Nazario Tantalo

On the discretization of physical momenta in lattice QCD

Abstract The adoption of two distinct boundary conditions for two fermions species on a finite lattice allows to deal with arbitrary relative momentum between the two particle species, in spite of the momentum quantization rule due to a limited physical box size. We test the physical significance of this topological momentum by checking in the continuum limit the validity of the expected energy–momentum dispersion relations.

Stability of lattice QCD simulations and the thermodynamic limit

We study the spectral gap of the Wilson-Dirac operator in two-flavour lattice QCD as a function of the lattice spacing a, the space-time volume V and the current-quark mass m. It turns out that the median of the probability distribution of the gap scales proportionally to m and that its width is practically equal to a/V1/2. In particular, numerical simulations are safe from accidental zero modes in the large-volume regime of QCD.

QCD with light Wilson quarks on fine lattices (I): first experiences and physics results

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.Recent conceptual, algorithmic and technical advances allow numerical simulations of lattice QCD with Wilson quarks to be performed at significantly smaller quark masses than was possible before. Here we report on simulations of two-flavour QCD at sea-quark masses from slightly above to approximately 1/4 of the strange-quark mass, on lattices with up to 64×32 3 points and spacings from 0.05 to 0.08 fm. Physical sea-quark effects are clearly seen on these lattices, while the lattice effects appear to be quite small, even without O(a) improvement. A striking result is that the dependence of the pion mass on the sea-quark mass is accurately described by leading-order chiral perturbation theory up to meson masses of about 500 MeV.

Leading isospin breaking effects on the lattice

We present a method to evaluate on the lattice the leading isospin breaking effects due to both the small mass difference between the up and down quarks and the QED interaction. Our proposal is applicable in principle to any QCD+QED gauge invariant hadronic observable that can be computed on the lattice. It is based on the expansion of the path integral in powers of the small parameters (md-mu)/ΛQCD and αem, where mf is the renormalized quark mass and αem the renormalized fine structure constant. In this paper we discuss in detail the general strategy of the method and the conventional, although arbitrary, separation of QCD from QED isospin breaking corrections. We obtain results for the pion mass splitting, Mπ+2-Mπ02=1.44(13)(16)×103  MeV2, for the Dashen’s theorem breaking parameter eγ=0.79(18)(18), for the light quark masses, [md-mu](MS ,2  GeV)=2.39(8)(17)  MeV, [mu/md](MS ,2  GeV)=0.50(2)(3), and for the flavor symmetry breaking parameters R and Q. We also update our previous results for the QCD isospin breaking corrections to the Kl2 decay rate and for the QCD contribution to the neutron-proton mass splitting. The numerical results of this paper have been obtained by using the gluon field configurations produced by the ETMC Collaboration with nf=2 dynamical quarks. We treated the dynamical quarks as electrically neutral particles (electroquenched approximation) and neglected a disconnected diagram in the charged and neutral pion mass splitting. We provide all the formulas necessary to remove these approximations and discuss in detail the estimate of the associated systematic uncertainties.

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.

Quenched lattice calculation of semileptonic heavy-light meson form factors

We calculate, in the continuum limit of quenched lattice QCD, the matrix elements of the heavy-heavy vector current between heavy-light pseudoscalar meson states. We present the form factors for different values of the initial and final meson masses at finite momentum transfer. In particular, we calculate the non-perturbative correction to the differential decay rate of the process B → Dlν including the case of a non-vanishing lepton mass.

Isospin breaking effects due to the up-down mass difference in lattice QCD

A bstractWe present a new method to evaluate with high precision leading isospin breaking effects due to the small mass difference between the up and down quarks using lattice QCD. Our proposal is applicable in principle to any hadronic observable which can be computed on the lattice. It is based on the expansion of the path-integral in powers of the small parameter md − mu. In this paper, we apply this method to compute the leading isospin breaking effects for several physical quantities of interest: the kaon meson masses, the kaon decay constant, the form factors of semileptonic Kℓ3 decays and the neutron-proton mass splitting.

Quenched lattice calculation of the B → Dłv decay rate

Abstract We calculate, in the continuum limit of quenched lattice QCD, the form factor that enters in the decay rate of the semileptonic decay B → D l ν . Making use of the step scaling method (SSM), previously introduced to handle two scale problems in lattice QCD, and of flavour twisted boundary conditions we extract G B → D ( w ) at finite momentum transfer and at the physical values of the heavy quark masses. Our results can be used in order to extract the CKM matrix element V c b by the experimental decay rate without model dependent extrapolations.

fB and two-scales problems in lattice QCD

Abstract A novel method to calculate f B on the lattice is introduced, based on the study of the dependence of finite size effects upon the heavy quark mass of flavoured mesons and on a non-perturbative recursive finite size technique. We avoid the systematic errors related to extrapolations from the static limit or to the tuning of the coefficients of effective Lagrangian and the results admit an extrapolation to the continuum limit. We perform a first estimate at finite lattice spacing, but close to the continuum limit, giving f B =170(11)(5)(22) MeV. We also obtain f B s =192(9)(5)(24) MeV. The first error is statistical, the second is our estimate of the systematic error from the method and the third the systematic error from the specific approximations adopted in this first exploratory calculation. The method can be generalized to two-scale problems in lattice QCD.

Parameters of heavy quark effective theory from N-f=2 lattice QCD

A bstractWe report on a non-perturbative determination of the parameters of the lattice Heavy Quark Effective Theory (HQET) Lagrangian and of the time component of the heavy-light axial-vector current with Nf = 2 flavors of massless dynamical quarks. The effective theory is considered at the 1/mh order, and the heavy mass mh covers a range from slightly above the charm to beyond the beauty region. These HQET parameters are needed to compute, for example, the b-quark mass, the heavy-light spectrum and decay constants in the static approximation and to order 1/mh in HQET. The determination of the parameters is done non-perturbatively. The computation reported in this paper uses the plaquette gauge action and two different static actions for the heavy quark described by HQET. For the light-quark action we choose non-perturbatively O(a)-improved Wilson fermions.