Abstract
We calculate non-singlet quark operator matrix elements of deep-inelastic scattering in the chiral limit including operators with total derivatives. This extends previous calculations with zero-momentum transfer through the operator vertex which provides the well-known anomalous dimensions for the evolution of parton distributions, as well as calculations in off-forward kinematics utilizing conformal symmetry. Non-vanishing momentum-flow through the operator vertex leads to mixing with total derivative operators under renormalization. In the limit of a large number of quark flavors nf and for low moments in full QCD, we determine the anomalous dimension matrix to fifth order in the perturbative expansion in the strong coupling αs in the MS‾-scheme. We exploit consistency relations for the anomalous dimension matrix which follow from the renormalization structure of the operators, combined with a direct calculation of the relevant diagrams up to fourth order.
Highlights
Within the gauge theory of the strong interaction, quantum chromodynamics (QCD), important nonperturbative information about the hadron structure is obtained from matrix elements of local operators between states with the same or different momenta
The constructive use of the conjugation in Eq (2.31) requires the evaluation of single and double sums over such structures. These sums are non-standard in the sense that they are outside the class of sums that can be solved by the algorithms encoded in the SUMMER program [37] in FORM, which has been a standard in the calculation of the forward anomalous dimensions
We have studied the renormalization of non-singlet quark operators appearing in deep-inelastic scattering, including total derivative operators
Summary
Within the gauge theory of the strong interaction, quantum chromodynamics (QCD), important nonperturbative information about the hadron structure is obtained from matrix elements of local operators between states with the same or different momenta. We perform explicit computations of the relevant OMEs up to four loops for non-zero momentum transfer through the operator vertex and derive a number of consistency relations for the respective anomalous dimensions which govern the mixing associated with total derivative operators. This checks and extends previous calculations for the leading-n f terms in the evolution of flavor non-singlet operators in off-forward kinematics up to five loops. The article is organized as follows: In Sec. 2 we set the stage, review the different basis choices for spin-N local non-singlet quark operators used in the literature and discuss their renormalization together with particular properties of the anomalous dimensions.
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