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Register a new userFlavour symmetry breaking and tuning the strange quark mass for 2+1 quark flavours
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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 masses 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.
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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 singlet 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 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 flavour 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 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 masses 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.
We present a determination of the charm quark mass in lattice QCD with three active quark flavours. The calculation is based on PCAC masses extracted from $N_mathrm{f}=2+1$ flavour gauge field ensembles at five different lattice spacings in a range from 0.087 fm down to 0.039 fm. The lattice action consists of the $mathrm{O}(a)$ improved Wilson-clover action and a tree-level improved Symanzik gauge action. Quark masses are non-perturbatively $mathrm{O}(a)$ improved employing the Symanzik-counterterms available for this discretisation of QCD. To relate the bare mass at a specified low-energy scale with the renormalisation group invariant mass in the continuum limit, we use the non-pertubatively known factors that account for the running of the quark masses as well as for their renormalisation at hadronic scales. We obtain the renormalisation group invariant charm quark mass at the physical point of the three-flavour theory to be $M_mathrm{c} = 1486(21),mathrm{MeV}$. Combining this result with five-loop perturbation theory and the corresponding decoupling relations in the $overline{mathrm{MS}}$ scheme, one arrives at a result for the renormalisation group invariant charm quark mass in the four-flavour theory of $M_mathrm{c}(N_mathrm{f}=4) = 1548(23),mathrm{MeV}$. In the $overline{mathrm{MS}}$ scheme, and at finite energy scales conventional in phenomenology, we quote $m^{overline{mathrm{MS}}}_{mathrm{c}}(m^{overline{mathrm{MS}}}_{mathrm{c}}; N_mathrm{f}=4)=1296(19),mathrm{MeV}$ and $m^{overline{mathrm{MS}}}_{mathrm{c}}(3,mathrm{GeV}; N_mathrm{f}=4)=1007(16),mathrm{MeV}$ for the renormalised charm quark mass
We present a lattice QCD calculation of the up, down, strange and charm quark masses performed using the gauge configurations produced by the European Twisted Mass Collaboration with Nf = 2 + 1 + 1 dynamical quarks, which include in the sea, besides two light mass degenerate quarks, also the strange and charm quarks with masses close to their physical values. The simulations are based on a unitary setup for the two light quarks and on a mixed action approach for the strange and charm quarks. The analysis uses data at three values of the lattice spacing and pion masses in the range 210 - 450 MeV, allowing for accurate continuum limit and controlled chiral extrapolation. The quark mass renormalization is carried out non-perturbatively using the RI-MOM method. The results for the quark masses converted to the bar{MS} scheme are: mud(2 GeV) = 3.70(17) MeV, ms(2 GeV) = 99.6(4.3) MeV and mc(mc) = 1.348(46) GeV. We obtain also the quark mass ratios ms/mud = 26.66(32) and mc/ms = 11.62(16). By studying the mass splitting between the neutral and charged kaons and using available lattice results for the electromagnetic contributions, we evaluate mu/md = 0.470(56), leading to mu = 2.36(24) MeV and md = 5.03(26) MeV.
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