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

Understand

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.