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Register a new userSU(2) and SU(3) chiral perturbation theory analyses on meson and baryon masses in 2+1 flavor lattice QCD
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We investigate the quark mass dependence of meson and baryon masses obtained from 2+1 flavor dynamical quark simulations performed by the PACS-CS Collaboration. With the use of SU(2) and SU(3) chiral perturbation theories up to NLO, we examine the chiral behavior of the pseudoscalar meson masses and the decay constants in terms of the degenerate up-down quark mass ranging form 3 MeV to 24 MeV and two choices of the strange quark mass around the physical value. We discuss the convergence of the SU(2) and SU(3) chiral expansions and present the results for the low energy constants. We find that the SU(3) expansion is not convergent at NLO for the physical strange quark mass. The chiral behavior of the nucleon mass is also discussed based on the SU(2) heavy baryon chiral perturbation theory up to NNLO. Our results show that the expansion is well behaved only up to m_pi^2 ~ 0.2 GeV^2.
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We have simulated QCD using 2+1 flavors of domain wall quarks on a $(2.74 {rm fm})^3$ volume with an inverse lattice scale of $a^{-1} = 1.729(28)$ GeV. The up and down (light) quarks are degenerate in our calculations and we have used four values for the ratio of light quark masses to the strange (heavy) quark mass in our simulations: 0.217, 0.350, 0.617 and 0.884. We have measured pseudoscalar meson masses and decay constants, the kaon bag parameter $B_K$ and vector meson couplings. We have used SU(2) chiral perturbation theory, which assumes only the up and down quark masses are small, and SU(3) chiral perturbation theory to extrapolate to the physical values for the light quark masses. While next-to-leading order formulae from both approaches fit our data for light quarks, we find the higher order corrections for SU(3) very large, making such fits unreliable. We also find that SU(3) does not fit our data when the quark masses are near the physical strange quark mass. Thus, we rely on SU(2) chiral perturbation theory for accurate results. We use the masses of the $Omega$ baryon, and the $pi$ and $K$ mesons to set the lattice scale and determine the quark masses. We then find $f_pi = 124.1(3.6)_{rm stat}(6.9)_{rm syst} {rm MeV}$, $f_K = 149.6(3.6)_{rm stat}(6.3)_{rm syst} {rm MeV}$ and $f_K/f_pi = 1.205(0.018)_{rm stat}(0.062)_{rm syst}$. Using non-perturbative renormalization to relate lattice regularized quark masses to RI-MOM masses, and perturbation theory to relate these to $bar{rm MS}$ we find $ m_{ud}^{bar{rm MS}}(2 {rm GeV}) = 3.72(0.16)_{rm stat}(0.33)_{rm ren}(0.18)_{rm syst} {rm MeV}$ and $m_{s}^{bar{rm MS}}(2 {rm GeV}) = 107.3(4.4)_{rm stat}(9.7)_{rm ren}(4.9)_{rm syst} {rm MeV}$.
We calculate the vector meson masses in $N_{rm f} = 2+1$ Wilson chiral perturbation theory at next-to-leading order. Generalizing the framework of heavy vector meson chiral perturbation theory, the quark mass and the lattice cutoff dependence of the vector meson masses is derived. Our chiral order counting assumes that the lattice cut-off artifacts are of the order of the typical pion momenta, $p sim aLambda_{rm QCD}^{2}$. This counting scheme is consistent with the one in the pseudo scalar meson sector where the O($a^2$) terms are included in the leading order chiral Lagrangian.
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 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 consider 2+1 flavor Wilson Chiral Perturbation Theory including the lattice spacing contributions of O($a^{2}$). We adopt a power counting appropriate for the unquenched lattice simulations carried out by the CP-PACS/JLQCD collaboration and compute the pseudo scalar meson masses to one loop. These expression are required to perform the chiral extrapolation of the CP-PACS/JLQCD lattice data.
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