SU2 isospin breaking effects in baryon octet (and decuplet) masses are due to a combination of up and down quark mass differences and electromagnetic effects. These mass differences are small. Between the Sigma and Lambda the mass splitting is much l
arger, but this is mostly due to their different wavefunctions. However there is now also mixing between these states. We determine the QCD mixing matrix and hence find the mixing angle and mass splitting.
Isospin breaking effects in baryon octet (and decuplet) masses are due to a combination of up and down quark mass differences and electromagnetic effects and lead to small mass splittings. Between the Sigma and Lambda this mass splitting is much larg
er, this being mostly due to their different wavefunctions. However when isospin is broken, there is a mixing between between these states. We describe the formalism necessary to determine the QCD mixing matrix and hence find the mixing angle and mass splitting between the Sigma and Lambda particles due to QCD effects.
By extending the SU(3) flavour symmetry breaking expansion from up, down and strange sea quark masses to partially quenched valence quark masses we propose a method to determine charmed quark hadron masses including possible QCD isospin breaking effe
cts. Initial results for some open charmed pseudoscalar meson states and singly and doubly charmed baryon states are encouraging and demonstrate the potential of the procedure. Essential for the method is the determination of the scale using singlet quantities, and to this end we also give here a preliminary estimation of the recently introduced Wilson flow scales.
By introducing an additional operator into the action and using the Feynman-Hellmann theorem we describe a method to determine both the quark line connected and disconnected terms of matrix elements. As an illustration of the method we calculate the
gluon contribution (chromo-electric and chromo-magnetic components) to the nucleon mass.
QCD lattice simulations yield hadron masses as functions of the quark masses. From the gradients of the hadron masses the sigma terms can then be determined. We consider here dynamical 2+1 flavour simulations, in which we start from a point of the fl
avour symmetric line and then keep the singlet or average quark mass fixed as we approach the physical point. This leads to highly constrained fits for hadron masses in a multiplet. The gradient of this path for a hadron mass then gives a relation between the light and strange sigma terms. A further relation can be found from the change in the singlet quark mass along the flavour symmetric line. This enables light and strange sigma terms to be estimated for the baryon octet.
QCD lattice simulations determine hadron masses as functions of the quark masses. From the gradients of these masses and using the Feynman-Hellmann theorem the hadron sigma terms can then be determined. We use here a novel approach of keeping the sin
glet quark mass constant in our simulations which upon using an SU(3) flavour symmetry breaking expansion gives highly constrained (i.e. few parameter) fits for hadron masses in a multiplet. This is a highly advantageous procedure for determining the hadron mass gradient as it avoids the use of delicate chiral perturbation theory. We illustrate the procedure here by estimating the light and strange sigma terms for the baryon octet.
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. 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.
We discuss a 3-flavour lattice QCD action with clover improvement in which the fermion matrix has single level stout smearing for the hopping terms together with unsmeared links for the clover term. With the (tree-level) Symanzik improved gluon actio
n this constitutes the Stout Link Non-perturbative Clover or SLiNC action. To cancel O(a) terms the clover term coefficient has to be tuned. We present here results of a non-perturbative determination of this coefficient using the Schroedinger functional and as a by-product a determination of the critical hopping parameter. Comparisons of the results are made with lowest order perturbation theory.
