Two-Loop DGLAP Splitting Functions from Light Cone Perturbation Theory

TL;DR

This paper demonstrates a two-loop calculation of the nonsinglet splitting function in Light Cone Perturbation Theory, showcasing the method's potential for systematic, high-precision QCD computations with clear physical interpretation.

Contribution

It introduces a feasible two-loop calculation method in LCPT for splitting functions, advancing higher order QCD computations with a transparent partonic picture.

Findings

Validated the regularization of poles in LCPT

Developed methods for loop calculations in LCPT

Paved the way for precision QCD calculations in gluon saturation regime

Abstract

We perform a two-loop calculation in Light Cone Perturbation Theory (LCPT) to evaluate the next-to-leading order nonsinglet splitting function. Our calculation demonstrates the methodology and feasibility of performing higher order calculations in LCPT. Since in Hamiltonian perturbation theory the longitudinal $k^+$ momentum is always positive, poles in $1/k^+$ can be regularized by a simple cutoff which cancels in physical results, without any associated ambiguities. For transverse momentum integrals we use dimensional regularization. Developing methods for loop calculations in LCPT paves the way for a systematical, automatizable procedure for precision calculations in this framework with a transparent physical partonic interpretation. This can provide a standard framework in higher order calculations in the gluon saturation regime of QCD.