Flavour blindness and patterns of flavour symmetry breaking in lattice simulations of up, down and strange quarks

TL;DR

This paper proposes a novel method for tuning quark masses in lattice QCD simulations by fixing the singlet quark mass, enabling more accurate extrapolations of hadron masses to their physical values.

Contribution

It introduces a group theory-based polynomial expansion approach for quark mass tuning that maintains constant singlet quark mass, improving extrapolation accuracy in lattice QCD.

Findings

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

The method allows determination of lattice spacing without physical point calibration.

Extension to partially quenched results is demonstrated.

Abstract

QCD lattice simulations with 2+1 flavours (when two quark flavours are mass degenerate) typically start at rather large up-down and strange quark masses and extrapolate first the strange quark mass and then the up-down quark mass to its respective physical value. Here we discuss an alternative method of tuning the quark masses, in which the singlet quark mass is kept fixed. Using group theory the possible quark mass polynomials for a Taylor expansion about the flavour symmetric line are found, first for the general 1+1+1 flavour case and then for the 2+1 flavour case. This ensures that the kaon always has mass less than the physical kaon mass. This method of tuning quark masses then enables highly constrained polynomial fits to be used in the extrapolation of hadron masses to their physical values. Numerical results for the 2+1 flavour case 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. Singlet quantities remain constant which allows the lattice spacing to be determined from hadron masses (without necessarily being at the physical point). Furthermore an extension of this programme to include partially quenched results is given.