Order-alpha_s^2 corrections to one-particle inclusive processes in DIS

TL;DR

This work computes the order α_s^2 QCD corrections to semi-inclusive DIS for gluon-initiated processes, focusing on the most singular pieces to extract the previously unknown NLO evolution kernels for fracture functions and to explicitly test factorization. A comprehensive treatment of overlapping singularities in multi-variable phase space is developed, enabling a consistent renormalization of parton densities, fragmentation functions, and fracture functions within the MSbar scheme. The authors derive the NLO non-homogeneous fracture-function kernels, showing their two-variable dependence and providing the corresponding evolution equations for fracture functions. Phenomenologically, the NLO contributions are generally small but become significant at small x_B, suggesting appreciable impact on target fragmentation and diffractive SIDIS channels.

Abstract

We analyze the order-$α_s^2$ QCD corrections to semi-inclusive deep inelastic scattering and present results for processes initiated by a gluon. We focus in the most singular pieces of these corrections in order to obtain the hitherto unknown NLO evolution kernels relevant for the non homogeneous QCD scale dependence of these cross sections, and to check explicitly factorization at this order. In so doing we discuss the prescription of overlapping singularities in more than one variable.

Figures (7)

• Figure 1: (a) Current and (b) target fragmentation processes.
• Figure 2: Born contribution to the cross sections
• Figure 3: Real and virtual contributions to the $\alpha_s$ cross sections
• Figure 4: Real contributions to the $\alpha_s^2$ cross sections
• Figure 5: One loop contributions to the $\alpha_s^2$$gq$ cross section. Diagrams obtained from the first four by reversing the quark line must be also taken into account.