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Register a new userMeson correlators in a finite volume near the chiral limit
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Authors
Hidenori Fukaya
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We report on the results of our calculation of meson correlators in a finite volume. The calculation is carried out in the quenched approximation near the chiral limit (down to Mq = 2.6 MeV) using the overlap fermion. For these small quark masses, the scalar and pseudo-scalar correlators are well approximated with a few hundred eigenmodes. The results for both connected and disconnected correlators are compared with the theoretical predictions of quenched chiral perturbation theory.
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A simulation of lattice QCD at (or even below) the physical pion mass is feasible on a small lattice size of sim 2 fm. The results are, however, subject to large finite volume effects. In order to precisely understand the chiral behavior in a finite volume, we develop a new computational scheme to interpolate the conventional epsilon and p regimes within chiral perturbation theory. In this new scheme, we calculate the two-point function in the pseudoscalar channel, which is described by a set of Bessel functions in an infra-red finite way as in the epsilon regime, while chiral logarithmic effects are kept manifest as in the p regime. The new ChPT formula is compared to our 2+1- flavor lattice QCD data near the physical up and down quark mass, mud sim 3 MeV on an L sim 1.8 fm lattice. We extract the pion mass = 99(4) MeV, from which we attempt a chiral interpolation of the observables to the physical point.
We present results for mesonic propagators in temporal and spatial directions at T below and above the deconfining transition in quenched QCD. Anisotropic lattices are used to get enough information in the temporal direction. We use the Wilson fermion action for light quarks and Fermilab action for heavy quarks.
We compute hadron masses and the lowest moments of unpolarized and polarized nucleon structure functions down to pion masses of 300 MeV, in an effort to make unambiguous predictions at the physical light quark mass.
A numerical study of quenched QCD for light quarks is presented using O(a) improved fermions. Particular attention is paid to the possible existence and determination of quenched chiral logarithms. A `safe region to use for chiral extrapolations appears to be at and above the strange quark mass.
We perform an analysis of the QCD lattice data on the baryon octet and decuplet masses based on the relativistic chiral Lagrangian. The baryon self energies are computed in a finite volume at next-to-next-to-next-to leading order (N$^3$LO), where the dependence on the physical meson and baryon masses is kept. The number of free parameters is reduced significantly down to 12 by relying on large-$N_c$ sum rules. Altogether we describe accurately more than 220 data points from six different lattice groups, BMW, PACS-CS, HSC, LHPC, QCDSF-UKQCD and NPLQCD. Values for all counter terms relevant at N$^3$LO are predicted. In particular we extract a pion-nucleon sigma term of 39$_{-1}^{+2}$ MeV and a strangeness sigma term of the nucleon of $sigma_{sN} = 84^{+ 28}_{-;4}$ MeV. The flavour SU(3) chiral limit of the baryon octet and decuplet masses is determined with $(802 pm 4)$ MeV and $(1103 pm 6)$ MeV. Detailed predictions for the baryon masses as currently evaluated by the ETM lattice QCD group are made.
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