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Collins-Soper kernel and reduced soft function in lattice QCD

Constantia Alexandrou1,2,*, Simone Bacchio2, Krzysztof Cichy3, Martha Constantinou4, Aniket Sen5,6, Gregoris Spanoudes1,†, Fernanda Steffens5,6, and Jacopo Tarello1,2,‡

  • *Contact author: alexand@ucy.ac.cy
  • †Contact author: spanoudes.gregoris@ucy.ac.cy
  • ‡Contact author: j.tarello@cyi.ac.cy
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Phys. Rev. D 113, 074506 – Published 9 April, 2026

DOI: https://doi.org/10.1103/5wft-9rtd

Abstract

We evaluate the Collins-Soper kernel and the reduced soft function in lattice QCD, incorporating O(αs) matching corrections. The calculation relies on the evaluation of the quasitransverse momentum–dependent wave function with asymmetric staple-shaped quark bilinear operators and four-point meson form factors. These quantities are computed nonperturbatively using two Nf=2+1+1 twisted-mass fermion ensembles with the same lattice spacing of a=0.093  fm: the first ensemble has a lattice size of 243×48 and a pion mass of 346 MeV, and the second one has a lattice size of 323×64 and a pion mass of 261 MeV. The Collins-Soper kernel and the soft function are needed for the determination of the transverse momentum–dependent parton distribution functions.

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Phys. Rev. D 113, 074506– Published 9 April, 2026
  • Received 4 October 2025
  • Accepted 19 March 2026
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