Renormalisation of quark propagators from twisted-mass lattice QCD at $N_f$=2

TL;DR

This paper non-perturbatively evaluates the quark field renormalisation constant $Z_q$ using twisted-mass lattice QCD, addressing lattice artefacts, non-perturbative effects, and their continuum scaling, with implications for understanding gluon condensates.

Contribution

It develops and tests accurate non-perturbative correction methods for $Z_q$ and studies the non-perturbative effects related to the gluon condensate in lattice QCD.

Findings

Lattice artefacts scale as $a^2p^2$

Non-perturbative effects contribute about 4% at 2 GeV

Estimated gluon condensate value agrees with independent methods

Abstract

We present results concerning the non-perturbative evaluation of the renormalisation constant for the quark field, $Z_q$, from lattice simulations with twisted mass quarks and three values of the lattice spacing. We use the RI'-MOM scheme. $Z_q$ has very large lattice spacing artefacts; it is considered here as a test bed to elaborate accurate methods which will be used for other renormalisation constants. We recall and develop the non-perturbative correction methods and propose tools to test the quality of the correction. These tests are also applied to the perturbative correction method. We check that the lattice spacing artefacts scale indeed as $a^2p^2$. We then study the running of $Z_q$ with particular attention to the non-perturbative effects, presumably dominated by the dimension-two gluon condensate $\VEV{A^2}$ in Landau gauge. We show indeed that this effect is present, and not small. We check its scaling in physical units confirming that it is a continuum effect. It gives a $\sim 4%$ contribution at 2 GeV. Different variants are used in order to test the reliability of our result and estimate the systematic uncertainties. Finally combining all our results and using the known Wilson coefficient of $\VEV{A^2}$ we find $g^2(\mu^2) \VEV{A^2}_{\mu^2\; CM} = 2.01(11)(^{+0.61}_{- 0.73}) \;\mathrm {GeV}^2$ at $\mu=10\, \mathrm{GeV}$, in fair agreement within uncertainties with the value indepently extracted from the strong coupling constant.