Wilson Quarks Research Articles

Equation of state in finite-temperature QCD with improved Wilson quarks

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.

A local formulation of lattice QCD without unphysical fermion zero modes

The problem of unphysical zero modes in lattice QCD with Wilson fermions can be solved in a clean way by including a mass term proportional to i ψγ 5τ 3ψ in the standard lattice theory with N f = 2 mass degenerate Wilson quarks. We argue that up to cutoff effects, this lattice theory is equivalent to standard lattice QCD, for suitable choices of the mass parameters and with a natural re-interpretation of observables. On-shell O( a) improvement can be implemented in a straightforward way.

Equation of state in finite-temperature QCD with improved Wilson quarks

Equation of state in finite-temperature QCD with improved Wilson quarks

Nucleon decay matrix elements with the Wilson quark action: an update

Nucleon decay matrix elements with the Wilson quark action: an update

Meson masses and energies near the critical temperature with improved quenched Wilson quarks

Meson masses and energies near the critical temperature with improved quenched Wilson quarks

Quenched light hadron spectrum

We present results of a large-scale simulation for the flavor nonsinglet light hadron spectrum in quenched lattice QCD with the Wilson quark action. Hadron masses are calculated at four values of lattice spacing in the range a approximately 0.1-0.05 fm on lattices with a physical extent of 3 fm at five quark masses corresponding to m(pi)/m(rho) approximately 0.75-0.4. The calculated spectrum in the continuum limit shows a systematic deviation from experiment, though the magnitude of deviation is contained within 11%. Results for decay constants and light quark masses are also reported.

Calculation of the strange quark mass using domain wall fermions

We present a first calculation of the strange quark mass using domain wall fermions. This paper contains an overview of the domain wall discretization and a pedagogical presentation of the perturbative calculation necessary for computing the mass renormalization. We combine the latter with numerical simulations to estimate the strange quark mass. Our final result in the quenched approximation is 95(26) MeV in the $\overline{\mathrm{MS}}$ scheme at a scale of 2 GeV. We find that domain wall fermions have a small perturbative mass renormalization, similar to Wilson quarks, and exhibit good scaling behavior.

αSfromΥspectroscopy with dynamical Wilson fermions

We estimate the QCD coupling constant from a lattice calculation of the bottomonium spectrum. The second order perturbative expansion of the plaquette expectation value is employed to determine ${\ensuremath{\alpha}}_{S}$ at a scale set by the $2S\ensuremath{-}1S$ and $1P\ensuremath{-}1S$ level splittings. The latter are computed in NRQCD in a dynamical gauge field background with two degenerate flavors of Wilson quarks at intermediate masses and extrapolated to the chiral limit. Combining the ${N}_{f}=2$ result with the quenched result at equal lattice spacing we extrapolate to the physical number of light flavors to find a value of ${\ensuremath{\alpha}}_{\overline{\mathrm{MS}}}^{(5)}{(m}_{Z})=0.1118(17).$ The error quoted covers both statistical and systematic uncertainties in the scale determination. An additional $5%$ uncertainty comes from the choice of the underlying sea quark formulation and from truncation errors in perturbative expansions.

KaonBparameter with the Wilson quark action using chiral Ward identities

A lattice QCD calculation of the kaon $B$ parameter ${B}_{K}$ is carried out with the Wilson quark action in the quenched approximation at $\ensuremath{\beta}{=6/g}^{2}=5.9--6.5.$ The mixing problem of the $\ensuremath{\Delta}s=2$ four-quark operators is solved nonperturbatively with full use of chiral Ward identities employing four external quarks with an equal off-shell momentum in the Landau gauge. This method, without invoking any effective theory, enables us to construct the weak four-quark operators exhibiting good chiral behavior. Our results for ${B}_{K}$ with the nonperturbative mixing coefficients show small scaling violation beyond the lattice cutoff ${a}^{\ensuremath{-}1}\ensuremath{\sim}2.5\mathrm{GeV}.$ Our estimate concludes ${B}_{K}(\mathrm{N}\mathrm{D}\mathrm{R},2\mathrm{}\mathrm{GeV})=0.69(7)$ at ${a}^{\ensuremath{-}1}=2.7--4.3\mathrm{GeV},$ which agrees with the value obtained with the Kogut-Susskind quark action. For comparison we also calculate ${B}_{K}$ with one-loop perturbative mixing coefficients. While this yields incorrect values at finite lattice spacing, a linear extrapolation to the continuum limit as a function of $a$ leads to a result consistent with those obtained with the Ward identity method.

A test of a new simulation algorithm for dynamical quarks

Some results of test runs on a $6^3\times 12$ lattice with Wilson quarks and gauge group SU(2) for a previously proposed fermion algorithm by A. Slavnov are presented.

Renormalization of the iso-singlet scalar density in lattice QCD with Wilson quarks

Due to the absence of an exact chiral symmetry in lattice QCD with Wilson fermions, the iso-singlet scalar density has to be renormalized both additively and multiplicatively. We propose to use chiral Ward identities between correlation functions derived from the Schrödinger functional to determine the relevant renormalization constants directly in the chiral limit. Although the method does not rely on perturbation theory, we here use it to determine the renormalization constants and to obtain an idea of the typical size of cutoff effects. Finally we comment on the prospects for a direct determination of the chiral condensate as expectation value of a renormalized scalar density.

Recent results on light hadron and quark masses

Recent results for the spectrum of light hadrons provide clear evidence for the failure of quenched QCD and encouraging signs that simulations with dynamical sea quarks rectify some of the discrepancies, although string breaking has not yet been observed. The use of perturbation theory to match lattice quark masses to continuum schemes remains questionable, but non-perturbative methods are poised to remove this uncertainty. The inclusion of dynamical sea quarks substantially reduces estimates of the light quark masses. New results for the lightest glueball and the lightest exotic hybrid state provide useful input to phenomenology, but still have limited or no treatment of mixing. The O( a)-improved Wilson quark action is well-established in quenched QCD for β ≥ 5.7, with most parameters obtainable non-pertubatively, in which range scaling violations are small. Progress has also been made with high-order improvement schemes for both Wilson and staggered quarks.

Hadron matrix elements for nucleon decay with the Wilson quark action

We report preliminary results of our study of matrix elements of baryon number violating operators which appear in the low-energy effective Lagrangian of (SUSY-)Grand Unified Theories. The calculation is performed on a 32 3 × 80 lattice at β = 6.1 using Wilson fermions in the quenched approximation. Our calculation is independent of details of (SUSY-)GUT models and covers all interesting decay modes.

An estimate of α S from bottomonium in unquenched QCD

We estimate the strong coupling constant from the perturbative expansion of the plaquette. The scale is set by the 2S-1S and 1P-1S splittings in bottomonium which are computed in NRQCD on dynamical gauge configurations with n f = 2 degenerate Wilson quarks at intermediate masses. We have increased the statistics of our spectrum calculation in order to reliably extrapolate in the sea-quark mass. We find a value of α MS ( m Z ) = 0.1118(26) which is somewhat lower than previous estimates within NRQCD.

Quenched light hadron spectrum with the Wilson quark action: Final results from CP-PACS

We report the final results of the CP-PACS calculation for the quenched light hadron spectrum with the Wilson quark action. Our data support the presence of quenched chiral singularities, and this motivates us to use mass formulae based on quenched chiral perturbation theory in order to extrapolate hadron masses to the physical point. Hadron masses and decay constants in the continuum limit show unambiguous systematic deviations from experiment. We also report the results for light quark masses.

Light quark masses using domain wall fermions

We compute the one—loop self—energy correction to the massive domain wall quark propagator. Combining this calculation with simulations at several gauge couplings, we estimate the strange quark mass in the continuum limit. The perturbative one—loop mass renormalization is comparable to that for Wilson quarks and considerably smaller than that for Kogut—Susskind quarks. Also, scaling violations appear mild in comparison to other errors at present. Given their good chiral behavior and these features, domain wall quarks are attractive for evaluating the light quark masses. Our preliminary quenched result is m s (2 GeV) = 82(15) MeV in the MS scheme.

O( a) improvement of lattice QCD with two flavors of Wilson quarks

We consider O)(a) improvement for two flavor lattice QCD. The improvement term in the action is computed non-perturbatively for a large range of the bare coupling. The position of the critical line and higher order lattice artifacts remaining after improvement are estimated. We also discuss the behavior of the HMC algorithm in our simulations.

Lattice QCD Calculation of the KaonBParameter with the Wilson Quark Action

The kaon $B$ parameter is calculated in quenched lattice QCD with the Wilson quark action. The mixing problem of the $\ensuremath{\Delta}s\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2$ four-quark operators is solved nonperturbatively with full use of chiral Ward identities, and this method enables us to construct the weak four-quark operators exhibiting good chiral behavior. We find ${B}_{K}(\mathrm{NDR},2\phantom{\rule{0ex}{0ex}}\mathrm{GeV})\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.69(7)$ (where NDR denotes naive dimensional regularization) at the lattice cutoff scale of ${a}^{\ensuremath{-}1}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2.7--4.3\mathrm{GeV}$.

Progress in finite-temperature lattice QCD

A review is given of developments in lattice studies of finite-temperature QCD. Recent results on the order and universality nature of chiral phase transition for two flavors of quarks carried out with the Kogut-Susskind quark action are summarized. Progress in understanding the phase diagram for the Wilson quark action is discussed. Results on the critical temperature, equation of state and screening masses are reviewed, and comparisons with perturbative predictions are made. Status of the long-standing issue of the high-density behavior of QCD is reported.

K+→π+π0decay amplitude with the Wilson quark action in quenched lattice QCD

We present a calculation for the ${K}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{0}$ decay amplitude using a quenched simulation of lattice QCD with the Wilson quark action at $\ensuremath{\beta}{=6/g}^{2}=6.1.$ The decay amplitude is extracted from the ratio, the $\stackrel{\ensuremath{\rightarrow}}{K}\ensuremath{\pi}\ensuremath{\pi}$ three-point function divided by either $K$ and $\ensuremath{\pi}$ meson two-point functions or $K$ meson two-point function and $I=2 \ensuremath{\pi}\ensuremath{\pi}$ four-point function; the two different methods yield consistent results. Finite size effects are examined with calculations made on ${24}^{3}\ifmmode\times\else\texttimes\fi{}64$ and ${32}^{3}\ifmmode\times\else\texttimes\fi{}64$ lattices, and are shown that they are explained by one-loop effects of chiral perturbation theory. The lattice amplitude is converted to the continuum value by employing a one-loop calculation of chiral perturbation theory, yielding a value in agreement with experiment if extrapolated to the chiral limit. We also report on the $K$ meson $B$ parameter ${B}_{K}$ obtained from the ${K}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{0}$ amplitude using chiral perturbation theory.