Improved Wilson Quarks Research Articles

On cutoff effects in lattice QCD from short to long distances

We discuss kinematical enhancements of cutoff effects at short and intermediate distances. Starting from a pedagogical example with periodic boundary conditions, we switch to the case of the Schrödinger functional, where the theoretical analysis is checked by precise numerical data with Nf=2 dynamical O(a)-improved Wilson quarks. Finally we present an improved determination of the renormalization of the axial current in that theory.

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.

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.

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.

Non-perturbative renormalization of the static axial current in two-flavour QCD

We perform the non-perturbative renormalization of matrix elements of the static-light axial current by a computation of its scale dependence in lattice QCD with two flavours of massless O(a) improved Wilson quarks. The regularization independent factor that relates any running renormalized matrix element of the axial current in the static effective theory to the renormalization group invariant one is evaluated in the Schroedinger functional scheme, where in this case we find a significant deviation of the non-perturbative running from the perturbative prediction. An important technical ingredient to improve the precision of the results consists in the use of modified discretizations of the static quark action introduced earlier by our collaboration. As an illustration how to apply the renormalization of the static axial current presented here, we connect the bare matrix element of the current to the B_s-meson decay constant in the static approximation for one value of the lattice spacing, a ~ 0.08 fm, employing large-volume N_f=2 data at beta=5.3.

Axial coupling constant of the nucleon for two flavors of dynamical quarks in finite and infinite volume

We present data for the axial coupling constant ${g}_{A}$ of the nucleon obtained in lattice QCD with two degenerate flavors of dynamical nonperturbatively improved Wilson quarks. The renormalization is also performed nonperturbatively. For the analysis we give a chiral extrapolation formula for ${g}_{A}$ based on the small scale expansion scheme of chiral effective field theory for two degenerate quark flavors. Applying this formalism in a finite volume, we derive a formula that allows us to extrapolate our data simultaneously to the infinite volume and to the chiral limit. Using the additional lattice data in finite volume, we are able to determine the axial coupling of the nucleon in the chiral limit without imposing the known value at the physical point.

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.

Non-perturbative quark mass renormalization in two-flavor QCD

The running of renormalized quark masses is computed in lattice QCD with two flavors of massless O ( a ) improved Wilson quarks. The regularization and flavor independent factor that relates running quark masses to the renormalization group invariant ones is evaluated in the Schrödinger functional scheme. Using existing data for the scale r 0 and the pseudoscalar meson masses, we define a reference quark mass in QCD with two degenerate quark flavors. We then compute the renormalization group invariant reference quark mass at three different lattice spacings. Our estimate for the continuum value is converted to the strange quark mass with the help of chiral perturbation theory.

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.

The pseudoscalar decay constant

We discuss insights that may be drawn from our recent 2 flavour O ( a ) –improved Wilson quark simulations. We discuss the evidence of the onset of chiral logarithms in the pion decay constant. An overview is given of current extrapolation methods and a modification of chiral perturbation theory is presented as an approach for sensibly extrapolating to the physical quark masses.

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.

Improved Wilson QCD simulations with light quark masses

We present results from simulations using 2 flavours of O(a)-improved Wilson quarks whose masses are about 1/3 of the physical strange quark mass. We present new data on the mass of the singlet pseudoscalar meson and evidence of the onset of chiral logarithms in the pion decay constant. The previously observed suppression of the topological susceptibility at lighter quark masses is confirmed. We report on the performance of the hybrid Monte Carlo algorithm at light quark masses.

Lattice study on kaon–pion scattering length in the I=3/2 channel

Using the tadpole improved Wilson quark action on small, coarse and anisotropic lattices, Kπ scattering length in the I=3/2 channel is calculated within quenched approximation. The results are extrapolated towards the chiral and physical kaon mass region. Finite volume and finite lattice spacing errors are also analyzed and a result in the infinite volume and continuum limit is obtained. Our result is compared with the results obtained using Roy equations, chiral perturbation theory, dispersion relations and the experimental data.

Simulating the Schrodinger functional with two pseudo-fermions: algorithmic study and the running mass

We present an algorithmic study for the simulation of two massless flavors of O(a) improved Wilson quarks with Schrödinger functional boundary conditions. The algorithm used is Hybrid Monte Carlo with two pseudo-fermion fields as proposed by M. Hasenbusch. A gain in CPU cost of a factor two is reached when compared to one pseudo-fermion field due to the larger possible step-size. This study is integrated in the ALPHA project for the computation of the running of the renormalized quark mass. We include an update on these physics results.

Non-perturbative renormalization of the axial current with improved Wilson quarks

We present a new normalization condition for the axial current, which is derived from the PCAC relation with non-vanishing mass. Using this condition reduces the O(r_0 m) corrections to the axial current normalization constant Z_A for an easier chiral extrapolation in the cases, where simulations at zero quark-mass are not possible. The method described here also serves as a preparation for a determination of Z_A in the full two-flavor theory.

Dynamical fermion simulations of QCD on anisotropic lattices

Abstract Simulations of QCD with two flavours of improved Wilson quarks on an anisotropic lattice are discussed. Methods for improving the performance of the Hybrid Monte Carlo (HMC) algorithm in these studies are described.

Light hadron spectrum in three-flavor QCD with O(a)-improved Wilson quark action

Abstract We report on a calculation of the light hadron spectrum and quark masses in three-flavor dynamical QCD using the non-perturbatively O(a)-improved Wilson quark action and a renormalization-group improved gauge action. Simulations are carried out on a 163 × 32 lattice at β = 1.9, where a−1 ≅ 2 GeV, with 6 ud quark masses corresponding to m π m ϱ ≅ 0.64–0.77 and 2 s quark masses close to the physical value. We observe that the inclusion of dynamical strange quark brings the lattice QCD meson spectrum to good agreement with experiment. Dynamical strange quarks also lead to a reduction of the uds quark masses by about 15%.

Negative-parity baryon spectrum in quenched anisotropic lattice QCD

We investigate the negative-parity baryon spectra in quenched lattice QCD. We employ the anisotropic lattice with standard Wilson gauge and O(a) improved Wilson quark actions at three values of lattice spacings with renormalized anisotropy xi=a_sigma/a_tau=4, where a_sigma and a_tau are spatial and temporal lattice spacings, respectively. The negative-parity baryons are measured with the parity projection. In particular, we pay much attention to the lowest SU(3) flavor-singlet negative-parity baryon, which is assigned as the Lambda(1405) in the quark model. For the flavor octet and decuplet negative-parity baryons, the calculated masses are close to the experimental values of corresponding lowest-lying negative-parity baryons. In contrast, the flavor-singlet baryon is found to be about 1.7 GeV, which is much heavier than the Lambda(1405). Therefore, it is difficult to identify the Lambda(1405) to be the flavor-singlet three-quark state, which seems to support an interesting picture of the penta-quark (uds qbar q) state or the N-Kbar molecule for the Lambda(1405).