V. G. Bornyakov

Dual superconductor scenario of confinement: A Systematic study of Gribov copy effects

We perform a study of the effects from maximal Abelian gauge Gribov copies in the context of the dual superconductor scenario of confinement, on the basis of a novel approach for the estimation of systematic uncertainties from incomplete gauge fixing. We present numerical results, in SU(2) lattice gauge theory, using the overrelaxed simulated annealing gauge-fixing algorithm. We find Abelian and non-Abelian string tensions to differ significantly, their ratio being 0.92(4) at {beta}=2.5115. An approximate factorization of the Abelian potential into monopole and photon contributions has been confirmed, the former giving rise to the Abelian string tension. {copyright} {ital 1996 The American Physical Society.}

Flavour blindness and patterns of flavour symmetry breaking in lattice simulations of up, down and strange quarks

QCD lattice simulations with 2+1 flavours (when two quark flavours are mass degenerate) typically start at rather large up-down and strange quark masses and extrapolate first the strange quark mass and then the up-down quark mass to its respective physical value. Here we discuss an alternative method of tuning the quark masses, in which the singlet quark mass is kept fixed. Using group theory the possible quark mass polynomials for a Taylor expansion about the flavour symmetric line are found, first for the general 1+1+1 flavour case and then for the 2+1 flavour case. This ensures that the kaon always has mass less than the physical kaon mass. This method of tuning quark masses then enables highly constrained polynomial fits to be used in the extrapolation of hadron masses to their physical values. Numerical results for the 2+1 flavour case confirm the usefulness of this expansion and an extrapolation to the physical pion mass gives hadron mass values to within a few percent of their experimental values. Singlet quantities remain constant which allows the lattice spacing to be determined from hadron masses (without necessarily being at the physical point). Furthermore an extension of this programme to include partially quenched results is given.

Abelian dominance and gluon propagators in the maximally Abelian gauge of SU(2) lattice gauge theory

Propagators of the diagonal and the off-diagonal gluons are studied numerically in the maximal Abelian gauge of SU(2) lattice gauge theory. It is found that in the infrared region the propagator of the diagonal gluon is strongly enhanced in comparison with the off-diagonal one. The enhancement factor is about 50 at our smallest momentum 325 MeV. We have also applied various fits to the propagator formfactors.

Anatomy of the lattice magnetic monopoles

We study the Abelian and non-Abelian action densitynear the monopole in the maximal Abelian gauge of SU(2) lattice gauge theory. We find that the non-Abelian action density near the monopoles belonging to the percolating cluster decreases when we approach the monopole center. Our estimate of the monopole radius is R_mon ~ 0.04 fm.

Tuning the strange quark mass in lattice simulations

Abstract QCD lattice simulations with 2 + 1 flavours typically start at rather large up-down and strange quark masses and extrapolate first the strange quark mass to its physical value and then the up-down quark mass. An alternative method of tuning the quark masses is discussed here in which the singlet quark mass is kept fixed, which ensures that the kaon always has mass less than the physical kaon mass. It can also take into account the different renormalisations (for singlet and non-singlet quark masses) occurring for non-chirally invariant lattice fermions and so allows a smooth extrapolation to the physical quark masses. This procedure enables a wide range of quark masses to be probed, including the case with a heavy up-down quark mass and light strange quark mass. Results show the correct order for the baryon octet and decuplet spectrum and an extrapolation to the physical pion mass gives mass values to within a few percent of their experimental values.

SU(2) lattice gluon propagator: Continuum limit, finite-volume effects, and infrared mass scale mIR

We study the scaling behavior and finite (physical) volume effects as well as the Gribov copy dependence of the SU(2) Landau gauge gluon propagator on the lattice. Our physical lattice sizes range from (3.0 fm){sup 4} to (7.3 fm){sup 4}. Considering lattices with decreasing lattice spacing but fixed physical volume we confirm (nonperturbative) multiplicative renormalizability and the approach to the continuum limit for the renormalized gluon propagator D{sub ren}(p) at momenta |p| > or approx. 0.6 GeV. The finite-volume effects and Gribov copy influence turn out small in this region. On the contrary, in the deeper infrared we found the Gribov copy influence strong and finite-volume effects, which still require special attention. The gluon propagator does not seem to be consistent with a simple polelike behavior {approx}(p{sup 2}+m{sub g}{sup 2}){sup -1} for momenta |p| < or approx. 0.6 GeV. Instead, a Gaussian-type fit works very well in this region. From its width - for a physical volume (5.0 fm){sup 4} - we estimate a corresponding infrared (mass) scale to be m{sub IR{approx}}0.7 GeV.

P-vortices and drama of Gribov copies

Abstract We present results of the careful study of the Gribov copies problem in SU (2) lattice gauge theory for the direct maximal center projection widely used in confinement studies. Applying simulated annealing algorithm we demonstrate that this problem is more severe than it was thought before. The projected (gauge noninvariant) string tension is not in the agreement with the physical string tension. We do not find any indications that P-vortices reproduce the full SU (2) string tension neither in the infinite volume limit nor in the continuum limit.

Probing the finite temperature phase transition with N(f) = 2 nonperturbatively improved Wilson fermions

The critical temperature and the nature of the QCD finite temperature phase transition are determined for

Infrared behavior and Gribov ambiguity in SU(2) lattice gauge theory

{N}_{f}=2

Dirac sheets and gauge fixing in U(1) lattice gauge theory

dynamical flavors of nonperturbatively improved Wilson fermions. The calculations are performed on large lattices with temporal extents