Three loop MSbar operator correlation functions for deep inelastic scattering in the chiral limit

Abstract

We compute a variety of operator-operator correlation functions to third order in the MSbar scheme in the chiral limit. These include combinations of quark bilinear currents with gauge invariant operators such as moments n = 2 and 3 of the flavour non-singlet Wilson operators of deep inelastic scattering and moment n = 2 of the transversity operator, as well as the correlation functions of the latter operators with themselves. The explicit values of these gauge independent correlation functions are required to assist with non-perturbative matching to lattice regularized calculations of the same quantities. As part of the computation we determine the mixing matrix of renormalization constants of these non-singlet currents with their associated total derivative operators at the same twist to three loops in MSbar. Such operators are crucial in extracting renormalization constants for the operator-operator correlation functions which are consistent with the corresponding renormalization group equation. As a by-product we deduce the R-ratio for the tensor current to third order in the MSbar scheme.

38 latex pages, 2 figures

References in corpus (7)

• The Three-Loop Splitting Functions in QCD: The Singlet Case
• The Longitudinal Structure Function at the Third Order
• A lattice determination of moments of unpolarised nucleon structure functions using improved Wilson fermions
• Renormalization of bilinear quark operators for the chirally improved lattice Dirac operator
• Three loop anomalous dimensions of higher moments of the non-singlet twist-2 Wilson and transversity operators in the MSbar and RI' schemes
• Nonperturbative renormalization of composite operators with overlap fermions
• The QCD Splitting Functions at Three Loops: Methods and Results

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