Quark pseudoscalar vertex and quark mass function with clover fermions : spontaneous symmetry breaking, OPE, symmetry restoration at small volume

TL;DR

This study investigates the quark mass function and chiral symmetry breaking on lattices, revealing a volume-dependent discontinuity indicating symmetry restoration and highlighting limitations of the operator product expansion at accessible momenta.

Contribution

It provides new insights into the volume dependence of chiral symmetry breaking and the limitations of OPE in lattice QCD with clover fermions.

Findings

Discontinuity in chiral properties at a critical volume around 1.2 fm.

Quark mass function collapses to zero below this volume.

OPE of the quark mass function is not operative at accessible momenta.

Abstract

We study the quark mass function on hypercubic lattices, in a large range of physical volumes and cutoffs. To avoid the very large Wilson term artefact, we exploit the relation between the quark mass function and the pseudoscalar vertex in the continuum. We extrapolate to the chiral limit. In function of the physical volume, we observe a striking discontinuity in the properties of chiral extrapolation around a physical volume $L_c 6 (GeV}^{-1}=1.2 fm$. It is present in the quark mass function, which collapses to zero, as well as in the pion mass and the quark condensate as directly calculated from the pseudoscalar correlator. It is strongly reminiscent of the phenomenon of chiral symmetry restoration observed by Neuberger and Narayanan at $N_C=\infty$ around the same physical length. In the case of spontaneous symmetry breaking, we confirm that the OPE of the quark mass function, involving the quark condensate, is not operative at the available momenta, even taking into account the unusually large high order corrections to the Wilson coefficient calculated by Chetyrkin and Maier ; the gap remains large, around a factor 2, even at the largest momenta available to us (p \simeg GeV)