Bilinear quark operator renormalization at generalized symmetric point

Abstract

We compute Green's functions with a bilinear quark operator inserted at non-zero momentum for a generalized momentum configuration to two loops. These are required to assist lattice gauge theory measurements of the same quantity in matching to the high energy behaviour. The flavour non-singlet operators considered are the scalar, vector and tensor currents as well as the second moment of the twist-2 Wilson operator used in deep inelastic scattering for the measurement of nucleon structure functions.Comment: 19 latex pages, 4 figures, anc directory contains electronic version of amplitude

RI/MOM and RI/SMOM renormalization of overlap quark bilinears on domain wall fermion configurations

“…In Refs. [13,28], two loop calculations of certain Green functions with bilinear quark operator insertions were performed for a general momentum configuration parametrized by ω ¼ q 2 =p 2 . For example, ω ¼ 0 and 1 correspond to the exceptional and symmetric momentum configuration respectively.…”

Symmetric point flavor singlet axial vector current renormalization at two loops

“…Such a configuration is a nonexceptional one and hence should avoid infrared problems. The extension of the early lattice work on operator renormalization at an exceptional point of [29,30] was extended to the nonexceptional case in [32] at one loop and later to two loops in a variety of articles [33][34][35][36][37]. More recently in the lattice study of [38] the operator renormalization constants for all the flavor nonsinglet quark bilinear operators were measured and it was demonstrated that for massless quarks those for the nonexceptional configuration were much more reliable in the infrared limit.…”

“…where the operator O corresponds to any one of (2.1) and (2.2). We use a similar notation to [35][36][37] and follow the general approach provided there. The two independent external momenta, p and q, satisfy the condition for the symmetric subtraction point which is [43,44]…”

“…Having isolated the only case we have to consider for singlet operators then in order to evaluate Γ A s we note that we have taken a different path to the partner computation of Γ A ns of [35][36][37]. To appreciate the contrast it is first best to summarize the earlier approach.…”

“…To appreciate the contrast it is first best to summarize the earlier approach. In [35][36][37] a projection method was used whereby the Green's function was decomposed into a basis of tensors consistent with the symmetries of the operator. For instance, for V this was for integers n with 0 ≤ n < ∞.…”