Lattice QCD Calculations of the Sigma Commutator

TL;DR

This paper demonstrates that the sigma commutator, a key indicator of chiral symmetry breaking in QCD, can be reliably calculated from lattice QCD data by respecting proper chiral behavior, yielding a value of 45-55 MeV.

Contribution

It shows how to extract the sigma commutator directly from lattice QCD calculations by ensuring correct chiral extrapolation, providing a practical method for this important quantity.

Findings

Sigma commutator estimated at 45-55 MeV

Reliable determination depends on proper chiral extrapolation

Lattice QCD can directly inform on chiral symmetry breaking

Abstract

As a direct source of information on chiral symmetry breaking within QCD, the sigma commutator is of considerable importance. With recent advances in the calculation of hadron masses within full QCD it is of interest to see whether the sigma commutator can be calculated directly from the dependence of the nucleon mass on the input quark mass. We show that provided the correct chiral behaviour of QCD is respected in the extrapolation to realistic quark masses one can indeed obtain a fairly reliable determination of the sigma commutator using present lattice data. Within two-flavour, dynamical-fermion QCD the value obtained lies in the range 45 to 55 MeV.