Unified description of seagull cancellations and infrared finiteness of gluon propagators

Abstract

We present a generalized theoretical framework for dealing with the important issue of dynamical mass generation in Yang-Mills theories, and, in particular, with the infrared finiteness of the gluon propagators, observed in a multitude of recent lattice simulations. Our analysis is manifestly gauge-invariant, in the sense that it preserves the transversality of the gluon self-energy, and gauge-independent, given that the conclusions do not depend on the choice of the gauge-fixing parameter within the linear covariant gauges. The central construction relies crucially on the subtle interplay between the Abelian Ward identities satisfied by the nonperturbative vertices and a special integral identity that enforces a vast number of 'seagull cancellations' among the oneand two-loop dressed diagrams of the gluon Schwinger-Dyson equation. The key result of these considerations is that the gluon propagator remains rigorously massless, provided that the vertices do not contain (dynamical) massless poles. When such poles are incorporated into the vertices, under the pivotal requirement of respecting the gauge symmetry of the theory, the terms comprising the Ward identities conspire in such a way as to still enforce the total annihilation of all quadratic divergences, inducing, at the same time, residual contributions that account for the saturation of gluon propagators in the deep infrared.

Schwinger mechanism in linear covariant gauges

“…As has been shown in a series of previous works [9,11,32,51], the existence of such solutions requires the inclusion of terms proportional to 1/q 2 in the fully dressed vertices appearing in the diagrams of Fig. 1.…”

“…In a series of articles [51,60,61], a particular framework for the study of the IR finiteness of the gluon propagator has been elaborated, which constitutes a particular realization of the Schwinger mechanism in a non-Abelian context [9,[62][63][64][65][66][67]. A central ingredient of this approach is the dynamical formation of longitudinally coupled massless bound-state excitations, whose main effect is to introduce poles in the nonperturbative vertices of the theory.…”

Evidence of ghost suppression in gluon mass scale dynamics

“…(2.3) remains rigorously massless [8]. The demonstration relies on the subtle interplay between the Ward-Takahashi identities (WTIs), satisfied by the vertices as q → 0, and an integral relation known as the "seagull identity" [8,55]. In fact, in the absence of massless poles, the Taylor expansion of both sides of Eqs.…”

“…It is well understood that, in order for the gluon mass scale generation to go through in the way described in [6][7][8], the STIs satisfied by the fundamental vertices must be realized in part by means of a longitudinally coupled pole term. This fact, in turn, imposes general restrictions on the structure of the form factors of these vertices; in this section we will study this issue for the case of the Bcc vertex μ , which, due to its reduced tensorial content, is particularly instructive.…”

“…The set of basic ideas underlying the approach put forth in [6,7], and more recently in [8], may be summarized as follows. At the level of the Schwinger-Dyson equation (SDE) that governs the dynamics of the gluon propagator within the PT-BFM scheme, the masslessness of the gluon is enforced nonperturbatively by means of a special integral identity ("seagull" identity [8,55]).…”