Towards a lattice calculation of the nucleon structure functions

Abstract

We have initiated a programme to compute the lower moments of the unpolarised and polarised deep inelastic structure functions of the nucleon in the quenched approximation. We review our progress to date.

Scaling of nonperturbativelyO(a)-improved Wilson fermions: Hadron spectrum, quark masses, and decay constants

“…Here we have analyzed O(100) configurations for c SW = 0 and O(300) configurations for c SW = 1.614. We employed both relativistic and non-relativistic wave functions [6,7], except for the high statistics runs where we only looked at the non-relativistic wave function in order to save computer time.…”

“…For the meson masses we found very little difference between using relativistic and non-relativistic wave functions, and we settled for relativistic wave functions (except for the high statistics runs). For the nucleon we have chosen non-relativistic wave functions [6] which performed slightly better because the effective mass plateaus extended to larger times. At β = 6.0 we repeated the lightest quark mass on 16 3 32 on the 24 3 32 lattice, for both improved and Wilson fermions.…”

“…To exhibit the effect of improvement, we have also done calculations with Wilson fermions on the same lattices. Most of our Wilson data come from our structure function calculations [6,7], and we combine this with masses from the literature at other β values to see the dependence on a clearly.…”

A preliminary lattice study of the glue in the nucleon

“…We shall not dwell here on details of the numerical calculations, [1,2], but just mention that the method we use to extract matrix elements from the lattice is standard, namely evaluating the ratio of 3-point to 2-point nucleon correlation functions. The 3-point function is easy to calculate: we simply multiply the 2-point function with the appropriate gluon operator for every configuration.…”

“…We have previously estimated the quark contribution from a lattice calculation (at least for the valence part in the quenched approximation) [1][2][3]. In this contribution we shall consider 1 x (g) .…”