Perturbative and Non-perturbative Lattice Calculations for the Study of Parton Distributions

We discuss how lattice calculations can be a useful tool for the study of structure functions. Particular emphasis is given to the perturbative renormalization of the operators.Comment: 6 pages. Talk presented at the 6th International Symposium on Radiative Corrections "RADCOR 2002" and 6th Zeuthen Workshop on Elementary Particle Theory "Loops and Legs 2002", Kloster Banz (Germany), September 8 to 13, 200

Perturbative renormalization of the first moment of structure functions for domain-wall QCD

Using the domain-wall formulation of lattice fermions, we have computed the one-loop renormalization factors of one-link operators which measure the first nontrivial moment of the unpolarized, polarized and transversity structure functions, in the flavor nonsinglet sector. The knowledge of these factors is necessary in order to extract physical numbers from domain-wall Monte Carlo simulations of parton distributions. We have automated the perturbative calculations by developing suitable FORM codes. The results show that in many instances the total renormalization factors are almost equal to one, and that hence the corresponding operators are, for the appropriate values of the Dirac mass $M$ and the coupling $g_0$, practically unrenormalized.Comment: REVTeX 4, 12 pages, 1 figure; changes in the final paragraphs of sections 1 and 5 concerning comparisons with previous results, plus correction of minor typos; final version, accepted for publication in Physical Review

Perturbative renormalization of the first two moments of non-singlet quark distributions with overlap fermions

Using the overlap-Dirac operator proposed by Neuberger, we have computed in lattice QCD the one-loop renormalization factors of ten operators which measure the lowest two moments of unpolarized and polarized non-singlet quark distributions. These factors are necessary to extract physical numbers from Monte Carlo simulations made with overlap fermions. An exact chiral symmetry is maintained in all our results, and the renormalization constants of corresponding unpolarized and polarized operators which differ by a $\gamma_5$ matrix have the same value. We have considered two lattice representations for each continuum operator. The computations have been carried out using the symbolic language FORM, in a general covariant gauge. In some simple cases they have also been checked by hand.Comment: 23 pages, 1 Postscript figure, uses elsevier style. Small corrections made in eqs. (6), (7), (13), (15), (17), (19), (20), (21) and (A.8), with no influence on the result