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Stefano Capitani

Publications and source records attributed to Stefano Capitani.

46 records · Page 3Linked to original sources
arXiv2000

Non-perturbative quark mass renormalization in quenched lattice QCD

The renormalization factor relating the bare to the renormalization group invariant quark masses is accurately calculated in quenched lattice QCD using a recursive finite-size technique. The result is presented in the form of a product of a universal factor times another factor, which depends on the details of the lattice theory but is easy to compute, since it does not involve any large scale differences. As a byproduct the Lambda-parameter of the theory is obtained with a total error of 8%.

hep-lat↗
arXiv1997

Study of Lattice Correlation Functions at Small Times using the QCD Sum Rules Continuum Model

In this paper we study the work of Leinweber by applying the Continuum Model of QCD Sum Rules (QCDSR) to the analysis of (quenched) lattice correlation functions. We expand upon his work in several areas: we study meson states as well as baryons; we analyse data from several lattice spacings; and we include data from the Sheikholeslami-Wohlert (clover) improved action. We find that the QCDSR Continuum Model Ansatz can reproduce the data, but only for non-physical values of its parameters. This leads us to reject it as a model for hadronic correlation functions. We study the non-relativistic quark model and conclude that it predicts essentially the same form for the correlation function as the QCDSR Continuum Model approach. Furthermore, because it doesn't have the Continuum Model's restrictions on the parameters, the non-relativistic quark model can be viewed as a successful Ansatz. As well as studying the validity or otherwise of the QCDSR Continuum Model approach, this paper defines 4-parameter fitting functions that can be used to fit lattice data even for a time window close to the source. These functions are shown to be an improvement over 2-exponential fits especially in the case of mesons. We encourage the application of this approach to situations where the conventional fitting procedures are problematic due to poor ground state dominance.

hep-lat↗
arXiv1997

QCD Sum Rules on the Lattice

We study the work of Leinweber by applying the Continuum Model of QCD Sum Rules (QCDSR) to the analysis of (quenched) lattice correlation functions. We expand upon his work in several areas and find that, while the QCDSR Continuum Model very adequately fits lattice data, it does so only for non-physical values of its parameters. The non-relativistic model is found to predict essentially the same form for the correlation functions as the QCDSR Continuum Model but without the latter's restrictions. By fitting lattice data to a general form which includes the non-relativistic quark model as a special case, we confirm it as the model of choice.

hep-lat↗
arXiv1996

DIS Structure Functions in Lattice QCD

In this talk I present the complete 1-loop perturbative computation of the renormalization constants and mixing coefficients of quark and gluon lattice operators of rank two and three whose hadronic elements enter in the determination of the first and second moment of Deep Inelastic Scattering Structure Functions, making use of the nearest-neighbor improved ``clover-leaf'' lattice QCD action. To perform the huge amount of calculations required for the evaluation of all the relevant Feynman diagrams, extensive use of symbolic manipulation languages like Schoonschip and Form has been made.

hep-lat↗
arXiv1996

Lattice DIS Structure Functions

We present the computation, in lattice QCD, of the renormalization constants and mixing coefficients of operators that measure the first two moments of DIS Structure Functions. These calculations have been performed using the Sheikholeslami-Wohlert O(a) improved ``clover'' action, which is known to reduce the systematic error associated with the finiteness of the lattice spacing a. Due to the complexities of the computations, we have developed, using the computer languages Schoonschip and Form, general codes that are able to automatically carry out all the analytic lattice manipulations.

hep-lat↗
arXiv1995

Deep Inelastic Scattering in Improved Lattice QCD. II. The second moment of structure functions

In this paper we present the 1-loop perturbative computation of the renormalization constants and mixing coefficients of the lattice quark operators of rank three whose hadronic elements enter in the determination of the second moment of Deep Inelastic Scattering (DIS) structure functions. We have employed in our calculations the nearest-neighbor improved ``clover-leaf'' lattice QCD action. The interest of using this action in Monte Carlo simulations lies in the fact that all terms which in the continuum limit are effectively of order $a$ ($a$ being the lattice spacing) have been demonstrated to be absent from on-shell hadronic lattice matrix elements. We have limited our computations to the quenched case, in which quark operators do not mix with gluon operators. We have studied the transformation properties under the hypercubic group of the operators up to the rank five (which are related to moments up to the fourth of DIS structure functions), and we discuss the choice of the operators considered in this paper together with the feasibility of lattice computations for operators of higher ranks. To perform the huge amount of calculations required for the evaluation of all the relevant Feynman diagrams, we have extensively used the symbolic manipulation languages Schoonschip and Form.

hep-lat↗
arXiv1995

The Use of Schoonschip and Form in Perturbative Lattice Calculations

Using the formal languages Schoonschip and Form, we have developed general codes that are able to carry out all the algebraic manipulations needed to perform analytic lattice calculations, starting from the elementary building blocks (propagators and vertices) of each Feynman diagram. The main difficulty resides in the fact that, although there are many built in instructions to deal with Dirac gamma-matrices, Schoonschip and Form have been conceived having in mind a continuum theory, which is invariant with respect to the Lorentz group. On the lattice, on the contrary, a field theory is only invariant with respect to the hypercubic group, contained in the (euclidean) Lorentz group and not every pair of equal indices should be summed over. Being impossible to directly use the `gammatrics' of Schoonschip and Form as they are, special routines have been developed to correctly treat gamma matrices on the lattice, while using as much as possible of the built in Schoonschip and Form commands. We have used our codes to compute, in 1-loop perturbation theory in lattice QCD, the renormalization constants and mixing coefficients of the operators that enter in the determination of the first two moments of deep inelastic scattering structure functions.

hep-lat↗
arXiv1994

A new formulation of the effective theory for heavy particles

We derive the effective theories for heavy particles with a functional integral approach by integrating away the states with high velocity and with high virtuality. This formulation is non-perturbative and has a close connection with the Wilson renormalization group transformation. The fixed point hamiltonian of our transformation coincides with the static hamiltonian and irrelevant operators can be identified with the usual $1/M$ corrections to the static theory. No matching condition has to be imposed between the full and the static theory operators with our approach. The values of the matching constants come out as a dynamical effect of the renormalization group flow.

hep-ph↗
arXiv1994

Deep Inelastic Scattering in Improved Lattice QCD. I. The first moment of structure functions

We present the complete 1-loop perturbative computation of the renormalization constants and mixing coefficients of the operators that measure the first moment of deep inelastic scattering structure functions, employing the nearest neighbor improved lattice QCD action. The interest of using this action in Monte Carlo simulations lies in the fact that all terms which in the continuum limit are effectively of order $a$ ($a$ being the lattice spacing) have been proven to be absent from on-shell hadronic lattice matrix elements. Because of the complexity of the calculations, we have checked the analytical expression of all Feynman diagrams using Schoonschip. To this end we have developed a suitable code designed to automatically carry out all the necessary lattice algebraic manipulations, starting from the elementary building blocks of each diagram. We have found discrepancies with some of the published numbers, but we are in agreement with the known results on the energy-momentum tensor.

hep-lat↗