On the massive gluon propagator, the PT-BFM scheme and the low-momentum behaviour of decoupling and scaling DSE solutions

Abstract

We study the low-momentum behaviour of Yang-Mills propagators obtained from Landau-gauge Dyson-Schwinger equations (DSE) in the PT-BFM scheme. We compare the ghost propagator numerical results with the analytical ones obtained by analyzing the low-momentum behaviour of the ghost propagator DSE in Landau gauge, assuming for the truncation a constant ghost-gluon vertex and a simple model for a massive gluon propagator. The asymptotic expression obtained for the regular or decoupling ghost dressing function up to the order O(q2) is proven to fit pretty well the numerical PT-BFM results. Furthermore, when the size of the coupling renormalized at some scale approaches some critical value, the numerical PT-BFM propagators tend to behave as the scaling ones. We also show that the scaling solution, implying a diverging ghost dressing function, cannot be a DSE solution in the PT-BFM scheme but an unattainable limiting case.The author is particularly indebted to Ph. Boucaud, J.P Leroy, A. Le Yaouanc, J. Micheli and O. Pene for very fruitful discussions at the initial stages of the work and to J. Papavassiliou and A. C. Aguilar also for very valuable discussions and comments, and specially for providing me with some unpublished results which were exploited in this paper. J. R-Q also acknowledges the Spanish MICINN for the support by the research project FPA2009-10773 and "Junta de Andalucia" by P07FQM02962

Nontrivial ghost-gluon vertex and the match of the Refined-Gribov-Zwanziger, Dyson-Schwinger equations, and lattice Yang-Mills propagators

“…[56] which, obtained at a typical deep UV scale of 10 GeV, gives ' 5ð1Þ GeV 2 . The two aforementioned condensate estimates imply a serious violation of the roughly derived rule (12), suggestive of important missing information. In particular, as we applied a treelevel RGZ formula to describe the lattice data and extract the condensate value, its natural renormalization scale should be the one obtained by solving Eq.…”

“…Though it may look appealing to actually solve the DSEs, it must be mentioned that they inevitably lead to an infinite number of coupled equations, and, consequently, assumptions/truncations must be made to obtain any kind of results. For SUðNÞ Yang-Mills gauge systems, usually quantized in the Landau gauge because of the special (renormalization) properties of this gauge, the DSEs for the propagators themselves are solved while the input vertices are either taken to be tree-level-like or modeled using information from, e.g., lattice simulations of the nonperturbative vertices when available [4,[6][7][8][9][10][11][12][13][14].…”

Infrared safe perturbative approach to Yang-Mills correlators

“…The most developed is based on the Schwinger-Dyson (SD) equations [5][6][7][8][9][10][11][12][13][14][15][16], which consist of an infinite set of coupled equations for the vertex functions. In order to make predictions, it is necessary to truncate in some way this infinite set.…”

“…The exponents governing these two power-laws are not independent. In the so-called decoupling solution (or massive solution) [9][10][11][12][13][14]16], the gluon propagator goes to a constant in the IR, and the ghost propagator is as singular as in the bare theory.…”

Subtracting infrared renormalons from Wilson coefficients: Uniqueness and power dependences on ΛQCD

“…Therefore, from Eqs. (18), (23) and (91), the coefficient of the (e 5/3 Λ 2 QCD /Q 2 ) nterm of X UV is revealed to be 4πB X (n)/β 0 . Incidentally, we have a similar relation for W (m) X+ in the massive gluon scheme as…”