X iv :h ep -l at /9 90 91 33 v 1 1 7 Se p 19 99 Heavy Quarkonia from Anisotropic and Isotropic Lattices ∗ CP-PACS Collaboration: A. Ali Khan, S. Aoki, R. Burkhalter, S. Ejiri, M. Fukugita, S. Hashimoto, N. Ishizuka, Y. Iwasaki, K. Kanaya, T. Kaneko, Y. Kuramashi, T. Manke, K. Nagai, M. Okawa, H.P. Shanahan, A. Ukawa and T. Yoshié Center for Computational Physics, University of Tsukuba, Tsukuba, Ibaraki 305-8577, Japan

We present recent Monte Carlo data for the axial charge of the nucleon obtained by the QCDSF-UKQCD collaboration for N-f = 2 dynamical quarks. A comparison with chiral perturbation theory in finite and infinite volume is attempted.

CP-PACS Collaboration A. Ali Khan, S. Aoki, R. Burkhalter, S. Ejiri, M. Fukugita, S. Hashimoto, N. Ishizuka, Y. Iwasaki, K. Kanaya, T. Kaneko, Y. Kuramashi, T. Manke, K. Nagai, M. Okawa, H. P. Shanahan, A. Ukawa, T. Yoshié Center for Computational Physics, University of Tsukuba, Tsukuba, Ibaraki 305-8577, Japan Institute of Physics, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan Institute for Cosmic Ray Research, University of Tokyo, Tanashi, Tokyo 188-8502, Japan High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801, Japan (March 16, 2006)

We present preliminary results for the axial and tensor charge of the nucleon obtained from simulations with N-f = 2 clover fermions. A comparison with chiral perturbation theory is attempted.

In the framework of relativistic SU(2)_f baryon chiral perturbation theory we calculate the volume dependence of the nucleon mass up to and including O(p^4). Since the parameters in the resulting finite size formulae are fixed from the pion mass dependence of the large volume nucleon masses and from phenomenology, we obtain a parameter-free prediction of the finite size effects. We present mass data from the recent N_f=2 simulations of the UKQCD and QCDSF collaborations and compare these data as well as published mass values from the dynamical simulations of the CP-PACS and JLQCD collaborations with the theoretical expectations. Remarkable agreement between the lattice data and the predictions of chiral perturbation theory in a finite volume is found.

The finite size effects on nucleon masses are calculated in relativistic chiral perturbation theory. Results are compared with two-flavor lattice results.

Light and heavy-light (b) hadrons are among the most interesting and among the most challenging quantities to calculate in lattice gauge theory. One would like to avoid discretization effects from very heavy quarks and to calculate chiral extrapolations and to calculate finite volume effects from light quarks or to minimize these effects. For this one uses effective theories: Chiral Perturbation Theory and Nonrelativistic QCD or Heavy Quark Effective Theory. Lattice results are reviewed on hadrons containing light quarks and light and b quarks, and discussed in the framework of effective theories.

Hasenbusch has proposed splitting the pseudo-fermionic action into two parts, in order to speed-up Hybrid Monte Carlo simulations of QCD. We have tested a different splitting, also using clover-improved Wilson fermions. An additional speed-up between 5 and 20% over the original proposal was achieved in production runs.

An algorithm for separating the high- and low-frequency molecular dynamics modes in hybrid Monte Carlo (HMC) simulations of gauge theories with dynamical fermions is presented. The separation is based on splitting the pseudo-fermion action into two parts, as was initially proposed by Hasenbusch. We propose to introduce different evolution time-scales for each part. We test our proposal in realistic simulations of two-flavor O(a) improved Wilson fermions. A speed-up of more than a factor of three compared to the standard HMC algorithm is observed in a typical run.

Received 26 November 2002DOI:https://doi.org/10.1103/PhysRevD.67.059901©2003 American Physical Society

For lattice calculations with light dynamical quarks, finite size effects have become an important aspect. We study finite size effects in nucleon masses on N-f = 2 dynamical lattices. of 1 - 2 fm. Predictions for the finite size effects are obtained in one-loop chiral perturbation theory.

We study the finite-temperature phase structure and the transition temperature of QCD with two flavors of dynamical quarks on a lattice with the temporal size $N_t=4$, using a renormalization group improved gauge action and the Wilson quark action improved by the clover term. The region of a parity-broken phase is identified, and the finite-temperature transition line is located on a two-dimensional parameter space of the coupling ($\beta=6/g^2$) and hopping parameter $K$. Near the chiral transition point, defined as the crossing point of the critical line of the vanishing pion mass and the line of finite-temperature transition, the system exhibits behavior well described by the scaling exponents of the three-dimensional O(4) spin model. This indicates a second-order chiral transition in the continuum limit. The transition temperature in the chiral limit is estimated to be $T_c = 171(4)$ MeV.

We investigate the chiral properties of quenched domain-wall QCD (DWQCD) at the lattice spacings ${a}^{\ensuremath{-}1}\ensuremath{\simeq}1$ and 2 GeV for both plaquette and renormalization-group (RG) improved gauge actions. In the case of the plaquette action we find that the quark mass defined through the axial Ward-Takahashi identity remains non-vanishing in the DWQCD chiral limit that the bare quark mass ${m}_{f}\ensuremath{\rightarrow}0$ and the length of the fifth dimension ${N}_{s}\ensuremath{\rightarrow}\ensuremath{\infty},$ indicating that chiral symmetry is not realized with quenched DWQCD up to ${a}^{\ensuremath{-}1}\ensuremath{\simeq}2$ GeV. The behavior is much improved for the RG-improved gauge action: while a nonvanishing quark mass remains in the chiral limit at ${a}^{\ensuremath{-}1}\ensuremath{\simeq}1$ GeV, the result at ${a}^{\ensuremath{-}1}\ensuremath{\simeq}2$ GeV is consistent with an exponentially vanishing quark mass in the DWQCD chiral limit, indicating the realization of exact chiral symmetry. An interpretation and implications are briefly discussed.

Chiral properties of QCD formulated with the domain-wall fermion (DWQCD) are studied using the anomalous quark mass m_5q and the spectrum of the 4-dimensional Wilson-Dirac operator. Numerical simulations are made with the standard plaquette gauge action and a renormalization-group improved gauge action. Results are reported on the density of zero eigenvalue obtained with the accumulation method, and a comparison is made with the results for m_5q.

We present a study of the topological susceptibility in lattice QCD with two degenerate flavors of dynamical quarks. The topological charge is measured on gauge configurations generated with a renormalization group improved gauge action and a mean held improved clover quark action at three values of beta = 6/g(2) with four sea quark masses at each beta. The lattice spacings at these beta 's are a approximate to 0.22, 0.16 and 0.11 fm at the physical up and down quark mass, which are fixed by the physical rho meson mass. The study is supplemented by simulations of pure SU(3) gauge theory with the same gauge action at 5 values of beta with lattice spacings 0.09 fm less than or similar toa less than or similar to0.27 fm. We employ a field-theoretic definition of the topological charge together with cooling. For the topological susceptibility in the continuum limit of pure SU(3) gauge theory we obtain chi (1/4)(t) = 197(-16)(+13) MeV where the error shows statistical and systematic ones added in quadrature, In full QCD chi (t) at heavy sea quark masses is consistent with that of pure SU(3) gauge theory. A decrease of chi (t) toward light quark masses, as predicted by the anomalous Ward-Takahashi identity for U(1) chiral symmetry, becomes clearer for smaller lattice spacings. The cross over in the behavior of chi (t) from heavy to light sea quark masses is discussed.

We study finite-temperature phase transition and equation of state for two-flavor QCD at N-t = 4 using an RG-improved gauge action and a meanfield-improved clover quark action. The pressure is computed using the integral method. The O(4) scaling of chiral order parameter is also examined.

We present a study of leptonic B meson decay constants in lattice QCD with two flavors (N-f = 2) of light dynamical quarks using nonrelativistic QCD for the heavy quark. Gauge configurations are generated with a renormalization-group improved gauge action and a mean-field-improved clover light quark action. Measurements are carried out at two values of beta = 6/g(2), each for four sea quark masses, corresponding to inverse lattice spacings a(-1) approximate to 1.3 and 1.8 GeV in the chiral limit of the sea quark. The continuum values of the decay constants are derived by evaluating the discretization errors at each finite lattice spacing. We find f(B)(Nf = 2) = 204(8)(29)(+44) MeV, f(Bs)(Nf = 2) = 242(9)(34)(+38) MeV, and f(Bs)(Nf = 2)/f(B)(Nf = 2) = 1.179(18)(23), where the errors listed are statistical, systematic and uncertainty due to choice of the physical quantity used to flx the scale. Comparison is made to quenched results (N-f = 0) obtained with the same action combination and matching lattice spacings. We find f(B)(Nf = 2)/f(B)(Nf = 0) = 1.07(5), f(Bs)(Nf = 2)/f(Bs)(Nf = 0) = 1.10(5) and (f(Bs)/f(B))(Nf = 2)/(f(Bs)/f(B))(Nf = 0) = 1.03(2), which indicate a 5-10 % increase in the values of the decay constants, but no appreciable change in the ratio f(Bs)/f(B), due to sea quarks.

We present a dynamical lattice calculation with two flavors for bottomonium states with an additional gluonic excitation. Using improved actions for the quarks and gauge fields at a lattice spacing of a approximate to0.1 fm, we find 10,977(61)(62) GeV for the energy of the lowest lying b (b) over barg hybrid, where the first error is statistical and the second denotes the systematic uncertainty due to the determination of scale. In a parallel quenched simulation we demonstrate explicitly that vacuum polarization effects are less than 10% of the splitting with the ground state.

We present a calculation of the B and D meson decay constants in lattice QCD with two (Nf=2) flavours of light dynamical quarks, using an O(a)-improved Wilson action for both light and heavy quarks and a renormalization-group improved gauge action. Simulations are made at three values of lattice spacing a=0.22, 0.16, 0.11 fm and four values of sea quark mass in the range m_PS/m_V \~= 0.8-0.6. Our estimate for the continuum values of the decay constants are fBd = 208(10)(11) MeV, fBs = 250(10)(13)(^{+8}_{-0}) MeV, fDd = 225(14)(14) MeV, fDs = 267(13)(17)(^{+10}_{-0}) MeV for Nf=2 where the statistical and systematic errors are separately listed, and the third error for fBs and fDs show uncertainty of determination of strange quark mass. We also carry out a set of quenched simulations using the same action to make a direct examination of sea quark effects. Taking the ratio of results for Nf=2 and Nf=0, we obtain fb^{Nf=2}/fb^{Nf=0} = 1.11(6), fbs^{Nf=2}/fbs^{Nf=0} = 1.14(5), fd^{Nf=2}/\fd^{Nf=0} = 1.03(6), fds^{Nf=2}/\fds^{Nf=0} = 1.07(5). They show a 10-15% increase in the Nf=2 results over those of Nf=0 for the B meson decay constants, while evidence for such a trend is statistically less clear for the D meson decay constants.

We report on a study of B mesons on N_f = 2 full QCD configurations using an RG-improved gauge action, NRQCD heavy quark action and tadpole-improved clover light quark action. Results on the heavy-light spectrum and the decay constants from 16^3x32 lattices at a^-1 1.5 GeV are presented, and compared with quenched results obtained with the same action combination at matching lattice spacings.