The ghost-antighost-gluon vertex from the Curci-Ferrari model: Two-loop corrections

TL;DR

This paper computes two-loop corrections to the ghost-antighost-gluon vertex within the Curci-Ferrari model, showing improved agreement with lattice data for SU(3) and providing insights into non-perturbative gauge theory behavior.

Contribution

It presents the first two-loop calculation of the ghost-antighost-gluon vertex in the Curci-Ferrari model, testing its predictive power against Monte-Carlo simulations.

Findings

Two-loop results improve agreement with lattice data for SU(3)

SU(2) case shows larger discrepancies, possibly due to stronger infrared coupling

Parameter fitting can reconcile propagator and vertex data reasonably

Abstract

The Curci-Ferrari model has been shown to provide a good grasp on pure Yang-Mills correlation functions in the Landau gauge, already at one-loop order. In a recent work, the robustness of these results has been tested by evaluating the two-loop corrections to the gluon and ghost propagators. We pursue this systematic investigation by computing the ghost-antighost-gluon vertex to the same accuracy in a particular kinematic configuration that makes the calculations simpler. Because both the parameters of the model and the normalizations of the fields have already been fixed in a previous work, the present calculation represents both a pure prediction and a stringent test of the approach. We find that the two-loop results systematically improve the comparison to Monte-Carlo simulations as compared to earlier one-loop results. The improvement is particularly significative in the SU($3$) case where the predicted ghost-antighost-gluon vertex is in very good agreement with the data. The same comparison in the SU($2$) case is not as good, however. This may be due to the presence of a larger coupling constant in the infrared in that case although we note that a similar mismatch has been quoted in non-perturbative continuum approaches. Despite these features of the SU($2$) case, it is possible to find sets of parameters fitting both the propagators and the ghost-antighost-gluon vertex to a reasonable accuracy.