Eigenvalues of a Wilson loop operator are gauge invariant and their distribution undergoes a transition at infinite N as the size of the loop is changed. We study this transition using the average characteristic polynomial associated with the Wilson loop operator. We derive the scaling function in a certain double scaling limit for two dimensional QCD and hypothesize that the transition in three and four dimensional QCD are in the same universality class. Numerical evidence for this hypothesisis provided in three dimensions
We review studies of QCD thermodynamics by lattice QCD simulations with dynamical Wilson quarks. After explaining the basic properties of QCD with Wilson quarks at finite temperature including the phase structure and the scaling properties around the chiral phase transition, we discuss the critical temperature, the equation of state and heavy-quark free energies.
We review our results for lattice QCD at finite temperature and density from analytical and numerical calculations with Wilson fermions and overlap fermions.
We study the hadronic spectrum in quenched lattice QCD using an improved Wilson fermion action (Hamber-Wu(1983),Eguchi-Kawamoto(1984)) at $β= 5.7$ and $β=6.0$. We find a systematic reduction of the finite spacing effects compared to the results obtained by using the standard Wilson action.
An explicit solution is found for the most general independent correlation functions in lattice QCD$_2$ with Wilson action. The large-$N$ limit of these correlations may be used to reconstruct the eigenvalue distributions of Wilson loop operators for arbitrary loops. Properties of these spectral densities are discussed in the region $β<β_c={1\over 2}$.
The phase structure of lattice QCD with two flavors and Wilson fermions is studied analytically. At $β=0$ we obtain rigorous lower and upper bounds for the critical hopping parameter $k_c(0)$ from a convergent hopping parameter expansion to infinite order. The result supports the value $k_c(0)=\frac{1}{4}$ observed in Monte Carlo simulations.
The first results on lattice at finite temperature $T$ and chemical potential $μ$ with 2+1 flavors of Wilson quarks are presented. We have studied the dependence of chiral phase transition and deconfinement phase transition on quark mass. Finite volume size analysis and Binder cumulants are used to determine the properties of phase transition. Phase diagram of QCD with 2+1 flavors of Wilson quarks are presented.
We use the transfer matrix formalism to derive non-perturbative sum rules in Wilson's lattice QCD with N_f flavours of quarks. The discretization errors on these identities are treated in detail. As an application, it is shown how the sum rules can be exploited to give improved estimates of the continuum spectrum and static potential.
We analyse the leading logarithmic corrections to the $a^2$ scaling of lattice artefacts in QCD, following the seminal work of Balog, Niedermayer and Weisz in the O(n) non-linear sigma model. Limiting the discussion to contributions from the action, the leading logarithmic corrections can be determined by the anomalous dimensions of mass-dimension 6 operators. These operators form a minimal on-shell basis of the Symanzik Effective Theory. We present results for non-perturbatively O($a$) improved Wilson and Ginsparg-Wilson quarks.
Stabilized Wilson fermions are a reformulation of Wilson clover fermions that incorporates several numerical stabilizing techniques, but also a local change of the fermion action - the original clover term being replaced with an exponentiated version of it. We intend to apply the stabilized Wilson fermions toolbox to the thermodynamics of QCD, starting on the $N_f=3$ symmetric line on the Columbia plot, and to compare the results with those obtained with other fermion discretizations.
The O(a^2) contributions to the chiral effective Lagrangian for lattice QCD with Wilson fermions are constructed. The results are generalized to partially quenched QCD with Wilson fermions as well as to the "mixed'' lattice theory with Wilson sea quarks and Ginsparg-Wilson valence quarks.
We perform an extensive study of autocorrelation of several observables in lattice QCD with two degenerate flavours of naive Wilson fermions and unimproved Wilson gauge action using DD-HMC algorithm. We show that (1) at a given lattice spacing, autocorrelation of topological susceptibility decreases with decreasing quark mass and autocorrelations of plaquette and Wilson loop do not increase with decreasing quark mass, (2) autocorrelation of topological susceptibility substantially increases with decreasing lattice spacing but autocorrelation of topological charge density correlator shows only …
We present a first scaling test of twisted mass QCD with pure Wilson quarks for a twisting angle of pi/2. We have computed the vector meson mass and the pseudoscalar decay constant for different values of beta at fixed value of r_0 m_PS. The results obtained in the quenched approximation are compared with data for pure Wilson and non-perturbatively O(a) improved Wilson computations. We show that our results from Wilson twisted mass QCD show clearly reduced lattice spacing errors, consistent with O(a) improvement and without the need of any improvement terms added. These results thus provide nu…
We report on the status of our simulations of two-colour QCD with two flavours of Wilson quarks, at nonzero chemical potential and diquark source. Preliminary results are presented for the static quark potential, gluon propagator, and meson and diquark spectrum.
We present preliminary results from UKQCD simulations at light quark masses using two flavours of non-pertubatively improved Wilson fermions. We report on the performance of the standard HMC algorithm at these quark masses where m_pi/m_rho < 0.5 in comparison with simulations using improved staggered quarks.
We apply a recent proposal to speed up the Hybrid-Monte-Carlo simulation of systems with dynamical fermions to two flavor QCD with clover-improvement. For our smallest quark masses we see a speed-up of more than a factor of two compared with the standard algorithm.
In this work we present a calculation of the Wilson Coefficients $C_1$ and $C_2$ of the Effective Weak Hamiltonian to all-orders in $α_s$, using lattice simulations. Given the current availability of lattice spacings we restrict our calculation to unphysically light $W$ bosons around 2 GeV and we study the systematic uncertainties of the two Wilson Coefficients.
We study aspects concerning numerical simulations of Lattice QCD with two flavors of dynamical Ginsparg-Wilson quarks with degenerate masses. A Hybrid Monte Carlo algorithm is described and the formula for the fermionic force is derived for two specific implementations. The implementation with optimal rational approximation method is favored both in CPU time and memory consumption.
We present results from an analysis of the light spectrum and the decay constants f_π and f_V^{-1} in Full QCD with n_f=2 Wilson fermions at a coupling of beta=5.6 on a 16^3x32 lattice.
A comprehensive number of integrals emerging in one-loop computations in a gauge perturbation theory on the lattice with Wilson fermions at $r=1$ is computed using the Burgio--Caracciolo--Pelissetto algorithm and the FORM package. An explicit analytical form of the recursion relations needed for such computations is presented.
We discuss color screening in 2+1 flavor QCD in terms of free energies of a static quark-antiquark pair. Thermal modifications of long distance correlations in quark-antiquark systems are studied in terms of static meson correlators. We calculate the Polyakov loop correlator, the color-singlet Wilson line correlator in Coulomb gauge and the cyclic Wilson loop on lattices using the HISQ/Tree action and almost physical quark mases with $N_τ= 4, 6, 8, 10, 12$. We present results in the continuum limit for temperatures up to $T \lesssim 650$ MeV and discuss the linear divergence of the cyclic Wils…
We study thermodynamic properties of 2+1 flavor QCD with improved Wilson quarks coupled with the RG improved Iwasaki glue, using the fixed scale approach. We present the results for the equation of state, renormalized Polyakov loop, and chiral condensate.
The structure of critical lines of vanishing pion mass for the Wilson quark action is examined in quenched lattice QCD. The numerical evidence is presented that critical lines spread into five branches beyond beta=5.6-5.7 at zero temperature. It is also shown that critical lines disappear in the deconfined phase for the case of finite temperatures.
We report on the scaling of basic hadronic observables in lattice QCD with N_f=2 maximally twisted Wilson dynamical quarks. We give preliminary results for some of the Gasser-Leutwyler low energy constants, the chiral condensate and the average mass of u and d quarks.
The nature of the chiral phase transition in lattice QCD is studied for the cases of 2, 3 and 6 flavors with degenerate Wilson quarks, mainly on a lattice with the temporal direction extension $N_t=4$. We find that the chiral phase transition is continuous for the case of 2 flavors, while it is of first order for 3 and 6 flavors.
We have determined the non-perturbative O(a)-improvement coefficient c_sw for four flavors of Wilson quarks with the plaquette gauge action in a range of beta >= 5. The data are fitted with several Pade approximation formulae to get an impression of the stability. A small extrapolation below beta=5 seems acceptable.
We show how the hopping parameter expansion at order $κ^2$ and $κ^4$ can be exploited in the simulation of lattice QCD with two flavours of degenerate Wilson fermions. A natural extension of this idea is a "UV-filtering" by using rooted polynomials. These approaches can be easily combined with, for example, mass preconditioning. First numerical tests are performed for the Wilson gauge action at $β=5.6$ and $κ=0.156$ and $0.1575$.
Many observables of interest in lattice QCD are extracted from correlation functions involving the vector current. If Wilson fermions are used, it is therefore of practical importance that, besides the action, the current be O($a$) improved in order to remove the leading discretization errors from the observables. Here we introduce and apply a new method to determine the improvement coefficient for the two most widely used discretizations of the current.
The WHOT-QCD Collaboration is pushing forward lattice studies of QCD at finite temperatures and densities using improved Wilson quarks. We first present results on QCD at zero and finite densities with two flavors of degenerate quarks (N_F=2 QCD) adopting the conventional fixed-Nt approach. We then report on the status of a study of N_F=2+1 QCD adopting a fixed-scale approach armed with the T-integration method which we have developed.
We present first results of a study of two flavour QCD with Wilson fermions at finite temperature. We have used tree level Symanzik improvement in both the gauge and fermion part of the action. In a first step we explore the phase diagramm on an $8^3 \times 4$ lattice, with particular emphasis on checking Aoki's conjecture with an improved action.
We develop a strategy for the non-perturbative determination of the O(a)-improvement coefficient c_sw for Wilson fermions with massive sea quarks. The improvement condition is defined via the PCAC relation in the Schrödinger functional. It is imposed along a line of constant physics designed to be close to the correct mass of the charm quark. The numerical work uses the tree-level improved Lüscher-Weisz gauge action in N_f=3+1 Lattice QCD.
We present the status of our study on the equation of state in 2+1 flavor QCD with non-perturbatively improved Wilson quarks coupled with the RG improved glue. We apply the T-integration method to non-perturbatively calculate the equation of state by the fixed-scale approach.
We describe the first steps in the extension of the Symanzik O($a$) improvement program for Wilson-type quark actions to anisotropic lattices, with a temporal lattice spacing smaller than the spatial one. This provides a fully relativistic and computationally efficient framework for the study of heavy quarks. We illustrate our method with accurate results for the quenched charmonium spectrum.
We calculate the third coefficient of the lattice beta function in QCD with Wilson fermions, extending the pure gauge results of Luescher and Weisz; we show how this coefficient modifies the scaling function on the lattice. We also calculate the three-loop average plaquette in the presence of Wilson fermions. This allows us to compute the lattice scaling function both in the standard and energy schemes.
All microscopic correlation functions of the spectrum of the Hermitian Wilson Dirac operator with any number of flavors with equal masses are computed. In particular, we give explicit results for the spectral density in the physical case with two light quark flavors. The results include the leading effect in the discretization error and are given for fixed index of the Wilson Dirac operator. They have been obtained starting from chiral Lagrangians for the generating function of the Dirac spectrum. Microscopic correlation functions of the real eigenvalues of the Wilson Dirac operator are comput…
The spectral flow of the low-lying eigenvalues of the improved and unimproved Wilson-Dirac operator is studied on instanton-like configurations and on thermalized quenched configurations at various $β$-values and lattice sizes. We also investigate the space-time localisation and chirality of the corresponding eigenvectors.
We calculate the 3-loop perturbative expansion of the average plaquette in lattice QCD with N_f massive Wilson fermions and gauge group SU(N). The corrections to asymptotic scaling in the corresponding energy scheme are also evaluated. We have also improved the accuracy of the already known pure gluonic results at 2 and 3 loops.
One major systematic uncertainty of lattice QCD results is due to the continuum extrapolation. For an asymptotically free theory like QCD one finds corrections of the form $a^{n_\mathrm{min}}[2b_0\bar{g}^2(1/a)]^{\hatΓ_i}$ with lattice spacing $a$, where $\bar{g}(1/a)$ is the running coupling at renormalisation scale $μ=1/a$ and $n_\mathrm{min}$ is a positive integer. $\hatΓ_i$ can take any positive or negative value, but is computable by next-to-leading order perturbation theory. It will impact convergence towards the continuum limit. Balog, Niedermayer and Weisz first pointed out how problem…
We study the performance of QCD simulations with dynamical Wilson fermions by combining the Hybrid Monte Carlo algorithm with parallel tempering on $10^4$ and $12^4$ lattices. In order to compare tempered with standard simulations, covariance matrices between sub-ensembles have to be formulated and evaluated using the general properties of autocorrelations of the parallel tempering algorithm. We find that rendering the hopping parameter $κ$ dynamical does not lead to an essential improvement. We point out possible reasons for this observation and discuss more suitable ways of applying parallel…
A gauge field link smearing method developed for calculations with staggered fermions, namely the use of unitarized fat7 links, is applied to mesonic and baryonic Wilson loop calculations. This method is found to be very effective for reducing statistical fluctuations for large Wilson loops. Examination of chromo-electric field distributions shows that self-interactions of the static sources are reduced when unitarized fat7 smearing is used but long-distance inter-quark effects are unchanged.
We report the current status of our systematic studies of the QCD thermodynamics by lattice QCD simulations with two flavors of improved Wilson quarks. We evaluate the critical temperature of two flavor QCD in the chiral limit at zero chemical potential and show the preliminary result. Also we discuss fluctuations at none-zero temperature and density by calculating the quark number and isospin susceptibilities and their derivatives with respect to chemical potential.
We derive the asymptotic lattice spacing dependence $a^n[2b_0\bar{g}^2(1/a)]^{\hatΓ_i}$ relevant for spectral quantities of lattice QCD, when using Wilson, O$(a)$ improved Wilson or Ginsparg-Wilson quarks. We give some examples for the spectra encountered for $\hatΓ_i$ including the partially quenched case, mixed actions and using two different discretisations for dynamical quarks. This also includes maximally twisted mass QCD relying on automatic O$(a)$ improvement. At O$(a^2)$, all cases considered have $\min_i\hatΓ_i\gtrsim -0.3$ if $N_\mathrm{f}\leq 4$, which ensures that the leading order…
We determine the parameter c_SW required for O(a)-improvement of the three flavor Wilson fermion action together with the tree-level Symanzik improved gauge action. The standard improvement condition is employed for a range of couplings. Additionally, we perform a check of the volume independence of c_SW and provide a preliminary estimate of the lattice spacing at our largest values of g_0^2.
Wilson's formulation of lattice QCD is attractive for many reasons, but perhaps mainly because of its simplicity and conceptual clarity. Numerical simulations of the Wilson theory (and of its improved versions) tend to be extremely demanding, however, to the extent that they rapidly become impractical at small quark masses. Recent advances in simulation algorithms now allow such simulations to be pushed to significantly smaller masses without having to compromise in other ways. Contact with chiral perturbation theory can thus be made and many physics questions can be addressed that previously …
We present a reduction method for Wilson Dirac fermions with non-zero chemical potential which generates a dimensionally reduced fermion matrix. The size of the reduced fermion matrix is independent of the temporal lattice extent and the dependence on the chemical potential is factored out. As a consequence the reduced matrix allows a simple evaluation of the Wilson fermion determinant for any value of the chemical potential and hence the exact projection to the canonical partition functions.
The phase structure of lattice QCD with Wilson fermions is discussed. Analytic and numerical evidences are given for the spontaneous breaking of parity and flavor symmetry, which naturally explains the existence of the massless pion at the critical hopping parameter $K_c$ without recourse to the chiral symmetry absent in the Wilson fermion formulation. New numerical evidences are also presented for the multiple structure of the critical lines in the weak coupling region. A connection between the phase structure and the finite temperature phase transition is briefly mentioned.
A quantitative comparison between the finite temperature behaviour of the staggered and Wilson fermion formulations are performed. The comparison is based on a physical quantity that is expected to be quite sensitive to the fermionic features of the action. For that purpose we use the height of the peak for $dχ_s/dT$, where $χ_s$ is the quark number susceptibility.
We report on a lattice investigation of improved quenched Wilson fermions above and below the confinement-deconfinement phase transition. Results on meson screening masses as well as spatial wave functions are presented. Moreover, the meson dispersion relation is studied. Below the critical temperature we do not observe any significant temperature effect while above $T_c$ the data are consistent with a leading free quark behavior.
The flavour singlet axial Ward identity with Osterwalder-Seiler twisted mass Wilson fermion action is studied on a finite lattice, with finite fermion mass and the Wilson parameter r up to 1. Approach to the infinite volume chiral limit and emergence of the anomaly is significantly better than that obtained with O(a) and O(a^2) improved fermion actions. We have shown explicitly that up to O(g^2), parity violating terms cancel in the Ward identity even at finite volume and finite lattice spacing.
We compute the O(g^2) contribution to the thermodynamic pressure for Wilson fermions in the standard, the twisted mass, and clover improved formulation in lattice perturbation theory, including finite mass effects. We compare the continuum approaches of these discretizations for the massive ideal and interacting gas. In all cases, for N_t \geq 8 cutoff effects of Wilson type fermions are comparable to those of staggered fermions, but asymptotic scaling requires $N_τ>10$.
The finite temperature lattice QCD with N_f=2 nonperturbatively improved Wilson fermions is studied on 16^3 8 lattice. Using abelian projection after fixing to MA gauge we determine the transition temperature for m_π/m_ρ \sim 0.8.
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.
We present results of finite temperature QCD from N_f=2 flavors of non-perturbatively improved Wilson fermions on lattices with N_t=8, 10 and 12. The transition temperature T_c is determined for the first time at lattice spacings as low as a = 0.08 fm, albeit at pion masses 1.3 < r_0 m_π. We furthermore compute the screening masses in various color channels at T>T_c.
It is well known that the block Krylov subspace solvers work efficiently for some cases of the solution of differential equations with multiple right-hand sides. In lattice QCD calculation of physical quantities on a given configuration demands us to solve the Dirac equation with multiple sources. We show that a new block Krylov subspace algorithm recently proposed by the authors reduces the computational cost significantly without loosing numerical accuracy for the solution of the O(a)-improved Wilson-Dirac equation.
We present further analyses of the finite-temperature phase structure of lattice QCD with the Wilson quark action based on spontaneous breakdown of parity-flavor symmetry. Results are reported on (i) an explicit demonstration of spontaneous breakdown of parity-flavor symmetry beyond the critical line, (ii) phase structure and order of chiral transition for the case of $N_f=4$ flavors, and (iii) approach toward the continuum limit.
We discuss the implementation of a Sheikholeslami-Wohlert term for simulations of lattice QCD with dynamical Wilson fermions as required by Symanzik's improvement program. We show that for the Hybrid Monte Carlo or Kramers equation algorithm standard even-odd preconditioning can be maintained. We design tests of the implementation using analytically and numerically computed cumulant expansions. We find that, for situations where the average number of Conjugate Gradient iterations exceeds 200, the overhead is only about 20%.
Finite-temperature phase structure of lattice QCD with the Wilson quark action is analyzed. We show that the critical line at finite temperatures, defined to be the line of vanishing pion screening mass, turns back toward strong coupling, forming a cusp on the $(β, K)$ plane, and that the line of thermal transition runs past the tip of the cusp without touching the critical line. Previous results are discussed in the light of our findings.
We present a new multigrid solver that is suitable for the Dirac operator in the presence of disordered gauge fields. The key behind the success of the algorithm is an adaptive projection onto the coarse grids that preserves the near null space. The resulting algorithm has weak dependence on the gauge coupling and exhibits mild critical slowing down in the chiral limit. Results are presented for the Wilson Dirac operator of the 2d U(1) Schwinger model.
We present details of our investigation of the Parallel Tempering algorithm. We consider the application of action matching technology to the selection of parameters. We then present a simple model of the autocorrelations for a particular parallel tempered system. Finally we present numerical results from applying the algorithm to lattice QCD with O(a)-improved dynamical fermions with twin ensemble systems
We present results of an ongoing study of two flavour QCD with Wilson fermions at finite temperature. We have used tree level Symanzik improvement in both the gauge and fermion part of the action. The phase diagram was previously determined on an $8^3 \times 4$ lattice and the existence of Aoki's phase demonstrated. On our current lattice of $12^2 \times 24 \times 4$ we have extended the set of observables and studied chiral and thermal properties at light quark masses.
