Evidence of the Schwinger Mechanism from Lattice QCD

In quantum chromodynamics (QCD), gluons acquire a mass scale through the action of the Schwinger mechanism. This mass emerges as a result of the dynamical formation of massless bound-states of gluons which manifest as longitudinally coupled poles in the vertices. In this contribution, we show how the presence of these poles can be determined from lattice QCD results for the propagators and vertices. The crucial observation that allows this determination is that the Schwinger mechanism poles induce modifications, called displacements, to the Ward identities (WIs) relating two- and three-point functions. Importantly, the displacement functions correspond precisely to the Bethe-Salpeter amplitudes of the massless bound-states. We apply this idea to the case of the three-gluon vertex in pure Yang-Mills SU(3). Using lattice results in the corresponding WI, we find an unequivocal displacement and show that it is consistent with the prediction based on the Bethe-Salpeter equation.

Automated summary

In quantum chromodynamics (QCD), the mass of gluons is generated by the Schwinger mechanism, where massless bound-states of gluons result in coupled poles in the vertices. This study presents a method to determine these poles using lattice QCD results for propagators and vertices. By examining the modifications in the Ward identities (WIs), known as displacements, induced by the Schwinger mechanism poles, the displacement functions are found to correspond to the Bethe-Salpeter amplitudes of the massless bound-states. This approach is applied to the three-gluon vertex in pure Yang-Mills SU(3), and the obtained displacement is consistent with predictions based on the Bethe-Salpeter equation.