Full QCD Simulations Research Articles

Recent results from the CP-PACS collaboration

We present an overview of recent results from the CP-PACS computer on the quenched light hadron spectrum and an on-going two-flavour full QCD study. We find that our quenched hadron mass results are compatible with the mass formulae predicted by quenched chiral perturbation theory, which we adopt in our final analysis. Quenched hadron masses in the continuum limit show unambiguous and systematic deviations from experiment. For our two-flavour full QCD simulation we present preliminary results on the light hadron spectrum, quark masses and the static potential. The question of dynamical sea quark effects in these quantities is discussed.

Decorrelating topology with HMC

The investigation of the decorrelation efficiency of the HMC algorithm with respect to vacuum topology is a prerequisite for trustworthy full QCD simulations, in particular for the computation of topology sensitive quantities. We demonstrate that for m π m ρ -ratios ≥ 0.69 sufficient tunneling between the topological sectors can be achieved, for two flavours of dynamical Wilson fermions close to the scaling region (β = 5.6). Our results are based on time series of length 5000 trajectories.

Tests of improved Kogut-Susskind fermion actions

Improved Kogut-Susskind quark actions containing repeatedly smeared links are studied to address the issue of flavor symmetry restoration. As a measure of the flavor symmetry restoration the mass spectrum of all the pions is computed. We present results for several variants of the “fat” actions that are suitable for full QCD simulations.

Testing improved actions for dynamical Kogut-Susskind quarks

We extend tests of {open_quotes}Naik{close_quotes} and {open_quotes}fat link{close_quotes} improvements of the Kogut-Susskind quark action to full QCD simulations, and verify that the improvements previously demonstrated in the quenched approximation also apply to dynamical quark simulations. We extend the study of flavor symmetry improvement to the complete set of pions and find that the nonlocal pions are significantly heavier than the local non-Goldstone pion. These results can be used to estimate the lattice spacing necessary for realistic simulations with this action. {copyright} {ital 1998} {ital The American Physical Society}

Finite density QCD in the chiral limit

We present the first results of an exact simulation of full QCD at finite density in the chiral limit. We have used a MFA (Microcanonical Fermionic Average) inspired approach for the reconstruction of the Grand Canonical Partition Function of the theory; using the fugacity expansion of the fermionic determinant we are able to move continuously in the (β − μ) plane with m = 0.

Potentials between heavy-light mesons from lattice and inverse scattering theory

We extend our investigation of heavy-light meson-meson interactions to a system consisting of a heavy-light meson and the corresponding antiparticle. An effective potential is obtained from meson-antimeson Green-functions computed in a quenched simulation with staggered fermions. Comparisons with a simulation using an O(a 2) tree-level and tadpole improved gauge action and a full QCD simulation show that lattice discretization errors and dynamical quarks have no drastic influence. Calculations from inverse scattering theory propose a similar shape for K potentials.

Quark masses with full QCD simulations

We calculate the masses of light and strange quarks using a high statistics lattice simulation of QCD with n f = 2 dynamical Wilson fermions. The simulation has been carried out at three different values of the sea quark mass. For each sea quark we have analyzed our data at five different values of the valence quark mass. This enables us to parameterize our results successfully in the ( m sea q,m valence q ) plane, using a linear ansatz according to first order chiral perturbation theory (CPBT). We find m ligt MS (2GeV) = 2.7(2)MeV , which is lower than the result found in quenched simulations. For the strange quark, in a sea of two dynamical light quarks, we obtain m strange MS (2GeV) = 140(20)MeV .

SESAM and T χL results for Wilson action—A status report

Results from two studies of full QCD with two flavours of dynamical Wilson fermions are presented. At beta=5.6, the region 0.83 > m_pi/m_rho > 0.56 at m_pia > 0.23 L^{-1} is explored. The SESAM collaboration has generated ensembles of about 200 statistically independent configurations on a 16^3 x 32-lattice at three different kappa-values and is entering the final phase of data analysis. The TXL simulation on a 24^3 x 40-lattice at two kappa-values has reached half statistics and data analysis has started recently, hence most results presented here are preliminary. The focus of this report is fourfold: we demonstrate that algorithmic improvements like fast Krylov solvers and parallel preconditioning recently introduced can be put into practise in full QCD simulations, we present encouraging observations as to the critical dynamics of the Hybrid Monte Carlo algorithm in the approach to the chiral limit, we mention signal improvements of noisy estimator techniques for disconnected diagrams to the pi-N sigma term, and we report on SESAM's results for light hadron spectrum, light quark masses, and heavy quarkonia.

A parallel SSOR preconditioner for lattice QCD

We present a parallelizable SSOR preconditioning scheme for Krylov subspace iterative solvers which proves to be efficient in lattice QCD applications involving Wilson fermions. Our preconditioner is based on a locally lexicographic ordering of the lattice points. In actual Hybrid Monte Carlo applications with the bi-conjugate gradient stabilized method BiCGstab, we achieve a gain factor of about 2 in the number of iterations compared to conventional odd-even preconditioning. Whether this translates into similar reductions in run time will depend on the parallel computer in use. We discuss implementation issues using the ‘Eisenstat-trick’ and machine specific advantages of the method for the APE100/Quadrics parallel computer. In a full QCD simulation on a 512-processor Quadrics QH4 we find a gain in cpu-time of a factor of 1.7 over odd-even preconditioning for a 24 3 × 40 lattice.

Molecular dynamics for full QCD simulations with an improved action

I derive the equation of motion in molecular dynamics for doing full lattice QCD simulations with clover quarks. The even-odd preconditioning technique, expected to significantly reduce the computational effort, is further developed for the simulations.

QCD with dynamical Wilson fermions—First results from SESAM

First results of a recently started simulation of full QCD with two flavours of sea-quarks at a coupling of β = 5.6 on a 163 × 32 lattice are presented. Emphasis is laid on the statistical significance that can be achieved by an “integrated luminosity” of 140 TFlop×hrs, for Hybrid Monte Carlo simulations at four intermediate values of mπmρ. The simulation takes place on the Quadrics QH2 at DESY/Zeuthen and DFG/Bielefeld. The performance is optimized by means of BiCGStab and the chronological inversion method of Brower et al. We discuss the systematic errors arising from lack of the molecular dynamic's reversibility on the 32-bit QH2. For plaquette and meson correlators we find integrated autocorrelation times of < 20 units of molecular dynamics time and exponential autocorrelation times of about 50 units. Using these results we perform preliminary measurements of the central potential and π and ρ correlators on independent configurations and obtain first estimates of the lattice spacings at three values of the dynamical hopping parameter.

Tuning up an oldtimer: Hybrid Monte Carlo with Wilson fermions

We show that BiCGStab inversion algorithm helps to speed up by 50 % the computation of the fermionic force inside the Hybrid Monte Carlo (HMC) simulation of full QCD with Wilson fermions, in the chiral regime of small quark masses.

APE results of hadron masses in full QCD simulations

We present numerical results obtained in full QCD with 2 flavors of Wilson fermions. We discuss the relation between the phase of Polyakov loops and the {\bf sea} quarks boundary conditions. We report preliminary results about the HMC autocorrelation of the hadronic masses, on a $16^3 \times 32$ lattice volume, at $\beta=5.55$ with $k_{sea}=0.1570$.

Manifestation of sea quark effects in the strong coupling constant in lattice QCD.

We demonstrate that sea quark effects of a magnitude expected from renormalization group considerations are clearly visible in the strong coupling constant measured in current full QCD simulations. Building on this result an estimate of ${\ensuremath{\alpha}}_{\stackrel{-}{\mathrm{MS}}}^{(5)}({M}_{Z})$ ($\stackrel{-}{\mathrm{MS}}$ denotes the modified minimal subtraction scheme) is made employing the charmonium $1S\ensuremath{-}1P$ mass splitting calculated on full QCD configurations generated with two flavors of dynamical Kogut-Susskind quarks to fix the scale.

Finite-size effects of hadron masses in lattice QCD: A comparative study for quenched and full QCD simulations.

A study of finite-size effects is carried out for hadron masses in the quenched simulation of lattice QCD using the Kogut-Susskind quark action. It is found that finite-size effects for quenched QCD are much smaller than those for full QCD, when hadron masses for the two cases are compared at the same physical lattice size and lattice spacing. Based on an extensive study of the boundary condition dependence of hadron masses we ascribe the origin of the difference to a partial cancellation of the finite-size effects among the Z(3)-related gauge configurations in quenched QCD; such a cancellation does not take place in full QCD due to Z(3) breaking effects of dynamical quarks. However, this does not mean finite-size errors are negligible in quenched QCD for lattice sizes of 2 to 3 fm used in current simulations; a still significant finite-size shift of hadron masses, especially of the nucleon mass, would pose a serious hindrance to obtaining the hadron mass spectrum at the few percent level aimed at in current quenched QCD simulations.

Status of APE100 and full QCD simulations

The poster reported the status of the APE100 project and the results of a first full QCD simulation performed on a 6 Gflops APE100 machine using the Hybrid Monte Carlo algorithm for 2 flavours Wilson fermions.

Full QCD hadron spectroscopy with two flavors of dynamical Kogut-Susskind quarks on the lattice.

A full lattice QCD simulation is carried out with two flavors of Kogut-Susskind staggered dynamical quarks using lattices of a size ranging from ${4}^{4}$ to ${20}^{4}$ at the gauge coupling constant $\ensuremath{\beta}=\frac{6}{{g}^{2}}=5.7$ with the quark mass of ${m}_{q}=0.01 \mathrm{and} 0.02$ in lattice units. Primary emphasis is given to the study of finite-lattice-size effects in the hadron mass spectrum. It is found that hadron masses suffer from substantial finite-size effects even for a lattice size of the order of 2 fm, showing the importance of a quantitative control of the effect for a comparison with the experimental spectrum at the accuracy of a few percent level. The finite-size correction is found to be well described by a power law in the lattice size, rather than an exponential form predicted by analytic formulas derived for point particles. It is suggested that the effect arises from the size of hadrons squeezed on a finite lattice. Finite-size effects on the realization of chiral symmetry are also studied. The behavior of the pion mass, the chiral condensate, and the mass splitting between parity partners all support a spontaneous breakdown of chiral symmetry for a large lattice size. Prediction from chiral Lagrangians on the size dependence of the chiral condensate does not describe the simulation results well, however, at least for the quark mass employed for the present study. Calculation of the pion decay constant with various relations derived from current algebra and partial conservation of axial-vector current gives ${f}_{\ensuremath{\pi}}=94(8)\ensuremath{-}105(9)$ MeV, with a method-dependent uncertainty contained within 10%. An examination is also made of the question of the dependence of hadron masses on hadron operators. Meson masses are basically operator independent, while baryon masses exhibit some operator dependence, necessitating further studies to resolve systematic uncertainties of this origin in the determination of the hadron mass spectrum.

The flavor dependence of the QCD finite temperature phase transition

We present finite temperature full QCD simulations on 16 3 × N t obtained with the 256-node Columbia Parallel processor during the last year. We see a first order transition with four flavors at N t = 4 for m q a = 0.01, 0.025, 0.0375, and 0.05, and at N t = 6 for m q a = 0.01 but not for m q a = 0.025, suggesting that the transition weakens as we move closer to the continuum limit. With two flavors at N t = 4 we do not see a transition for m q a = 0.01 and 0.025. With three flavors at N t = 4 we see a first order transition for m q a = 0.025; fixing m u, d a = 0.025 and increasing the strange quark mass to m s a = 0.1 we find no evidence of a transition and that m K / m p = 0.46(1), raising the possibility that in nature QCD may not undergo a finite temperature phase transition.

On the existence of a phase transition for QCD with three light quarks.

We report full QCD simulations on a 16{sup 3}{times}4 lattice. For two degenerate flavors no finite-temperature phase transition is found for quark masses of {ital ma}=0.01 and 0.025, where {ital a} is the lattice spacing, while for three degenerate flavors a first-order transition is easily seen for {ital ma}=0.025. Nature, with nearly massless up and down quarks and one heavier strange quark, lies between these two cases. For {ital m}{sub {ital u}},{ital d}{ital da}=0.025 and {ital m}{sub {ital s}}{ital a}=0.1 we find that {ital m}{sub {ital K}}/{ital m}{sub {rho}}=0.46(1) and that no transition occurs, calling into question the existence of a QCD phase transition.

The QCD phase transition with four flavors of light quarks

We have performed four-flavor, full QCD simulations on 16 3 × N t lattices with N t = 4 and 6 and with quark masses ma = 0.01, 0.025, 0.0375 and 0.05 where a is the lattice spacing. For N t = 4 a first-order transition is seen for all four mass values and the chiral m→0 limit is easily recognized for the two lightest mass values. For N t = 6 we see a weak first-order transition for ma = 0.01 but find that it has disappeared for ma = 0.025 showing that the transition becomes more easily destabilized by the quark mass as the lattice spacing is reduced.