arXiv subjects
Publications and source records attributed to R. Petronzio.
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.
We present the current status of the apeNEXT project. Aim of this project is the development of the next generation of APE machines which will provide multi-teraflop computing power. Like previous machines, apeNEXT is based on a custom designed processor, which is specifically optimized for simulating QCD. We discuss the machine design, report on benchmarks, and give an overview on the status of the software development.
Recent data on the Nachtmann moments of the unpolarized proton structure function F2p, obtained at low momentum transfer with the CLAS detector at Jefferson Lab, are interpreted in terms of the dominance of the elastic coupling of the virtual photon with extended substructures inside the proton. The CLAS data exhibit a new type of scaling behavior and the resulting scaling function can be interpreted as a constituent form factor consistent with the elastic nucleon data. A constituent size of ~ 0.2 - 0.3 fm is obtained.
We compute charm and bottom quark masses in the quenched approximation and in the continuum limit of lattice QCD. We make use of a step scaling method, previously introduced to deal with two scale problems, that allows to take the continuum limit of the lattice data. We determine the RGI quark masses and make the connection to the MSbar scheme. The continuum extrapolation gives us a value m_b^{RGI} = 6.73(16) GeV for the b-quark and m_c^{RGI} = 1.681(36) GeV for the c-quark, corresponding respectively to m_b^{MSbar}(m_b^{MSbar}) = 4.33(10) GeV and m_c^{MSbar}(m_c^{MSbar}) = 1.319(28) GeV. The latter result, in agreement with current estimates, is for us a check of the method. Using our results on the heavy quark masses we compute the mass of the Bc meson, M_{Bc} = 6.46(15) GeV.
We compute non-perturbatively the evolution of the twist-2 operators corresponding to the average momentum of non-singlet quark densities. The calculation is based on a finite-size technique, using the Schrödinger Functional, in quenched QCD. We find that a careful choice of the boundary conditions, is essential, for such operators, to render possible the computation. As a by-product we apply the non-perturbatively computed renormalization constants to available data of bare matrix elements between nucleon states.
We report on recent results for the pion matrix element of the twist-2 operator corresponding to the average momentum of non-singlet quark densities. For the first time finite volume effects of this matrix element are investigated and come out to be surprisingly large. We use standard Wilson and non-perturbatively improved clover actions in order to control better the extrapolation to the continuum limit. Moreover, we compute, fully non-perturbatively, the renormalization group invariant matrix element, which allows a comparison with experimental results in a broad range of energy scales. Finally, we discuss the remaining uncertainties, the extrapolation to the chiral limit and the quenched approximation.
We compute the decay constants for the heavy--light pseudoscalar mesons in the quenched approximation and continuum limit of lattice QCD. Within the Schrodinger Functional framework, we make use of the step scaling method, which has been previously introduced in order to deal with the two scale problem represented by the coexistence of a light and a heavy quark. The continuum extrapolation gives us a value $f_{B_s} = 192(6)(4)$ MeV for the $B_s$ meson decay constant and $f_{D_s} = 240(5)(5)$ MeV for the $D_s$ meson.
We discuss the usage of continuous external momenta for computing renormalization factors as needed to renormalize operator matrix elements. These kind of external momenta are encoded in special boundary conditions for the fermion fields. The method allows to compute certain renormalization factors on the lattice that would have been very difficult, if not impossible, to compute with standard methods. As a result we give the renormalization group invariant step scaling function for a twist-2 operator corresponding to the average momentum of non-singlet quark densities.
Recent experimental determinations of the Nachtmann moments of the inelastic structure function of the proton F2p(x, Q**2), obtained at Jefferson Lab, are analyzed for values of the squared four-momentum transfer Q**2 ranging from ~ 0.1 to ~ 2 (GeV/c)**2. It is shown that such inelastic proton data exhibit a new type of scaling behavior and that the resulting scaling function can be interpreted as a constituent form factor consistent with the elastic nucleon data. These findings suggest that at low momentum transfer the inclusive proton structure function originates mainly from the elastic coupling with extended objects inside the proton. We obtain a constituent size of ~ 0.2 - 0.3 fm.
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.
We discuss a novel method to calculate fB on the lattice 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. This method avoids 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 show the results of a first estimate at finite lattice spacing, but close to the continuum limit, giving fB = 170(11)(5)(22)MeV. We also obtain fBs = 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.
In this paper we extend the estimate of the value of the lattice spacing a in units of the r0 scale at values of the bare coupling larger than those available. By using results from the computation of the renormalised coupling in the Schroedinger functional formalism we find that from beta \simeq 7 onward the behaviour predicted by asymptotic freedom at tree loop describes very well the data if a value of (r0 Lambda) slightly lower then the latest available is used. We also show that, by sticking to the current value, an effective four loop term can describe as well the data. The systematic relative error on the lattice spacing induced by the choice of the procedure is between 1% and 3% for 6.92 < beta < 8.5.
A non perturbative computation of the evolution of singlet parton densities without gauge--fixing requires a gauge invariant gluon source operator. Within the Schrödinger Functional scheme (SF), such a source can be defined in terms of path ordered products of gauge links, connected to the time boundaries. In this paper we adopt this definition and perform a one loop lattice computation of the renormalization constants of the twist--2 operators that correspond to the second moment of singlet parton densities. This calculation fixes the connection between the lattice SF scheme where a non perturbative evaluation of the absolute normalization of singlet parton densities can be made at low energy and the $\bar{MS}$ scheme where one can extract the experimental values.
APENEXT is a new generation APE processor, optimized for LGT simulations. The project follows the basic ideas of previous APE machines and develops simple and cheap parallel systems with multi T-Flops processing power. This paper describes the main features of this new development.
This paper presents the status of the APEmille project, which is essentially completed, as far as machine development and construction is concerned. Several large installations of APEmille are in use for physics production runs leading to many new results presented at this conference. This paper briefly summarizes the APEmille architecture, reviews the status of the installations and presents some performance figures for physics codes.
A renormalization group transformation suitable for spin glass models and, more generally, for disordered models, is presented. The procedure is non-standard in both the nature of the additional interactions and the coarse graining transformation, that is performed on the overlap probability measure (which is clearly non-Gibbsian). Universality classes are thus naturally defined on a large set of models, going from $\Z_2$ and Gaussian spin glasses to Ising and fully frustrated models, and others.
We present the results of a non-perturbative determination of the pion matrix element of the twist-2 operator corresponding to the average momentum of non-singlet quark densities. The calculation is made within the Schroedinger functional scheme. We report the results of simulations done with the standard Wilson action and with the non-perturbatively improved clover action and we show that their ratio correctly extrapolates, in the continuum limit, to a value compatible with the residual correction factor expected from perturbation theory.
We compute, within the Schrödinger functional scheme, a renormalization group invariant renormalization constant for the first moment of the non-singlet parton distribution function. The matching of the results of our non-perturbative calculation with the ones from hadronic matrix elements allows us to obtain eventually a renormalization group invariant average momentum of non-singlet parton densities, which can be translated into a preferred scheme at a specific scale.