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An extraction of the Collins-Soper kernel from a joint analysis of experimental and lattice data

Artur Avkhadiev, Valerio Bertone, Chiara Bissolotti, Matteo Cerutti, Yang Fu, Simone Rodini, Phiala Shanahan, Michael Wagman, Yong Zhao

TL;DR

The Collins-Soper kernel (CSK) governs nonperturbative TMD evolution but is not directly probed by experiments; this work performs the first joint CSK extraction by blending experimental Drell–Yan data with lattice CSK calculations using a neural-network parametrization of TMDs and two methods: Bayesian reweighting and a simultaneous fit. The inclusion of lattice data shifts the nonperturbative parameter $g_2$ by about 10% and reduces its uncertainty by roughly 40–50%, yielding $g_2$ values around $0.165$–$0.167$ and showing consistency between methods. The results indicate no tension between datasets and that lattice inputs substantially improve CSK determinations and TMD evolution control. This approach demonstrates the tangible impact of lattice QCD on precision TMD phenomenology and motivates further joint analyses in the nonperturbative regime.

Abstract

We present a first joint extraction of the Collins-Soper kernel (CSK) combining experimental and lattice QCD data in the context of an analysis of transverse-momentum-dependent distributions (TMDs). Based on a neural-network parametrization, we perform a Bayesian reweighting of an existing fits of TMDs using lattice data, as well as a joint TMD fit to lattice and experimental data. We consistently find that the inclusion of lattice information shifts the central value of the CSK by approximately 10% and reduces its uncertainty by 40-50%, highlighting the potential of lattice inputs to improve TMD extractions.

An extraction of the Collins-Soper kernel from a joint analysis of experimental and lattice data

TL;DR

The Collins-Soper kernel (CSK) governs nonperturbative TMD evolution but is not directly probed by experiments; this work performs the first joint CSK extraction by blending experimental Drell–Yan data with lattice CSK calculations using a neural-network parametrization of TMDs and two methods: Bayesian reweighting and a simultaneous fit. The inclusion of lattice data shifts the nonperturbative parameter by about 10% and reduces its uncertainty by roughly 40–50%, yielding values around – and showing consistency between methods. The results indicate no tension between datasets and that lattice inputs substantially improve CSK determinations and TMD evolution control. This approach demonstrates the tangible impact of lattice QCD on precision TMD phenomenology and motivates further joint analyses in the nonperturbative regime.

Abstract

We present a first joint extraction of the Collins-Soper kernel (CSK) combining experimental and lattice QCD data in the context of an analysis of transverse-momentum-dependent distributions (TMDs). Based on a neural-network parametrization, we perform a Bayesian reweighting of an existing fits of TMDs using lattice data, as well as a joint TMD fit to lattice and experimental data. We consistently find that the inclusion of lattice information shifts the central value of the CSK by approximately 10% and reduces its uncertainty by 40-50%, highlighting the potential of lattice inputs to improve TMD extractions.

Paper Structure

This paper contains 8 sections, 14 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Baseline TMD fit
  3. Lattice data
  4. Joint extraction of the CSK
  5. Reweighting
  6. Simultaneous fit
  7. Conclusion
  8. Acknowledgments

Figures (2)

  • Figure 1: MC replica distribution of $g_2$ from the baseline fit (red), after reweighting (green), and from the simultaneous fit (blue). The points above the distributions display the respective central values and one-$\sigma$ uncertainties.
  • Figure 2: The CSK as a function of $b$ at $\mu= 2$ GeV as obtained from the baseline of fit of Ref. Bacchetta:2025ara (red band), from reweighting (green band), and from the simultaneous fit of experimental and lattice data (blue band). Bands correspond to one-$\sigma$ uncertainties. Data points correspond to the extraction of Ref. Avkhadiev:2024mgd. The bottom inset shows the ratio to the baseline predictions at large values of $b$.