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 ph
ysical 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.
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 m
asses 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.
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 m
asses 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. It can also take into account the different renormalisations (for singlet and non-singlet quark masses) occurring for non-chirally invariant lattice fermions and so allows a smooth extrapolation to the physical quark masses. This procedure enables a wide range of quark masses to be probed, including the case with a heavy up-down quark mass and light strange quark mass. Results show the correct order for the baryon octet and decuplet spectrum and an extrapolation to the physical pion mass gives mass values to within a few percent of their experimental values.
QCD results are presented for a 2+1 flavour fermion clover action (which we call the SLiNC action). A method of tuning the quark masses to their physical values is discussed. In this method the singlet quark mass is kept fixed, which solves the probl
em of different renormalisations (for singlet and non-singlet quark masses) occuring for non-chirally invariant lattice fermions. This procedure enables a wide range of quark masses to be probed, including the case with a heavy up-down quark mass and light strange quark mass. Preliminary results show the correct splittings for the baryon (octet and) decuplet spectrum.
