L. Del Debbio

Detection of center vortices in the lattice Yang-Mills vacuum

We discuss the implementation of the {open_quotes}direct{close_quotes} maximal center gauge (a gauge which maximizes the lattice average of the squared-modulus of the trace of link variables), and its use in identifying Z{sub 2} center vortices in Yang-Mills vacuum configurations generated by lattice Monte Carlo calculations. We find that center vortices identified in the vacuum state account for the full asymptotic string tension. Scaling of vortex densities with lattice coupling, change in vortex size with cooling, and sensitivity to Gribov copies are discussed. Preliminary evidence is presented, on small lattices, for center dominance in SU(3) lattice gauge theory. {copyright} {ital 1998} {ital The American Physical Society}

Conformal versus confining scenario in SU(2) with adjoint fermions

The masses of the lowest-lying states in the meson and in the gluonic sector of an SU(2) gauge theory with two Dirac flavors in the adjoint representation are measured on the lattice at a fixed value of the lattice coupling {beta}=4/g{sub 0}{sup 2}=2.25 for values of the bare fermion mass m{sub 0} that span a range between the quenched regime and the massless limit, and for various lattice volumes. Even for light constituent fermions the lightest glueballs are found to be lighter than the lightest mesons. Moreover, the string tension between two static fundamental sources strongly depends on the mass of the dynamical fermions and becomes of the order of the inverse squared lattice linear size before the chiral limit is reached. The implications of these findings for the phase of the theory in the massless limit are discussed and a strategy for discriminating between the (near-)conformal and the confining scenario is outlined.

Lattice-constrained parametrizations of form factors for semileptonic and rare radiative B decays

Abstract We describe all the form factors for semileptonic and radiative B decays to the same light vector meson with just two parameters and the two form factors for semileptonic B decays to a light pseudoscalar meson with a further two or three parameters. This provides simple parametrizations of the form factors for the physical B 0 →ρ + l − ν l , B 0 →π + l − ν l and B →K ∗ γ decays. The parametrizations are consistent with heavy quark symmetry, kinematic constraints and lattice results, which we use to determine the parameters. In addition, we test versions of the parametrizations consistent (or not) with light-cone sum rule scaling relations at q2=0.

Decay constants of B and D mesons from non-perturbatively improved lattice QCD

The decay constants of B and D mesons are computed in quenched lattice QCD at two dierent values of the coupling. The action and operators areO(a )i mproved with non-perturbative coecients where available. The results are fB = 218 +5 5 +5 41 MeV, fD = 220 +3 3 +2 24 MeV, fBs = 242 +4 4 +13 48 MeV, fDs = 241 +2 2 +7 30 MeV. Systematic errors are discussed in detail. Results for vector decay constants, avour symmetry breaking ratios of decay constants, the pseudoscalar-vector mass splitting and D meson masses are also presented.

QCD with light Wilson quarks on fine lattices (II): DD-HMC simulations and data analysis

In this second report on our recent numerical simulations of two-flavour QCD, we provide further technical details on the simulations and describe the methods we used to extract the meson masses and decay constants from the generated ensembles of gauge fields. Among the topics covered are the choice of the DD-HMC parameters, the issue of stability, autocorrelations and the statistical error analysis. Extensive data tables are included as well as a short discussion of the quark-mass dependence in partially quenched QCD, supplementing the physics analysis that was presented in the first paper in this series.

Space-time symmetries and the Yang-Mills gradient flow

A bstractThe recent introduction of the gradient flow has provided a new tool to probe the dynamics of quantum field theories. The latest developments have shown how to use the gradient flow for the exploration of symmetries, and the definition of the corresponding renormalized Noether currents. In this paper we introduce infinitesimal translations along the gradient flow for gauge theories, and study the corresponding Ward identities. This approach is readily generalized to the case of gauge theories defined on a lattice, where the regulator breaks translation invariance. The Ward identities in this case lead to a nonperturbative renormalization of the energy-momentum tensor. We discuss an application of this method to the study of dilatations and scale invariance on the lattice.

Detecting dual superconductivity in the ground state of gauge theory

Abstract We explicitly construct a monopole creation operator: its vacuum expectation value is a disorder parameter for dual superconductivity, in that it signals a spontaneous breaking of the U(1) symmetry corresponding to monopole charge conservation. This operator is tested by numerical simulations in compact U(1) gauge theory. Our construction provides a general recipe for detection of the condensation of any topological soliton. In particular our operator can be used to detect dual superconductivity of the QCD vacuum.

Colour confinement as dual Meissner effect:

Abstract We demonstrate that confinement in SU (2) gauge theory is produced by dual superconductivity of the vacuum. We show that for T T c (temperature of the deconfining phase transition) the U (1) symmetry related to monopole charge conservation is spontaneously broken; for T > T c the symmetry is restored.

SU(2)

Abstract We measure field-strength and their correlators in presence of a static q q pair by numerical simulations. We give an interpretation of these data in terms of quadratic and quartic cumulants.

gauge theory

We present results for the matrix elements relevant for proton decay in grand unified theories (GUTs). The calculation is performed at a fixed lattice spacing α -1 = 1.73(3) GeV using 2 + 1 flavors of domain-wall fermions on lattices of size 16 3 X 32 and 24 3 X 64 with a fifth dimension of length 16. We use the indirect method which relies on an effective field theory description of proton decay, where we need to estimate the low-energy constants, a = -0.0112(25) GeV 3 and β = 0.0120(26) GeV 3 . We relate these low-energy constants to the proton decay matrix elements using leading order chiral perturbation theory. These can then be combined with experimental bounds on the proton lifetime to bound parameters of individual GUTs.