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.     

Chiral phase transition in lattice QCD with dynamical quarks

The effect of virtual light quark loops on the chiral phase transition in lattice QCD with staggered fermions is investigated by employing the pseudo-fermion Monte Carlo method on a 6³ × 2 lattice. The variation in the order parameter $\text{〈}\text{ψ}\text{ψ〉}$ is found to become less sharp than the quenched case, indicating a second order chiral phase transitioon in the full theory.     

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.     

Spontaneous chiral-symmetry breaking of lattice QCD with massless dynamical quarks

One of the most challenging issues in QCD is the investigation of spontaneous chiral-symmetry breaking, which is characterized by the non-vanishing chiral condensate when the bare fermion mass is zero. In standard methods of the lattice gauge theory, one has to perform expensive simulations at multiple bare quark masses, and employ some modeled functions to extrapolate the data to the chiral limit. This paper applies the probability distribution function method to computing the chiral condensate in lattice QCD with massless dynamical quarks, without any ambiguous mass extrapolation. The results for staggered quarks indicate that this might be a promising and efficient method for investigating the spontaneous chiral-symmetry breaking in lattice QCD, which deserves further investigation.     

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.     

The phase structure of lattice QCD with two flavors of Wilson quarks and renormalization group improved gluons

The effect of changing the lattice action for the gluon field on the recently observed [F. Farchioni, R. Frezzotti, K. Jansen, I. Montvay, G.C. Rossi, E. Scholz, A. Shindler, N. Ukita, C. Urbach, I. Wetzorke, Eur. Phys. J. C 39, 421 (2005); hep-lat/0406039] first order phase transition near zero quark mass is investigated by replacing the Wilson plaquette action by the DBW2 action. The lattice action for quarks is unchanged: it is in both cases the original Wilson action. It turns out that Wilson fermions with the DBW2 gauge action have a phase structure where the minimal pion mass and the jump of the average plaquette are decreased, when compared to Wilson fermions with Wilson plaquette action at similar values of the lattice spacing. Taking the DBW2 gauge action is advantageous also from the point of view of the computational costs of numerical simulations.Received: 29 October 2004, Revised: 7 March 2005, Published online: 31 May 2005     

Incorporating dynamical light quarks in lattice QCD at finite temperature

Using the pseudo-fermion Monte Carlo method we investigate the chiral and the deconfinement phase transitions in the SU(3) gauge theory with dynamical staggered fermions on a 6³ × 2 lattice. The energy density of the gluonic sector ε_G, the average thermal Wilson loop |L| and the order parameter are found to have a rapid variation in the same range of β (=6/g²). The variation is similar to that observed in the quenched theory but is at a smaller value of β.     

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.     

QCD potentials with dynamical quarks at finite temperatures

We investigate the potential between a static quark-antiquark pair in the full QCD vacuum. The dynamical quark sea is considered both by Kogut-Susskind and Wilson fermions. Two temperatures T below and above the phase transition T_c are studied. The behavior of the interquark potential in the full quantum field is driven by the explicitly broken Z₃ symmetry in the fermionic action for T<T_c and by an additional spontaneous Z₃ symmetry breaking for T<T_c.     

A numerical study of Langevin QCD with dynamical quarks

QCD with four flavours of dynamical staggered quarks of mass ma=0.1 is simulated on a 4⁴ lattice, using two versions of the second order Langevin algorithm with bilinear noise: the naive version and one which compensates for the non-integrable term which appears to first order in the discrete Langevin time step size. Comparison with the results of an exact numerical computation of the fermion determinant reveals that these algorithms yield accurate results only at rather small values of the step size. The correction due to the non-integrable term is quantitatively unimportant for such step sizes.     

The pion form factor from lattice QCD with two dynamical flavours

We compute the electromagnetic form factor of the pion, using non-perturbatively O(a) improved Wilson fermions. The calculations are done for a wide range of pion masses and lattice spacings. We check for finite size effects by repeating some of the measurements on smaller lattices. The large number of lattice parameters we use allows us to extrapolate to the physical point. For the square of the charge radius we find fm², in good agreement with experiment. PACS 12.38.Gc; 13.40.Gp; 14.40.-n