Charmed and strange pseudoscalar meson decay constants from HISQ simulations

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 $m_{s}^{\bar{\rm MS}}(2 {\rm GeV}) = 107.3(4.4)_{\rm stat}(9.7)_{\rm ren}(4.9)_{\rm syst} {\rm MeV}$.

Light quark masses are calculated in lattice QCD with two degenerate flavors of dynamical quarks. The calculations are made with improved actions with lattice spacing a = 0.22-0.11 fm. In the continuum limit we find m(M&Smacr;)(ud)(2 GeV) = 3.44(+0.14)(-0.22) MeV using the pi and rho meson masses as physical input, and m(M&Smacr;)(s)(2 GeV) = 88(+4)(-6) MeV or 90(+5)(-11) MeV with the K or straight phi meson mass as additional input. The quoted errors represent statistical and systematic combined, the latter including those from continuum and chiral extrapolations, and from renormalization factors. Compared to quenched results, two flavors of dynamical quarks reduce quark masses by about 25%.

We present precise lattice computations for the b-quark mass, the quark mass ratios m(b)/m(c) and m(b)/m(s) as well as the leptonic B-decay constants. We employ gauge configurations with four dynamical quark flavors, up-down, strange and charm, at three values of the lattice spacing (a similar to 0.06-0.09 fm) and for pion masses as low as 210 MeV. Interpolation in the heavy quark mass to the bottom quark point is performed using ratios of physical quantities computed at nearby quark masses exploiting the fact that these ratios are exactly known in the static quark mass limit. Our results are also extrapolated to the physical pion mass and to the continuum limit and read m(b)((MS) over bar, m(b)) = 4.26(10) GeV, m(b)/m(c) = 4.42(8), m(b)/m(s) = 51.4(1.4), f(Bs) = 229(5) MeV, f(B) = 193(6) MeV, f(Bs)/f(B) = 1.184(25) and (f(Bs)/f(B))/(f(K)/f pi) = 0.997(17).

Partially quenched chiral perturbation theory and numerical simulations

Light hadron spectrum with two flavors of O(a) improved dynamical quarks: final results from JLQCD

The SU(3) flavour symmetry breaking expansion in up, down and strange quark masses is extended from hadron masses to meson decay constants. This allows a determination of the ratio of kaon to pion decay constants in QCD. Furthermore when using partially quenched valence quarks the expansion is such that SU(2) isospin breaking effects can also be determined. It is found that the lowest order SU(3) flavour symmetry breaking expansion (or Gell-Mann–Okubo expansion) works very well. Simulations are performed for 2+1 flavours of clover fermions at four lattice spacings.

CP-PACS results for quenched QCD spectrum with the Wilson action

We present results for the static interquark potential, light meson and baryon masses, and light pseudoscalar meson decay constants obtained from simulations of domain wall QCD with one dynamical flavour approximating the s quark, and two degenerate dynamical flavours with input bare masses ranging from m{sub s} to m{sub s}/4 approximating the u and d quarks. We compare these quantities obtained using the Iwasaki and DBW2 improved gauge actions, and actions with larger rectangle coefficients, on 16{sup 3}x32 lattices. We seek parameter values at which both the chiral symmetry breaking residual mass due to the finite lattice extent in the fifth dimension and the Monte Carlo time history for topological charge are acceptable for this set of quark masses at lattice spacings above 0.1 fm. We find that the Iwasaki gauge action is best, demonstrating the feasibility of using QCDOC to generate ensembles which are good representations of the QCD path integral on lattices of up to 3 fm in spatial extent with lattice spacings in the range 0.09-0.13 fm. Despite large residual masses and a limited number of sea quark-mass values with which to perform chiral extrapolations, our results for light hadronic physics scale and agree with experimental measurementsmore » within our statistical uncertainties.« less

The QCD phase transition with 2, 3, and 4 flavors of dynamical quarks

We present results for ${f}_{B},$ ${f}_{{B}_{s}},$ ${f}_{D},$ ${f}_{{D}_{s}}$ and their ratios in the presence of two flavors of light sea quarks ${(N}_{f}=2).$ We use Wilson light valence quarks and Wilson and static heavy valence quarks; the sea quarks are simulated with staggered fermions. Additional quenched simulations with nonperturbatively improved clover fermions allow us to improve our control of the continuum extrapolation. For our central values the masses of the sea quarks are not extrapolated to the physical u, d masses; that is, the central values are ``partially quenched.'' A calculation using ``fat-link clover'' valence fermions is also discussed but is not included in our final results. We find, for example, ${f}_{B}{=190(7)(}_{\ensuremath{-}17}^{+24}{)(}_{\ensuremath{-}2}^{+11}{)(}_{\ensuremath{-}0}^{+8})\mathrm{MeV},$ ${f}_{{B}_{s}}{/f}_{B}{=1.16(1)(2)(2)(}_{\ensuremath{-}0}^{+4}),$ ${f}_{{D}_{s}}{=241(5)(}_{\ensuremath{-}26}^{+27}{)(}_{\ensuremath{-}4}^{+9}{)(}_{\ensuremath{-}0}^{+5})\mathrm{MeV},$ and ${f}_{B}{/f}_{{D}_{s}}{=0.79(2)(}_{\ensuremath{-}4}^{+5}{)(3)(}_{\ensuremath{-}0}^{+5}),$ where in each case the first error is statistical and the remaining three are systematic: the error within the partially quenched ${N}_{f}=2$ approximation, the error due to the missing strange sea quark and to partial quenching, and an estimate of the effects of chiral logarithms at small quark mass. The last error, though quite significant in decay constant ratios, appears to be smaller than has been recently suggested by Kronfeld and Ryan, and Yamada. We emphasize, however, that as in other lattice computations to date, the lattice $u,d$ quark masses are not very light and chiral log effects may not be fully under control.

Lattice QCD with light dynamical quarks

We present the results of the physical point simulation in 2+1 flavor lattice QCD with the nonperturbatively $O(a)$-improved Wilson quark action and the Iwasaki gauge action at $\beta=1.9$ on a $32^3 \times 64$ lattice. The physical quark masses together with the lattice spacing is determined with $m_\pi$, $m_K$ and $m_\Omega$ as physical inputs. There are two key algorithmic ingredients to make possible the direct simulation at the physical point: One is the mass-preconditioned domain-decomposed HMC algorithm to reduce the computational cost. The other is the reweighting technique to adjust the hopping parameters exactly to the physical point. The physics results include the hadron spectrum, the quark masses and the pseudoscalar meson decay constants. The renormalization factors are nonperturbatively evaluated with the Schr{\"o}dinger functional method. The results are compared with the previous ones obtained by the chiral extrapolation method.

Light hardon properties with improved staggered quarks

We report on our study of QCD thermodynamics with 2 ¡ 1 flavors of dynamical quarks.In this proceeding we present several thermodynamic quantities and our recent calculation of the critical temperature.In order to investigate the thermodynamic properties of QCD near the continuum limit we adopt improved staggered (p4) quarks coupled with tree-level Symanzik improved glue on N t ¢ 4 and 6 lattices.The simulations are performed with a physical value of the strange quark mass and light quark masses which are in the range of m q £ m s ¢ 0¤ 05 ¥ 0¤ 4. The lightest quark mass corresponds to a pion mass of about 150 MeV.

Effects of heavy sea quarks on the low energy physics are described by an effective theory where the expansion parameter is the inverse quark mass, 1/M. At leading order in 1/M (and neglecting light quark masses) the dependence of any low energy quantity on the heavy quark mass is given in terms of the ratio of Λ parameters of the effective and the fundamental theory. We define a function describing the scaling with the mass M. Our study of perturbation theory suggests that its perturbative expansion is very reliable for the bottom quark and also seems to work very well at the charm quark mass. The same is then true for the ratios of Λ(4)/Λ(5) and Λ(3)/Λ(4), which play a major rôle in connecting (almost all) lattice determinations of αMS¯(3) from the three-flavor theory with αMS¯(5)(MZ). Also the charm quark content of the nucleon, relevant for dark matter searches, can be computed accurately from perturbation theory.In order to further test perturbation theory in this situation, we investigate a very closely related model, namely QCD with Nf=2 heavy quarks. Our non-perturbative information is derived from simulations on the lattice, with masses up to the charm quark mass and lattice spacings down to about 0.023 fm followed by a continuum extrapolation. The non-perturbative mass dependence agrees within rather small errors with the perturbative prediction at masses around the charm quark mass. Surprisingly, from studying solely the massive theory we can make a prediction for the ratio Q0,21/t0=[Λt0(0)]Nf=2/[Λt0]Nf=0, which refers to the chiral limit in Nf=2. Here t0 is the Gradient Flow scale of [1]. The uncertainty for Q is estimated to be 2.5%. For the phenomenologically interesting Λ(3)/Λ(4), we conclude that perturbation theory introduces errors which are at most at the 1.5% level, smaller than other current uncertainties.