Renormalization of Twist-Four Operators in QCD

TL;DR

This paper derives comprehensive two-particle renormalization group kernels for twist-four operators in QCD, utilizing conformal symmetry to relate complex kernels to known quasipartonic results, facilitating evolution equations for generalized parton distributions.

Contribution

It provides a complete set of two-particle kernels for twist-four QCD operators, showing they can be obtained from existing quasipartonic results via symmetry considerations.

Findings

Derived 2->2 and 2->3 kernels for twist-four operators.

Kernels can be reconstructed from quasipartonic results using symmetry.

Results applicable to evolution equations for generalized parton distributions.

Abstract

Extending the work by Bukhvostov, Frolov, Lipatov and Kuraev (BFLK) on the renormalization of quasipartonic operators we derive a complete set of two-particle renormalization group kernels that enter QCD evolution equations to twist-four accuracy. It is shown that the 2->2 evolution kernels which involve ``non-partonic'' components of field operators, and, most remarkably, also 2->3 kernels do not require independent calculation and can be restored from the known results for quasipartonic operators using conformal symmetry and Lorentz transformations. The kernels are presented for the renormalization of light-ray operators built of chiral fields in a particular basis such that the conformal symmetry is manifest. The results can easily be recast in momentum space, in the form of evolution equations for generalized parton distributions.