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Soft and virtual corrections to semi-inclusive DIS up to four loops in QCD

Saurav Goyal1,2,*, Sven-Olaf Moch3,†, Vaibhav Pathak1,2,‡, Narayan Rana4,2,§, and V. Ravindran1,2,∥

  • *Contact author: sauravg@imsc.res.in
  • †Contact author: sven-olaf.moch@desy.de
  • ‡Contact author: vaibhavp@imsc.res.in
  • §Contact author: narayan.rana@niser.ac.in
  • ∥Contact author: ravindra@imsc.res.in
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Phys. Rev. D 113, 034004 – Published 10 February, 2026

DOI: https://doi.org/10.1103/p81j-bq5t

Abstract

We develop the threshold resummation formalism for semi-inclusive deep-inelastic scattering (SIDIS) using their factorization property and renormalization group invariance. This allows us to obtain the soft and virtual (SV) and next-to SV (NSV) corrections for the SIDIS cross section beyond second order in QCD as well as to systematically resum threshold logarithms to all orders in Mellin space. Thanks to the recent results on next-to-next-to-leading order (NNLO) QCD corrections for the SIDIS and four loop results on the vector form factor and Altarelli-Parisi splitting functions in QCD, we obtain all the SV corrections at fourth order in strong coupling constant as except a pure delta function term resulting from the real emissions. The numerical analysis on the impact of resummed contributions at next-to-next-to leading logarithmic (NNLL¯) accuracy matched with the exact fixed order NNLO results on the cross section demonstrates very good perturbative stability of the perturbation prediction, including the reduced dependence on the renormalization and factorization scales μR and μF.

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Phys. Rev. D 113, 034004– Published 10 February, 2026
  • Received 15 August 2025
  • Accepted 17 November 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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