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Convergence of heavy-flavor parton distribution functions at small x and its impact on future ep colliders

S. O. Kara*

  • *Contact author: seyitokankara@gmail.com
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Phys. Rev. D 113, 015020 – Published 20 January, 2026

DOI: https://doi.org/10.1103/r4vm-x3qd

Abstract

The small-x regime remains a key testing ground for perturbative QCD and future lepton-hadron collider physics. We demonstrate that the long-standing ∼30% spread among global next-to-next-to-leading-order parton distribution functions (PDFs) for heavy-flavor parton densities at small x has now converged below ≈17%. Using the latest nnpdf4.0, ct18, and msht20 sets, we quantify a maximal relative deviation of Δmax≃16.8% at x=10−6 and Q=100  GeV. This convergence, further stabilized by consistent αs and scale variations, marks a new precision frontier for the heavy-flavor sector. We evaluate the phenomenological impact for heavy-quark electroproduction at future ep colliders (LHeC and FCC–eh), showing that PDF-driven cross section uncertainties for e−p→e−cc¯X and e−p→e−bb¯X have been reduced by nearly a factor of 2 compared to 2013 estimates.

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Phys. Rev. D 113, 015020– Published 20 January, 2026
  • Received 17 October 2025
  • Accepted 2 January 2026
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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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