet bound states are observed in physical spectra. More generally, we are interested in the physical class of unphysical particles that give rise to observable bound states [1][2][3].The propagators of these unphysical particles are usually studied in the Euclidean space where the correlators emerge by lattice simulations [4][5][6][7][8][9][10][11][12][13] or by numerical solution of a coupled set of integral equations [14][15][16][17][18][19][20][21][22][23]. They are well interpolated by regular functions on the negative real axis of the squared momentum p 2 = −p 2 E .…”