Threshold resummation of Semi-Inclusive Deep-Inelastic Scattering

TL;DR

This paper develops a threshold resummation framework for semi-inclusive deep-inelastic scattering (SIDIS), extending previous work on Drell-Yan processes, and provides explicit resummation coefficients up to NNLL accuracy.

Contribution

It introduces a comprehensive resummation approach for SIDIS, analyzing soft and collinear radiation limits, and computes resummation coefficients up to next-to-next-to-leading log order.

Findings

Resummed expressions derived for all soft limits in SIDIS.

Explicit NNLL resummation coefficients obtained in the nonsinglet channel.

Reproduction of recent next-to-leading power results from single-soft resummation.

Abstract

We derive threshold resummation of semi-inclusive deep-inelastic scattering (SIDIS), by building upon previous results by some of us for the resummation of the Drell-Yan process at fixed rapidity, which is related to SIDIS by crossing. We consider both a double-soft limit, in which both the Bjorken and the fragmentation scaling variables tend to their threshold value, and single soft limits in which either of them does. We show that in the former limit only soft radiation contributes, and in the latter limit only collinear radiation, and we derive resummed expressions for the coefficient functions in all cases. We determine explictly resummation coefficients in the nonsinglet channel up to next-to-next-to-leading log by comparing to recent fixed next-to-next-to-leading order results. Expanding out the single-soft resummation we reproduce recent next-to-leading power results.