Chiral symmetry breaking in QCD Lite

TL;DR

This study confirms chiral symmetry breaking in QCD through lattice simulations, showing low mode condensation matches theoretical predictions and providing precise ratios for key QCD parameters.

Contribution

First lattice QCD computation of spectral density and related quantities confirming chiral symmetry breaking with controlled extrapolation to continuum and chiral limits.

Findings

Low quark modes condense in the continuum as predicted by Banks-Casher.

The rate of condensation agrees with the GMOR relation.

Precise determination of QCD parameters like  and F.

Abstract

A distinctive feature of the presence of spontaneous chiral symmetry breaking in QCD is the condensation of low modes of the Dirac operator near the origin. The rate of condensation must be equal to the slope of (Mpi^2 Fpi^2)/2 with respect to the quark mass m in the chiral limit, where Mpi and Fpi are the mass and the decay constant of the Nambu-Goldstone bosons. We compute the spectral density of the (Hermitian) Dirac operator, the quark mass, the pseudoscalar meson mass and decay constant by numerical simulations of lattice QCD with two light degenerate Wilson quarks. We use CLS lattices at three values of the lattice spacing in the range 0.05-0.08 fm, and for several quark masses corresponding to pseudoscalar mesons masses down to 190 MeV. Thanks to this coverage of parameters space, we can extrapolate all quantities to the chiral and continuum limits with confidence. The results show that the low quark modes do condense in the continuum as expected by the Banks-Casher mechanism, and the rate of condensation agrees with the Gell-Mann-Oakes-Renner (GMOR) relation. For the renormalisation-group-invariant ratios we obtain [\Sigma^RGI]^(1/3)/F =2.77(2)(4) and Lambda^MSbar/F = 3.6(2), which correspond to [\Sigma^\MSbar(2 GeV)]^(1/3) =263(3)(4) MeV and F=85.8(7)(20) MeV if FK is used to set the scale by supplementing the theory with a quenched strange quark.