Non-perturbative improvement and renormalization of the axial current in N_f=3 lattice QCD

Abstract

Wilson fermions [1] are a popular way of discretizing fermions in lattice QCD. Their maindrawback is that they break chiral symmetry. As a consequence, they are afflicted with dis-cretization errors linear in the lattice spacing a. These O(a) errors can be removed by addingthe Sheikholeslami-Wohlert term (clover term) to the Wilson action [2] and further improvementterms to the matrix elements of interest. This method of O(a) improvement has become knownas ‘Symanzik improvement program’ [3, 4]. Moreover, currents which are conserved in a chiraltheory and hence need not be renormalized require a finite renormalization with Wilson fermions.One of these currents is the isovector axial current which we are concerned with in this work.The isovector axial current is a quark bilinear and in its bare form it can be written asA