Lattice QCD Green’s functions in maximally Abelian gauge: Infrared Abelian dominance and the quark sector

Abstract

Functional equations like exact renormalisation group and Dyson-Schwinger equations have contributed to a better understanding of non-perturbative phenomena in quantum field theories in terms of the underlying Green functions. In Yang-Mills theory especially the Landau gauge has been used, as it is the most accessible gauge for these methods. In the maximally Abelian gauge first results have been obtained which are very encouraging because Abelian infrared dominance has been found: The Abelian part of the gauge field propagator is enhanced at low momenta and thereby dominates the dynamics in the infrared. Also the ambiguity of two different types of solutions (decoupling and scaling) exists in both gauges. It is demonstrated how the two solutions are related in the maximally Abelian gauge. As in all two-point Dyson-Schwinger equations of the MAG the infrared dominant diagrams are sunset diagrams, in addition, a BPHZ regularisation and renormalisation of a test system with a sunset-like diagram is presented.

A non-perturbative study of matter field propagators in Euclidean Yang–Mills theory in linear covariant, Curci–Ferrari and maximal Abelian gauges

“…Quite importantly, the tree-level quark propagator (135) is in qualitative agreement with the very recent lattice results reported in [69]. Such an agreement works as a highly non-trivial check of the non-perturbative matter coupling proposed here.…”

“…Therefore, the action of quark matter fields coupled with the gauge sector in a non-perturbative way is expressed, in local form, as Quite importantly, the tree-level quark propagator (135) is in qualitative agreement with the very recent lattice results reported in [69]. Such an agreement works as a highly nontrivial check of the non-perturbative matter coupling proposed here.…”

More on the nonperturbative Gribov-Zwanziger quantization of linear covariant gauges

“…In the Coulomb gauge, a scaling behavior for the spatial propagator at equal time was observed in D = 3, while a decoupling behavior for the same propagator was found in D = 4, see [37]. In the maximal Abelian gauge, the diagonal gluon propagator turns out to be of the scaling type in D = 2 and decoupling in D = 3, 4, see [38] and [39][40][41][42][43][44] for various lattice studies over the years.…”

Study of the all orders multiplicative renormalizability of a local matter confining Gribov-Zwanziger action in the MAG

“…This work focus at continuing the analytic study of the non-perturbative behaviour of the matter fields in the maximal Abelian gauge started in [12,8], along the lines recently outlined in [24,23,16] for the Landau gauge case, where it has been possible to recover the behaviour of the propagators for scalar and spinor fields observed in lattice simulations in [40,41,27,50] from an analytic point of view [16]. This study is relevant in the MAG context because it would allow us to extend the Abelian dominance hypotesis to matter sector and thus make predictions about the propagator of scalars and quark fields which might be compared to lattice numerical simulations [56].…”