Generalized double-logarithmic large-x resummation in inclusive deep-inelastic scattering

TL;DR

This paper derives all-order resummation formulas for the highest large-x logarithms in splitting and coefficient functions in deep-inelastic scattering, revealing small corrections for splitting functions but significant effects for coefficient functions.

Contribution

It provides a novel all-order resummation of the highest large-x logarithms in key DIS functions using a new approach based on their iterative structure and Kinoshita-Lee-Nauenberg cancellations.

Findings

Resummation corrections are small for splitting functions.

Resummation corrections are large for coefficient functions.

Closed-form resummation involves new special functions.

Abstract

We present all-order results for the highest three large-x logarithms of the splitting functions P_qg and P_gq and of the coefficient functions C_phi,q, C_2,g and C_L,g for structure functions in Higgs- and gauge-boson exchange DIS in massless perturbative QCD. The corresponding coefficients have been derived by studying the unfactorized partonic structure functions in dimensional regularization independently in terms of their iterative structure and in terms of the constraints imposed by the functional forms of the real- and virtual-emission contributions together with their Kinoshita--Lee-Nauenberg cancellations required by the mass-factorization theorem. The numerical resummation corrections are small for the splitting functions, but partly very large for the coefficient functions. The highest two (three for C_L,g) logarithms can be resummed in a closed form in terms of new special functions recently introduced in the context of the resummation of the leading logarithms