The calculation of the hadron spectrum in lattice QCD with dynamical quarks

Hadron masses are calculated on an 8³×16 lattice using four flavors of staggered fermions to generate the gauge configurations, but using Wilson fermions to calculate the hadron propagators. The identification of a value of the Wilson hopping parameter with the value of the bare quark mass used in the simulations is discussed.     

QCD thermodynamics with dynamical overlap fermions

We study QCD thermodynamics using two flavors of dynamical overlap fermions with quark masses corresponding to a pion mass of 350 MeV. We determine several observables on _Nt=6$N_t=6$ and 8 lattices. All our runs are performed with fixed global topology. Our results are compared with staggered ones and a nice agreement is found.     

A lattice Dirac operator for QCD with light dynamical quarks

In QCD chiral symmetry is explicitly broken by quark masses, the effect of which can be described reliably by chiral perturbation theory. Effects of explicit chiral symmetry breaking by the lattice regularisation of the Dirac operator, typically parametrised by the residual mass, should be negligible for almost all observables if the residual mass of the Dirac operator is much smaller than the quark mass. However, maintaining a small residual mass becomes increasingly expensive as the quark mass decreases towards the physical value and the continuum limit is approached. We investigate the feasibility of using a new approximately chiral Dirac operator with a small residual mass as an alternative to overlap and domain wall fermions for lattice simulations. Our Dirac operator is constructed from a Zolotarev rational approximation for the matrix sign function that is optimal for bulk modes of the hermitian kernel Dirac operator but not for the low-lying parts of its spectrum. We test our operator on various ³²³×64${32}^3\times 64$ lattices, comparing the residual mass and the performance of the Hybrid Monte Carlo algorithm at a similar lattice spacing and pion mass with a hyperbolic tangent operator as used by domain wall fermions. We find that our approximations have a significantly smaller residual mass than domain wall fermions at a similar computational cost, and still admit topological charge change.     

Unquenched complex dirac spectra at nonzero chemical potential: two-color QCD lattice data versus matrix model

We compare analytic predictions of non-Hermitian chiral random matrix theory with the complex Dirac operator eigenvalue spectrum of two-color lattice gauge theory with dynamical fermions at nonzero chemical potential. The Dirac eigenvalues come in complex conjugate pairs, making the action of this theory real and positive for our choice of two staggered flavors. This enables us to use standard Monte Carlo simulations in testing the influence of the chemical potential and quark mass on complex eigenvalues close to the origin. We find excellent agreement between the analytic predictions and our data for two different volumes over a range of chemical potentials below the chiral phase transition. In particular, we detect the effect of unquenching when going to very small quark masses.     

Single flavor staggered fermions

Based on recent work by Adams, I construct a lattice fermion operator that fully lifts the staggered flavor degeneracy. The resulting operator is of Wilson type but smaller by a factor of 4, better conditioned and contains 3 instead of 15 doublers. It is further suggested that this operator may be used as a candidate kernel operator to an overlap construction. Prospects for practical applications and potential problems of the new discretizations are briefly discussed.     

Quark chiral condensate from the overlap quark propagator

From the overlap lattice quark propagator calculated in the Landau gauge,we determine the quark chiral condensate by fitting operator product expansion formulas to the lattice data.The quark propagators are computed on domain wall fermion configurations generated by the RBC-UKQCD Collaborations with N_f = 2 + 1flavors.Three ensembles with different light sea quark masses are used at one lattice spacing 1/a = 1.75(4) Ge V.We obtain ψψ (2 GeV)MS =(-304(15)(20) MeV)~3in the SU(2) chiral limit.     

N-to-Delta axial transition form factors from lattice QCD

We evaluate the N to Delta axial transition form factors in lattice QCD with no dynamical sea quarks, with two degenerate flavors of dynamical Wilson quarks, and using domain wall valence fermions with three flavors of staggered sea quarks. We predict the ratio C(5)(A)(q(2))/C(3)(V)(q(2)) relevant for parity violating asymmetry experiments and verify the off-diagonal Goldberger-Treiman relation.     

Topological susceptibility in lattice QCD with unimproved Wilson fermions

We address a long standing problem regarding topology in lattice simulations of QCD with unimproved Wilson fermions. Earlier attempt with unimproved Wilson fermions at β=5.6 to verify the suppression of topological susceptibility with decreasing quark mass (mq) was unable to unambiguously confirm the suppression. We carry out systematic calculations for two degenerate flavours at two different lattice spacings (β=5.6 and 5.8). The effects of quark mass, lattice volume and the lattice spacing on the spanning of different topological sectors are presented. We unambiguously demonstrate the suppression of the topological susceptibility with decreasing quark mass, expected from chiral Ward identity and chiral perturbation theory.     

The goldstone pion in SU(2) lattice QCD at low quark mass: Scaling and finite size effects

Results for the pion sector of an extensive numerical simulation of quenched SU(2) QCD with staggered fermions are presented. A wide range of quark masses, gauge couplings and lattice sizes is investigated. The systematic and statistical errors are carefully analyzed. Finite size effects occurring on small lattices and/or at low quark masses are studied in detail. When they are absent or weak, we find that the pion mass and coupling constant verify approximate scaling behaviour at low quark mass for β ≳ 2.4. We determine the K and π coupling constants to be in the ratio 1.25(5). At β = 2.3, we show that the square pion mass contains a substantial contribution which is non-linear in the quark mass and renders chiral limit extrapolations less reliable.     

Optimised Dirac operators on the lattice: construction,properties and applications

We review a number of topics related to block variable renormalisation group transformations of quantum fields on the lattice, and to the emerging perfect lattice actions. We first illustrate this procedure by considering scalar fields. Then we proceed to lattice fermions, where we discuss perfect actions for free fields, for the Gross‐Neveu model and for a supersymmetric spin model. We also consider the extension to perfect lattice perturbation theory, in particular regarding the axial anomaly and the quark gluon vertex function. Next we deal with properties and applications of truncated perfect fermions, and their chiral correction by means of the overlap formula. This yields a formulation of lattice fermions, which combines exact chiral symmetry with an optimisation of further essential properties. We summarise simulation results for these so‐called overlap‐hypercube fermions in the two‐flavour Schwinger model and in quenched QCD. In the latter framework we establish a link to Chiral Perturbation Theory, both, in the p‐regime and in the ϵ‐regime. In particular we present an evaluation of the leading Low Energy Constants of the chiral Lagrangian – the chiral condensate and the pion decay constant – from QCD simulations with extremely light quarks.     

QCD on the lattice and light hadron spectroscopy

Results in lattice Quantum Chromodynamics with fermions are reviewed. Estimates for the hadron spectrum on large lattices without and with light fermion polarization loops are discussed, and the results for different fermion regularizations are compared. The effects of the loops are found to be significant in lattice units, but to a greater part they can be reabsorbed in a redefinition of the overall scale. New estimates for the light quark masses with Wilson fermions are also presented. They differ substantially from previous estimates obtained by other methods in the continuum, and are much smaller. Finally it is argued that staggered fermions can lead to some anomalous results, which arise because of the doubling problem.     

New overlap construction of Weyl fermions on the lattice

In a recent article Hasenfratz and von Allmen have suggested a fixed point action for two flavors of Weyl fermions on the lattice with gauge group SU(2). The block-spin transformation they use maps the chiral and vector symmetries of the underlying vector theory onto two equations of the Ginsparg–Wilson (GW) type. We show that an overlap Dirac operator can be constructed which solves both GW equations simultaneously. We discuss the properties of this overlap operator and its projection onto lattice Weyl fermions which seems to be free of artefacts, in particular the projection operators are independent of the gauge field.     

Staggered fermions and rotation-gauge invariance

We study the rotational invariance of the staggered fermions on the lattice by considering them as spin-zero fields in a quenched gauge field background. The non-integer spin fermionic fields are reconstructed. Bilinear operators (i.e. meson fields) in terms of the quark fields on a cube are classified according to the representations of the discrete rotational group.     

Numerical study of dense adjoint matter in two color QCD

We identify the global symmetries of SU(2) lattice gauge theory with N flavors of staggered fermion in the presence of a quark chemical potential , for fermions in both fundamental and adjoint representations, and anticipate likely patterns of symmetry breaking at both low and high densities. Results from numerical simulations of the model with N = 1 adjoint flavor on a lattice are presented, using both hybrid Monte Carlo and Two-Step Multi-Boson algorithms. It is shown that the sign of the fermion determinant starts to fluctuate once the model enters a phase with non-zero baryon charge density. HMC simulations are not ergodic in this regime, but TSMB simulations retain ergodicity even in the dense phase, and in addition appear to show superior decorrelation. The HMC results for the equation of state and the pion mass show good quantitative agreement with the predictions of chiral perturbation theory, which should hold only for . The TSMB results incorporating the sign of the determinant support a delayed onset transition, consistent with the pattern of symmetry breaking expected for N = 1. Received: 20 June 2000 / Published online: 31 August 2000     

Transverse spin structure of the nucleon from lattice-QCD simulations

We present the first calculation in lattice QCD of the lowest two moments of transverse spin densities of quarks in the nucleon. They encode correlations between quark spin and orbital angular momentum. Our dynamical simulations are based on two flavors of clover-improved Wilson fermions and Wilson gluons. We find significant contributions from certain quark helicity flip generalized parton distributions, leading to strongly distorted densities of transversely polarized quarks in the nucleon. In particular, based on our results and recent arguments by Burkardt [Phys. Rev. D 72, 094020 (2005)], we predict that the Boer-Mulders function h(1/1), describing correlations of transverse quark spin and intrinsic transverse momentum of quarks, is large and negative for both up and down quarks.     

Diquark mass differences from unquenched lattice QCD

We calculate diquark correlation functions in the Landau gauge on the lattice using overlap valence quarks and 2+1-flavor domain wall fermion configurations. Quark masses are extracted from the scalar part of quark propagators in the Landau gauge. The scalar diquark quark mass difference and axial vector scalar diquark mass difference are obtained for diquarks composed of two light quarks and of a strange and a light quark. The light sea quark mass dependence of the results is examined. Two lattice spacings are used to check the discretization effects.The coarse and fine lattices are of sizes 24~3×64 and 32~3×64 with inverse spacings 1/a = 1.75(4) Ge V and 2.33(5) Ge V,respectively.     

Hadronic spectroscopy in lattice QCD with dynamical staggered quark loops

We have made a high statistics hadron mass calculation at β = 5.4 on a 6³ × 24 lattice, for the two flavour fully coupled staggered QCD. We show that the systematic error of the pseudofermionic method is small for mass measurements. As has already been shown for Wilson fermions, we find that the effect of the quark loops can be readsorbed in a shift of the coupling constant. At the quark mass values (am) = 0.2, 0.1 we also find that the proton-rho mass ratio is no longer than in the quenched theory.     

Static quark anti-quark free and internal energy in two-flavor QCD

We study the change in free and internal energy due to the presence of a heavy quark anti-quark pair in a thermal heat bath in QCD with two flavors of staggered quarks at finite temperature. We discuss string breaking below as well as screening above the transition. Similarities and differences to the quenched case are discussed.Arrival of the final proofs: 24 March 2005PACS: 11.15.Ha, 11.10.Wx, 12.38.Mh, 25.75.Nq     

Chiral symmetry, quark mass, and scaling of the overlap fermions

The chiral symmetry relation and scaling of the overlap fermions are studied numerically on the quenched lattices at 3 couplings with about the same physical volume. We find that the generalized Gell-Mann-Oakes-Renner relation is satisfied to better than 1% down to the smallest quark mass at m(0)a = 0.006. We also obtain the quark mass from the PCAC relation and the pseudoscalar masses. The renormalization group invariant quark mass is shown to be fairly independent of scale. The pi and rho masses at a fixed m(pi)/m(rho) ratio indicate small O(a(2)) corrections. It is found that the critical slowing down sets in abruptly at a very small quark mass close to those of the physical u and d quarks.