Wilson Quark Action Research Articles

Equation of state and heavy-quark free energy at finite temperature and density in two flavor lattice QCD with Wilson quark action

We study the equation of state at finite temperature and density in two-flavor QCD with the renormalization group improved gluon action and the clover-improved Wilson quark action on a ${16}^{3}\ifmmode\times\else\texttimes\fi{}4$ lattice. Along the lines of constant physics at ${m}_{\mathrm{PS}}/{m}_{\mathrm{V}}=0.65$ and 0.80, we compute the second and forth derivatives of the grand canonical partition function with respect to the quark chemical potential ${\ensuremath{\mu}}_{q}=({\ensuremath{\mu}}_{u}+{\ensuremath{\mu}}_{d})/2$ and the isospin chemical potential ${\ensuremath{\mu}}_{I}=({\ensuremath{\mu}}_{u}\ensuremath{-}{\ensuremath{\mu}}_{d})/2$ at vanishing chemical potentials, and study the behaviors of thermodynamic quantities at finite ${\ensuremath{\mu}}_{q}$ using these derivatives for the case ${\ensuremath{\mu}}_{I}=0$. In particular, we study density fluctuations at nonezero temperature and density by calculating the quark number and isospin susceptibilities and their derivatives with respect to ${\ensuremath{\mu}}_{q}$. To suppress statistical fluctuations, we also examine new techniques applicable at low densities. We find a large enhancement in the fluctuation of the quark number when the density increased near the pseudocritical temperature, suggesting a critical point at finite ${\ensuremath{\mu}}_{q}$ terminating the first order transition line between hadronic and quark-gluon-plasma phases. This result agrees with the previous results using staggered-type quark actions qualitatively. Furthermore, we study heavy-quark free energies and Debye screening masses at finite density by measuring the first and second derivatives of these quantities for various color channels of heavy quark-quark and quark-antiquark pairs. The results suggest that, to the leading order of ${\ensuremath{\mu}}_{q}$, the interaction between two quarks becomes stronger at finite densities, while that between quark and antiquark becomes weaker.

Physical point simulation in2+1flavor lattice QCD

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.

Hyperon–nucleon force from lattice QCD

We calculate potentials between a proton and a Ξ0 (hyperon with strangeness −2) through the equal-time Bethe–Salpeter wave function, employing quenched lattice QCD simulations with the plaquette gauge action and the Wilson quark action on (4.5 fm)4 lattice at the lattice spacing a≃0.14 fm. The ud quark mass in our study corresponds to mπ≃0.37 and 0.51 GeV, while the s quark mass corresponds to the physical value of mK. The central pΞ0 potential has a strong (weak) repulsive core in the S01 (S13) channel for r≲0.6 fm, while the potential has attractive well at medium and long distances (0.6 fm≲r≲1.2 fm) in both channels. The sign of the pΞ0 scattering length and its quark mass dependence indicate a net attraction in both channels at low energies.

2+1flavor lattice QCD toward the physical point

We present the first results of the PACS-CS project which aims to simulate 2+1 flavor lattice QCD on the physical point with the nonperturbatively $O(a)$-improved Wilson quark action and the Iwasaki gauge action. Numerical simulations are carried out at the lattice spacing of $a=0.0907(13)$fm on a $32^3\times 64$ lattice with the use of the DDHMC algorithm to reduce the up-down quark mass. Further algorithmic improvements make possible the simulation whose ud quark mass is as light as the physical value. The resulting PS meson masses range from 702MeV down to 156MeV, which clearly exhibit the presence of chiral logarithms. An analysis of the PS meson sector with SU(3) ChPT reveals that the NLO corrections are large at the physical strange quark mass. In order to estimate the physical ud quark mass, we employ the SU(2) chiral analysis expanding the strange quark contributions analytically around the physical strange quark mass. The SU(2) LECs ${\bar l}_3$ and ${\bar l}_4$ are comparable with the recent estimates by other lattice QCD calculations. We determine the physical point together with the lattice spacing employing $m_\pi$, $m_K$ and $m_\Omega$ as input. The hadron spectrum extrapolated to the physical point shows an agreement with the experimental values at a few % level of statistical errors, albeit there remain possible cutoff effects. We also find that our results of $f_\pi=134.0(4.2)$MeV, $f_K=159.4(3.1)$MeV and $f_K/f_\pi=1.189(20)$ with the perturbative renormalization factors are compatible with the experimental values. For the physical quark masses we obtain $m_{\rm ud}^\msbar=2.527(47)$MeV and $m_{\rm s}^\msbar=72.72(78)$MeV extracted from the axial-vector Ward-Takahashi identity with the perturbative renormalization factors.

LATTICE QCD SIMULATION OF HYPERON-NUCLEON POTENTIAL

We calculate pΞ0 potentials from the equal-time Bethe-Salpeter amplitude measured in the quenched QCD simulation with the spatial lattice volume, (4.4 fm)3. The standard Wilson gauge action with the gauge coupling β = 5.7 on 324 lattice together with the standard Wilson quark action is used. The hopping parameter κud = 0.1678 is chosen for u and d quarks, which corresponds to mπ ≃ 0.37 GeV . The physical strange quark mass is used by taking the parameter κs = 0.1643 which is deduced from the physical K meson mass. The lattice spacing a = 0.1420 fm is determined by the physical ρ meson mass. We find that the pΞ0 potential has sizable spin dependence. Strong repulsive core is found in 1S0 channel while the effective central potential in the 3S1 channel has relatively weak repulsive core. The potentials also have weak attractive parts in the medium to long distance region (0.6 fm ≲ r ≲ 1.2 fm ) in both of the 1S0 and 3S1 channels.

Light-quark masses from unquenched lattice QCD

We calculate the light meson spectrum and the light quark masses by lattice QCD simulation, treating all light quarks dynamically and employing the Iwasaki gluon action and the nonperturbatively $O(a)$-improved Wilson quark action. The calculations are made at the squared lattice spacings at an equal distance ${a}^{2}\ensuremath{\simeq}0.005$, 0.01, and $0.015\text{ }\text{ }{\mathrm{fm}}^{2}$, and the continuum limit is taken assuming an $O({a}^{2})$ discretization error. The light meson spectrum is consistent with experiment. The up, down, and strange quark masses in the $\overline{\mathrm{MS}}$ scheme at 2 GeV are $\overline{m}=({m}_{u}+{m}_{d})/2={3.55}_{\ensuremath{-}0.28}^{+0.65}\text{ }\text{ }\mathrm{MeV}$ and ${m}_{s}={90.1}_{\ensuremath{-}6.1}^{+17.2}\text{ }\text{ }\mathrm{MeV}$ where the error includes statistical and all systematic errors added in quadrature. These values contain the previous estimates obtained with the dynamical $u$ and $d$ quarks within the error.

Nuclear Force from Lattice QCD

The nucleon-nucleon (NN) potential is studied by lattice QCD simulations in the quenched approximation, using the plaquette gauge action and the Wilson quark action on a 32(4) [approximately (4.4 fm)(4)] lattice. A NN potential V(NN)(r) is defined from the equal-time Bethe-Salpeter amplitude with a local interpolating operator for the nucleon. By studying the NN interaction in the (1)S(0) and (3)S(1) channels, we show that the central part of V(NN)(r) has a strong repulsive core of a few hundred MeV at short distances (r approximately < 0.5 fm) surrounded by an attractive well at medium and long distances. These features are consistent with the known phenomenological features of the nuclear force.

Thermodynamics of two-flavour lattice QCD with an improved Wilson quark action at non-zero temperature and density

We report the current status of our systematic studies of the QCD thermodynamics by lattice QCD simulations with two flavours of improved Wilson quarks. We evaluate the critical temperature of two-flavour QCD in the chiral limit at a zero chemical potential and show the preliminary result. Also we discuss fluctuations at non-zero temperature and density by calculating the quark number and isospin susceptibilities and their derivatives with respect to the chemical potential.

Non-perturbative improvement of the axial current with three dynamical flavors and the Iwasaki gauge action

We perform a non-perturbative determination of the improvement coefficient c_A to remove O(a) discretization errors in the axial vector current in three-flavor lattice QCD with the Iwasaki gauge action and the standard O$(a)$-improved Wilson quark action. An improvement condition with a good sensitivity to c_A is imposed at constant physics. Combining our results with the perturbative expansion, c_A is now known rather precisely for 1/a \gtrsim 1.6 GeV.

Heavy-quark free energy, Debye mass, and spatial string tension at finite temperature in two flavor lattice QCD with Wilson quark action

We study Polyakov loop correlations and spatial Wilson loop at finite temperature in two-flavor QCD simulations with the RG-improved gluon action and the clover-improved Wilson quark action on a ${16}^{3}\ifmmode\times\else\texttimes\fi{}4$ lattice. From the line of constant physics at ${m}_{\mathrm{PS}}/{m}_{\mathrm{V}}=0.65$ and 0.80, we extract the heavy-quark free energies, the effective running coupling ${g}_{\mathrm{eff}}(T)$ and the Debye screening mass ${m}_{D}(T)$ for various color channels of heavy quark-quark and quark-antiquark pairs above the critical temperature. The free energies are well approximated by the screened Coulomb form with the appropriate Casimir factors at high temperature. The magnitude and the temperature dependence of the Debye mass are compared to those of the next-to-leading-order thermal perturbation theory and to a phenomenological formula in terms of ${g}_{\mathrm{eff}}(T)$. We make a comparison between our results with the Wilson quark action and the previous results with the staggered quark action. The spatial string tension is also studied in the high temperature phase and is compared to the next-to-next-leading-order prediction in an effective theory with dimensional reduction.

A NUMERICAL STUDY OF IMPROVED WILSON QUARK ACTIONS ON ANISOTROPIC LATTICES

Tadpole improved Wilson quark actions with clover terms on anisotropic lattices are studied numerically. Using asymmetric lattice volumes, the pseudo-scalar meson dispersion relations are measured for 8 lowest lattice momentum modes with quark mass values ranging from the strange to the charm quark with various values of the gauge coupling β and 3 different values of the bare speed of light parameter ν. These results can be utilized to extrapolate or interpolate to obtain the optimal value for the bare speed of light parameter νopt(m) at a given gauge coupling for all bare quark mass values m. In particular, the optimal values of ν at the physical strange and charm quark mass are given for various gauge couplings. The lattice action with these optimized parameters can then be used to study physical properties of hadrons involving either light or heavy quarks.

A NUMERICAL STUDY OF IMPROVED QUARK ACTIONS ON ANISOTROPIC LATTICES

Tadpole improved Wilson quark actions with clover terms on anisotropic lattices are studied numerically. Using asymmetric lattice volumes, the pseudoscalar meson dispersion relations are measured for eight lowest lattice momentum modes with quark mass values ranging from the strange to the charm quark with various values of the gauge coupling β and three different values of the bare speed of light parameter ν. These results can be utilized to extrapolate or interpolate to obtain the optimal value for the bare speed of light parameter ν opt (m) at a given gauge coupling for all bare quark mass values m. In particular, the optimal values of ν at the physical strange and charm quark mass are given for various gauge couplings. The lattice action with these optimized parameters can then be used to study physical properties of hadrons involving either light or heavy quarks.

Spin3/2pentaquarks in anisotropic lattice QCD

A high-precision mass measurement for the pentaquark (5Q) Theta^+ in J^P=3/2^{\pm} channel is performed in anisotropic quenched lattice QCD using a large number of gauge configurations as N_{conf}=1000. We employ the standard Wilson gauge action at beta=5.75 and the O(a) improved Wilson (clover) quark action with kappa=0.1210(0.0010)0.1240 on a 12^3 \times 96 lattice with the renormalized anisotropy as a_s/a_t = 4. The Rarita-Schwinger formalism is adopted for the interpolating fields. Several types of the interpolating fields with isospin I=0 are examined such as (a) the NK^*-type, (b) the (color-)twisted NK^*-type, (c) a diquark-type. The chiral extrapolation leads to only massive states, i.e., m_{5Q} \simeq 2.1-2.2 GeV in J^P=3/2^- channel, and m_{5Q} = 2.4-2.6 GeV in J^P=3/2^+ channel. The analysis with the hybrid boundary condition(HBC) is performed to investigate whether these states are compact 5Q resonances or not. No low-lying compact 5Q resonance states are found below 2.1GeV.

Search for the possibleS=+1pentaquark states in quenched lattice QCD

We study spin $\frac12$ hadronic states in quenched lattice QCD to search for a possible $S=+1$ pentaquark resonance. Simulations are carried out on $8^3\times 24$, $10^3\times 24$, $12^3\times 24$ and $16^3\times 24$ lattices at $\beta$=5.7 at the quenched level with the standard plaquette gauge action and the Wilson quark action. We adopt a Dirichlet boundary condition in the time direction for the quark to circumvent the possible contaminations due to the (anti)periodic boundary condition for the quark field, which are peculiar to the pentaquark. By diagonalizing the $2\times 2$ correlation matrices constructed from two independent operators with the quantum numbers $(I,J)=(0,\frac12)$, we successfully obtain the energies of the lowest state and the 2nd-lowest state in this channel. The analysis of the volume dependence of the energies and spectral weight factors indicates that a resonance state is likely to exist slightly above the NK threshold in $(I,J^P)=(0,\frac12^-)$ channel.

Publisher’s Note: NonperturbativeO(a)improvement of Wilson quark action in three-flavor QCD with plaquette gauge action [Phys. Rev. D71, 054505 (2005)

Publisher’s Note: Nonperturbative<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>O</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>a</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>improvement of Wilson quark action in three-flavor QCD with plaquette gauge action [Phys. Rev. D<b>71</b>, 054505 (2005)

NonperturbativeO(a)improvement of Wilson quark action in three-flavor QCD with plaquette gauge action

We perform a non-perturbative determination of the O(a)-improvement coefficient c_SW for the Wilson quark action in three-flavor QCD with the plaquette gauge action. Numerical simulations are carried out in a range of \beta=12.0-5.2 on a single lattice size of 8^3x16 employing the Schr\"odinger functional setup of lattice QCD. As our main result, we obtain an interpolation formula for c_SW and the critical hopping parameter K_c as a function of the bare coupling. This enables us to remove O(a) scaling violation from physical observables in future numerical simulation in the wide range of \beta. Our analysis with a perturbatively modified improvement condition for c_SW suggests that finite volume effects in c_SW are not large on the 8^3x16 lattice. We investigate N_f dependence of c_SW by additional simulations for N_f=4, 2 and 0 at \beta=9.6. As a preparatory step for this study, we also determine c_SW in two-flavor QCD at \beta=5.2. At this \beta, several groups carried out large-scale calculations of the hadron spectrum, while no systematic determination of c_SW has been performed.

Pentaquark baryon in anisotropic lattice QCD

The penta-quark(5Q) baryon is studied in anisotropic quenched lattice QCD with renormalized anisotropy a_s/a_t=4 for a high-precision mass measurement. The standard Wilson action at beta=5.75 and the O(a) improved Wilson quark action with kappa=0.1210(0.0010)0.1240 are employed on a 12^3 \times 96 lattice. Contribution of excited states is suppressed by using a smeared source. We investigate both the positive- and negative-parity 5Q baryons with I=0 and spin J=1/2 using a non-NK-type interpolating field. After chiral extrapolation, the lowest positive-parity state is found to have a mass, m_{Theta}=2.25 GeV, which is much heavier than the experimentally observed Theta^+(1540). The lowest negative-parity 5Q appears at m_{Theta}=1.75 GeV, which is near the s-wave NK threshold. To distinguish spatially-localized 5Q resonances from NK scattering states, we propose a new general method imposing a ``Hybrid Boundary Condition (HBC)'', where the NK threshold is artificially raised without affecting compact five-quark states. The study using the HBC method shows that the negative-parity state observed on the lattice is not a compact 5Q but an s-wave NK-scattering state.

Meson-Meson Scattering on Anisotropic Lattices

Using the tadpole improved Wilson quark action on small, coarse,and anisotropic lattices, meson-meson scattering lengths arecalculated within quenched approximation. The study coverspion-pion scattering in the I = 2 channel and kaon-pion scatteringin the I = 3/2 channel. The results are extrapolated towards thechiral limit. Finite volume and finite lattice spacing errors arealso analyzed and results in the infinite volume and continuumlimit are obtained. Our results are compared with the resultsobtained using Roy equations, chiral perturbation theory,dispersion relations, and the experimental data. We also compareour results with other lattice results on the scattering lengths.

Light Hadron Spectrum, Renormalization Constants and Light Quark Masses with Two Dynamical Fermions

The results of a preliminary partially quenched ( N f = 2 ) study of the light hadron spectrum, renormalization constants and light quark masses are presented. Numerical simulations are carried out with the LL-SSOR preconditioned Hybrid Monte Carlo with two degenerate dynamical fermions, using the plaquette gauge action and the Wilson quark action at β = 5.8 . Finite volume effects have been investigated employing two lattice volumes: 16 3 × 48 and 24 3 × 48. Configurations have been generated at four values of the sea quark mass corresponding to M P S / M V ≃ 0.6 ÷ 0.8 .

Light hadron spectrum in 2+1 flavor full QCD by CP-PACS and JLQCD Collaborations

CP-PACS and JLQCD Collaborations are carrying out a joint project of the 2+1 flavor full QCD with the RG-improved gauge action and the non-perturbatively O ( a ) -improved Wilson quark action. This simulation removes quenching effects of all three light quarks, which is the last major uncertainty in lattice QCD. In this report we present our results for the light meson spectrum and quark masses on a 20 3 × 40 lattice at the lattice spacing a ≃ 0.10 fm.