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

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