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

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 $a^2{p}^2$. 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 $g^2(μ^2) \VEV{A^2}_{μ^2\; CM} = 2.01(11)(^{+0.61}_{- 0.73}) \;\mathrm {GeV}^2$ at $\mu =10\mathrm{GeV}$, in fair agreement within uncertainties with the value indepently extracted from the strong coupling constant.

38 pages, 8 tables, 8 figures

References in corpus (1)

• On the reduction of hypercubic lattice artifacts

Cited by in corpus (11)

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• Overlap quark propagator near the physical pion mass
• Numerical indication that center vortices drive dynamical mass generation in QCD
• RI/(S)MOM renormalizations of overlap quark bilinears with different levels of hypercubic smearing
• Renormalization constants for $N_{\mathrm{f}}=2+1+1$ twisted mass QCD
• Gribov copies in the quark propagator
• Screened massive expansion of the quark propagator in the Landau gauge
• Testing OPE for ghosts, gluons and ${\alpha }_s$