Nucleon matrix elements with domain wall fermions

The structure of the nucleon is one of the fundamental problems that lattice QCD can address. In the last few years, substantial efforts have been made by several groups [1,2,3,4] in calculating the non-perturbative matrix elements relevant to nucleon structure. Up to now only Wilson fermions, improved and unimproved, have been used in both the quenched approximation and in full QCD. In this report we examine the feasibility of studying nucleon matrix elements with domain wall fermions in the quenched approximation. Domain wall fermions have only O(a) lattice artifacts, non-perturbative renormalization works very well, and have no problem with exceptional configurations [5,6]. Furthermore, the chiral symmetry they preserve on the lattice eliminates mixings with lower dimensional operators, rendering the renormalization of certain matrix elements significantly simpler. For the above reasons, a study of the nucleon structure with domain wall fermions is definitely important. We study the nucleon matrix elements relevant to the leading twist contributions to the moments of the nucleon structure functions. The leading twist matrix elements are: