Leading logarithmic large-x resummation of off-diagonal splitting functions and coefficient functions

TL;DR

This paper derives all-order leading-logarithmic expressions for off-diagonal splitting and coefficient functions in large-x deep-inelastic scattering, revealing new functions and their behavior in supersymmetric limits.

Contribution

It introduces a novel function for off-diagonal splitting functions and provides all-order resummation formulas in the large-x limit for DIS and related processes.

Findings

Splitting functions vanish in the supersymmetric limit C_A - C_F to 0.

Coefficient functions remain finite and are expressed in terms of the new function.

Results apply to fragmentation functions and semi-inclusive e^+ e^- annihilation.

Abstract

We analyze the iterative structure of unfactorized partonic structure functions in the large-x limit, and derive all-order expressions for the leading-logarithmic off-diagonal splitting functions P_gq and P_qg and the corresponding coefficient functions C_phi,q and C_2,g in Higgs- and gauge-boson exchange deep-inelastic scattering. The splitting functions are given in terms of a new function not encountered in perturbative QCD so far, and vanish maximally in the supersymmetric limit C_A - C_F to 0. The coefficient functions do not vanish in this limit, and are given by simple expressions in terms of the above new function and the well-known leading-logarithmic threshold exponential. Our results also apply to the evolution of fragmentation functions and semi-inclusive e^+ e^- annihilation.