Threshold resummation of Semi-Inclusive Deep-Inelastic Scattering

TL;DR

This work extends asymmetric threshold resummation to SIDIS by exploiting crossing with Drell–Yan and adapting direct-QCD techniques to two scaling variables, $x$ and $z$. It analyzes double-soft and two single-soft limits, showing that the former is dominated by soft radiation and the latter by collinear radiation, and provides resummed coefficient functions up to NNLL in the nonsinglet channel, fixed by comparison to NNLO SIDIS results. The authors explicitly determine the NNLL resummation coefficients in the double-soft case and derive new single-soft results, matching them to fixed-order data and reproducing leading-power NLP terms upon expansion. The framework relies on a single soft scale in each limit and offers a path toward precise SIDIS phenomenology near threshold, with potential extensions to all partonic channels and explicit fixed-order matching for applications at the Electron-Ion Collider. The results also serve as a nontrivial cross-check of crossing relations between SIDIS and Drell–Yan threshold 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.

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