RI/MOM renormalization constants (N_f=4) and the strong coupling constant (N_f=2+1+1) from twisted-mass QCD

TL;DR

This paper computes renormalization constants and the strong coupling constant in twisted-mass QCD, employing a non-perturbative artifact removal method to analyze their running behavior and extract the gluon condensate.

Contribution

It introduces the 'egalitarian' method for non-perturbative removal of hypercubic artifacts in RI/MOM renormalization studies of twisted-mass QCD.

Findings

Successful extraction of $Z_q$ and $eta_s$ over a wide momentum range.

Determination of the Landau gauge gluon condensate $<A^2>$.

Validation of the 'egalitarian' method for artifact removal.

Abstract

We study RI/MOM renormalization constants of bilinear quark operators for $N_f=4$ and the strong coupling constant for $N_f=2+1+1$ using Wilson twisted-mass fermions. We use the "egalitarian" method to remove H(4) hypercubic artifacts non-perturbatively, which enables us to study physical quantities in a wide range of momenta. We then apply OPE in studying the running behavior of $Z_q$ and $\alpha_s$, from which we are able to extract the Landau gauge dimension-two gluon condensate $<A^2>$ which is of phenomenological interest.