Twist-two matrix elements at finite and infinite volume

Abstract

We present one-loop results for the forward twist-two matrix elements relevant to the unpolarised, helicity and transversity baryon structure functions, in partially-quenched (N_f=2 and N_f=2+1) heavy baryon chiral perturbation theory. The full-QCD limit can be straightforwardly obtained from these results and we also consider SU(2|2) quenched QCD. Our calculations are performed in finite volume as well as in infinite volume. We discuss features of lattice simulations and investigate finite volume effects in detail. We find that volume effects are not negligible, typically around 5--10% in current partially-quenched and full QCD calculations, and are possibly larger in quenched QCD. Extensions to the off-forward matrix elements and potential difficulties that occur there are also discussed.Comment: 35 pages, 7 figures, typos correcte

Finite volume effects for meson masses and decay constants

“…The details of the pion kinematics will be discussed in the next section, and the isospin index refers to the t-channel. One immediately verifies that (21) agrees with the modified Lüscher formula in one dimension to first order in the density n B -the density factor n B in the integrand is the outcome of the resummation over n in (18) if n is taken as a one-dimensional vector. Schenk has carried the expansion of (21) one step further and determined the contributions of order n 2 B to the pion mass at finite temperature: in this extension, effects generated by three-body collisions are explicitly accounted for.…”

“…Lüscher then concentrates on the leading exponential contributions (those with |n| = 1), and shows that, if one disregards terms which are exponentially suppressed with respect to exp(−λ π ), three of the four integrations in (18) can be performed explicitly and the result (13) is obtained. The same reasoning, however, applies also to all other terms in the sum in (18): for each of the terms with |n| > 1, one can obtain its leading exponential contribution by performing exactly the same steps that Lüscher did for the |n| = 1 term and work out three of the four integrations explicitly. It is easy to keep track of the vector n in doing these manipulations, and to get the resummed formula…”

“…Contributions to the integral (18) which are due to singularities in either the propagator G 0 or the vertex function Γ which are further away from the real axis than M π . These singularities show up only if one considers the vertex function at one loop, or the propagator at two-loop accuracy and beyond.…”

“…(8,9,12) represent quickly converging expressions. Several observables have been worked out at one-loop order [5,6,7,8,10,11,17,18], but to date no two-loop result obtained in this setup has appeared.…”

Axial coupling constant of the nucleon for two flavors of dynamical quarks in finite and infinite volume

“…[6]. The volume dependence of such matrix elements has also been studied by several methods [7,8,9] and we shall compare our procedure in some detail with that of Beane and Savage [7].…”