Flavour symmetry breaking and tuning the strange quark mass for 2+1 quark flavours

TL;DR

This paper proposes an alternative method for tuning quark masses in lattice QCD simulations by fixing the singlet quark mass, leading to more accurate extrapolations of hadron masses to physical values.

Contribution

It introduces a new approach to quark mass tuning in lattice QCD that maintains the kaon mass below its physical value and employs group theory for constrained polynomial fits.

Findings

Extrapolated hadron masses agree within a few percent of experimental values.

The method simplifies the quark mass tuning process.

Group theory-based polynomial expansions improve fit accuracy.

Abstract

QCD lattice simulations with 2+1 flavours typically start at rather large up-down and strange quark masses and extrapolate first the strange quark mass to its physical value and then the up-down quark mass. An alternative method of tuning the quark masses is discussed here in which the singlet quark mass is kept fixed, which ensures that the kaon always has mass less than the physical kaon mass. Using group theory the possible quark mass polynomials for a Taylor expansion about the flavour symmetric line are found, which enables highly constrained fits to be used in the extrapolation of hadrons to the physical pion mass. Numerical results confirm the usefulness of this expansion and an extrapolation to the physical pion mass gives hadron mass values to within a few percent of their experimental values.