Abstract
In Quantum Chromodynamics, 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 three-gluon 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 3 standard deviations.
Highlights
The systematic study of the fundamental n-point correlation (Green’s) functions, such as propagators and vertices, forms an essential element in the ongoing quest for unraveling the nonperturbative properties and underlying dynamical mechanisms of Quantum Chromodynamics (QCD) [1]
We present a detailed derivation of the non-Abelian Ward identity obeyed by the pole-free part of the three-gluon vertex in the softgluon limit, and determine the smoking-gun displacement that the onset of the Schwinger mechanism produces to the standard result
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
Summary
The systematic study of the fundamental n-point correlation (Green’s) functions, such as propagators and vertices, forms an essential element in the ongoing quest for unraveling the nonperturbative properties and underlying dynamical mechanisms of Quantum Chromodynamics (QCD) [1] In recent years, this challenging problem has been tackled by means of approaches formulated in the continuum, such as the Schwinger-Dyson equations (SDEs) [2–12] or the functional renormalization group [13–17], in conjunction with numerous gauge-fixed lattice simulations [18–27]. The displacement originating from the onset of the Schwinger mechanism, to be denoted by Cðr2Þ, may be calculated by appropriately combining this form factor with all other constituents that enter into the WI of the three-gluon vertex; all of them are available from lattice simulations, with the exception of a particular partial derivative, denoted by Wðr2Þ, related to the ghost-gluon kernel that appears in the STI [107,108].
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