Exploring smoking-gun signals of the Schwinger mechanism in QCD

Abstract

In QCD, the Schwinger mechanism endows the gluons with an effective mass through the dynamical formation of massless bound-state poles that are longitudinally coupled. The presence of these poles affects profoundly the infrared properties of the interaction vertices, inducing crucial modifications to their fundamental Ward identities. Within this general framework, we present a detailed derivation of the non-Abelian Ward identity obeyed by the pole-free part of the threegluon vertex in the soft-gluon limit, and determine the smoking-gun displacement that the onset of the Schwinger mechanism produces to the standard result. Quite importantly, the quantity that describes this distinctive feature coincides formally with the bound-state wave function that controls the massless pole formation. Consequently, this signal may be computed in two independent ways: by solving an approximate version of the pertinent Bethe-Salpeter integral equation, or by appropriately combining the elements that enter in the aforementioned Ward identity. For the implementation of both methods we employ two-and three-point correlation functions obtained from recent lattice simulations, and a partial derivative of the ghost-gluon kernel, which is computed from the corresponding Schwinger-Dyson equation. Our analysis reveals an excellent coincidence between the results obtained through either method, providing a highly nontrivial self-consistency check for the entire approach. When compared to the null hypothesis, where the Schwinger mechanism is assumed to be inactive, the statistical significance of the resulting signal is estimated to be three standard deviations.

Gluon condensates and effective gluon mass

“…We have also compared our result for the mass gap with that obtained with the longitudinal Schwinger mechanism within the framework of the pinch technique [30], see Appendix F and the very recent analysis see [98]. This analysis leads to m (Schwinger) gap = 0.320 (35) GeV, which is in excellent agreement with our estimate.…”

“…According to one of the main approaches put forth in a number of works [98,[109][110][111][112], the generation of an effective gluon mass proceeds through the non-Abelian implementation of the well-known Schwinger mechanism [113][114][115][116]. Within this scenario, the fundamental vertices that enter in the DSE of the gluon propagator, ∆(q 2 ), contain longitudinally coupled massless poles, which eventually trigger the result ∆ −1 (0) := m 2 gap .…”

On Gauge Consistency In Gauge-Fixed Yang-Mills Theory

“…There, the present results are compared to lattice data. For recent results see in particular [6] (fRG) and [7,[54][55][56][57] (DSE). The longitudinal scalar part Γ AA in ( 14) contains the gauge fixing part that diverges in the Landau gauge limit ξ → 0 and a regular contribution, that originates from the breaking of BRST invariance for finite k and vanishes in the limit k → 0.…”

Theory and phenomenology of the three-gluon vertex

“…5. Nonetheless, as has been recently demonstrated in [36], the massless poles leave smoking-gun signals of their presence, by inducing finite displacements to the non-Abelian Ward identity satisfied by the pole-free part of the three-gluon vertex. Quite interestingly, this displacement is identical to the Bethe-Salpeter amplitude that controls the dynamical formation of the massless poles [78][79][80][81], thus establishing a powerful constraint on the entire mass generating mechanism put forth in a series of works (see [36] and references therein).…”

“…Several of these works have underscored the subtle interplay of the three-gluon vertex with the two-point sector of the theory, and in particular the mass-generating patterns associated with the gluon and ghost propagators [7][8][9][10][11][12][13][14][15][31][32][33][34][35]. As a result, the three-gluon vertex provides an outstanding testing ground for a variety of physical ideas and field-theoretic mechanisms [36][37][38][39][40][41]. In this presentation we provide a synopsis of some of the most important findings of this exploration.…”