On higher-order flavour-singlet splitting and coefficient functions at large x

TL;DR

This paper analyzes the large-x behavior of flavor-singlet splitting functions and coefficient functions in perturbative QCD, predicting their double-logarithmic contributions and leading-logarithmic behavior at all orders.

Contribution

It provides the first leading-logarithmic large-x predictions for flavor-singlet splitting and coefficient functions at all orders in alpha_s, extending known third-order results.

Findings

Double-logarithmic contributions at order alpha_s^4 predicted from third-order results.

Leading-logarithmic large-x behavior of splitting functions and coefficients derived for all orders.

Suppression of these quantities by powers of 1-x compared to threshold terms.

Abstract

We discuss the large-x behaviour of the splitting functions P_qg and P_gq and of flavour-singlet coefficient functions, such as the gluon contributions C_2,g and C_L,g to the structure functions F_2,L, in massless perturbative QCD. These quantities are suppressed by one or two powers of 1-x with respect to the 1/(1-x) terms which are the subject of the well-known threshold exponentiation. We show that the double-logarithmic contributions to P_qg, P_gq and C_L at order alpha_s^4 can be predicted from known third-order results and present, as a first step towards a full all-order generalization, the leading-logarithmic large-x behaviour of P_qg, P_gq and C_2,g at all orders in alpha_s.