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An analysis of the pion mass and pion decay constant is performed using mixed-action Lattice QCD calculations with domain-wall valence quarks on ensembles of rooted, staggered n_f = 2+1 MILC configurations. Calculations were performed at two lattice spacings of b~0.125 fm and b~0.09 fm, at two strange quark masses, multiple light quark masses, and a number of lattice volumes. The ratios of light quark to strange quark masses are in the range 0.1 <= m_l / m_s <= 0.6, while pion masses are in the range 235 < m_pi < 680 MeV. A two-flavor chiral perturbation theory analysis of the Lattice QCD calculations constrains the Gasser-Leutwyler coefficients bar{l}_3 and bar{l}_4 to be bar{l}_3 = 4.04(40)(+73-55) and bar{l}_4 = 4.30(51)(+84-60). All systematic effects in the calculations are explored, including those from the finite lattice space-time volume, the finite lattice spacing, and the finite fifth dimension in the domain-wall quark action. A consistency is demonstrated between a chiral perturbation theory analysis at fixed lattice spacing combined with a leading order continuum extrapolation, and the mixed-action chiral perturbation theory analysis which explicitly includes the leading order discretization effects. Chiral corrections to the pion decay constant are found to give f_pi / f = 1.062(26)(+42-40) where f is the decay constant in the chiral limit. The most recent scale setting by the MILC Collaboration yields a postdiction of f_pi = 128.2(3.6)(+4.4-6.0)(+1.2-3.3) MeV at the physical pion mass.
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We measure the pion mass and decay constant on ensembles generated by the Wuppertal-Budapest Collaboration, and extract the NLO low-energy constants l_3 and l_4 of SU(2) chiral perturbation theory. The data are generated in 2+1 flavor simulations with Symanzik glue and 2-fold stout-smeared staggered fermions, with pion masses varying from 135 MeV to 400 MeV, lattice scales between 0.7 GeV and 2.0 GeV, and m_s kept at its physical value. Furthermore, by excluding the lightest mass points, we are able to test the reliability of SU(2) chPT as a tool to extrapolate towards the physical point from higher pion masses.
We have performed fits of the pseudoscalar masses and decay constants, from a variety of RBC-UKQCD domain wall fermion ensembles, to $SU(2)$ partially quenched chiral perturbation theory at next-to leading order (NLO) and next-to-next-to leading order (NNLO). We report values for 9 NLO and 8 linearly independent combinations of NNLO partially quenched low energy constants, which we compare to other lattice and phenomenological determinations. We discuss the size of successive terms in the chiral expansion and use our large set of low energy constants to make predictions for mass splittings due to QCD isospin breaking effects and the S-wave $pi pi$ scattering lengths. We conclude that, for the range of pseudoscalar masses explored in this work, $115~mathrm{MeV} lesssim m_{rm PS} lesssim 430~mathrm{MeV}$, the NNLO $SU(2)$ expansion is quite robust and can fit lattice data with percent-scale accuracy.
We perform a detailed, fully-correlated study of the chiral behavior of the pion mass and decay constant, based on 2+1 flavor lattice QCD simulations. These calculations are implemented using tree-level, O(a)-improved Wilson fermions, at four values of the lattice spacing down to 0.054 fm and all the way down to below the physical value of the pion mass. They allow a sharp comparison with the predictions of SU(2) chiral perturbation theory (chi PT) and a determination of some of its low energy constants. In particular, we systematically explore the range of applicability of NLO SU(2) chi PT in two different expansions: the first in quark mass (x-expansion), and the second in pion mass (xi-expansion). We find that these expansions begin showing signs of failure around M_pi=300 MeV for the typical percent-level precision of our N_f=2+1 lattice results. We further determine the LO low energy constants (LECs), F=88.0 pm 1.3pm 0.3 and B^msbar(2 GeV)=2.58 pm 0.07 pm 0.02 GeV, and the related quark condensate, Sigma^msbar(2 GeV)=(271pm 4pm 1 MeV)^3, as well as the NLO ones, l_3=2.5 pm 0.5 pm 0.4 and l_4=3.8 pm 0.4 pm 0.2, with fully controlled uncertainties. We also explore the NNLO expansions and the values of NNLO LECs. In addition, we show that the lattice results favor the presence of chiral logarithms. We further demonstrate how the absence of lattice results with pion masses below 200 MeV can lead to misleading results and conclusions. Our calculations allow a fully controlled, ab initio determination of the pion decay constant with a total 1% error, which is in excellent agreement with experiment.
We study various representations of infrared effective theory of SU(2) Gluodynamics as a (quantum) perfect lattice action. In particular we derive a monopole action and a string model of hadrons from SU(2) Gluodynamics. These are lattice actions which give almost cut-off independent physical quantities even on coarse lattices. The monopole action is determined by numerical simulations in the infrared region of SU(2) Gluodynamics. The string model of hadrons is derived from the monopole action by using BKT transformation. We illustrate the method and evaluate physical quantities such as the string tension and the mass of the lowest state of the glueball analytically using the string model of hadrons. It turns out that the classical results in the string model is near to the one in quantum SU(2) Gluodynamics.
Recent progress in lattice QCD calculations of nucleon structure will be presented. Calculations of nucleon matrix elements and form factors have long been difficult to reconcile with experiment, but with advances in both methodology and computing resources, this situation is improving. Some calculations have produced agreement with experiment for key observables such as the axial charge and electromagnetic form factors, and the improved understanding of systematic errors will help to increase confidence in predictions of unmeasured quantities. The long-omitted disconnected contributions are now seeing considerable attention and some recent calculations of them will be discussed.
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