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First study of polarized proton-proton scattering with small- $x$ helicity evolution

Daniel Adamiak ¹, Nicholas Baldonado ², Yuri V. Kovchegov ³, Ming Li³, W. Melnitchouk ⁴, Daniel Pitonyak ⁵, Nobuo Sato⁴, Matthew D. Sievert², Andrey Tarasov ^6,7 et al. (JAM Collaboration (Small- $x$ Analysis Group)

Andrey Tarasov ^6,7 and Yossathorn Tawabutr⁸ (JAM Collaboration (Small- $x$ Analysis Group)

¹Department of Physics, Michigan State University, 567 Wilson Rd, East Lansing, Michigan 48824, USA
²Department of Physics, New Mexico State University, Las Cruces, New Mexico 88003, USA
³Department of Physics, The Ohio State University, Columbus, Ohio 43210, USA
⁴Jefferson Lab, Newport News, Virginia 23606, USA
⁵Department of Physics, Lebanon Valley College, Annville, Pennsylvania 17003, USA
⁶Department of Physics, North Carolina State University, Raleigh, North Carolina 27695, USA
⁷Joint BNL-SBU Center for Frontiers in Nuclear Science (CFNS) at Stony Brook University, Stony Brook, New York 11794, USA
⁸Department of Physics, Faculty of Science, Chulalongkorn University, 254 Phaya Thai Rd, Wang Mai, Pathum Wan, Bangkok 10330, Thailand

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Phys. Rev. D 112, 094032 – Published 19 November, 2025

DOI: https://doi.org/10.1103/9gnx-ycs4

Abstract

We perform a phenomenological study of helicity-dependent parton distribution functions (PDFs) using small- $x$ helicity evolution equations, incorporating for the first time single-inclusive jet production data in polarized proton-proton ( $p p$ ) scattering at parton momentum fractions $x < 0.1$ . We also simultaneously include double-longitudinal spin asymmetries in inclusive and semi-inclusive deep-inelastic scattering probing $x < 0.1$ . Employing the polarized small- $x$ pure-glue calculation of $p p \to g X$ for the jet production cross section, we modify the large- $N_{c} & N_{f}$ KPS-CTT evolution equations by setting $N_{f} = 0$ to replicate the large- $N_{c}$ (pure-glue) limit, while retaining external quark flavors for the spinor field operators. We find that the $p p$ data have a considerable impact on the helicity PDFs at small $x$ , reducing their uncertainties and leading to a total quark and gluon helicity in the proton for $x < 0.1$ of $- 0.04 \pm 0.23$ . Combining our analysis with a recent JAM helicity PDF analysis of the world polarized data, which includes $x > 0.1$ , we find a total quark and gluon helicity contribution for $x > 10^{- 7}$ of between 0.02 and 0.51.

Physics Subject Headings (PhySH)

Corrections

30 December, 2025

Correction: A missing funding statement has been added to the Acknowledgments.

Article Text

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Phys. Rev. D 112, 094032– Published 19 November, 2025

Vol. 112, Iss. 9 — 1 November 2025

Received 9 April 2025
Accepted 7 October 2025
Corrected 30 December 2025

DOI: https://doi.org/10.1103/9gnx-ycs4

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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First study of polarized proton-proton scattering with small- $x$ helicity evolution

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First study of polarized proton-proton scattering with small-x helicity evolution

Abstract

Physics Subject Headings (PhySH)

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References (166)

First study of polarized proton-proton scattering with small- $x$ helicity evolution