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Parton distribution and fragmentation functions with massive gluons

Gustavo B. Bopsin1,*, Bruno El-Bennich1,2,†, Gastão Krein1,‡, Fernando E. Serna3,§, and Roberto C. da Silveira1,∥

  • *Contact author: gustavo.bopsin@unesp.br
  • †Contact author: bennich@unifesp.br
  • ‡Contact author: gastao.krein@unesp.br
  • §Contact author: fernando.serna@unisucrevirtual.edu.co
  • ∥Contact author: rc.silveira@unesp.br
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Phys. Rev. D 112, 114023 – Published 16 December, 2025

DOI: https://doi.org/10.1103/ygrj-pglg

Abstract

The correct description of the hadron’s structure requires understanding how quarks and gluons form the observable hadrons and how they are distributed within them. Two key nonperturbative quantities encapsulate this information: parton distribution functions (PDFs) and fragmentation functions (FFs). The former define a probabilistic light-front momentum distribution of partons within a hadron, whereas the latter describe the hadronization process of high-energy partons. Computing these functions analytically poses significant challenges, as it demands models that accurately incorporate the nonperturbative infrared dynamics of quantum chromodynamics (QCD). In this work, we compute the pion PDF and its elementary and full FFs using the Curci-Ferrari (CF) model. This model enables the exploration of nonperturbative QCD effects by introducing a gluon-mass scale within the Landau gauge QCD Lagrangian. The two-point quark and gluon correlation functions derived from the CF model agree well with lattice-QCD results and reproduce the pion decay constant in the chiral limit, consistent with chiral perturbation theory. The resulting pion PDF and FFs computed with the CF quark propagator and pion Bethe-Salpeter amplitude are in good qualitative and quantitative agreement with those obtained using the Qin-Chang model, a benchmark approach to nonperturbative QCD. These findings support the broader applicability of the Curci-Ferrari model in hadron phenomenology.

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Phys. Rev. D 112, 114023– Published 16 December, 2025
  • Received 26 July 2025
  • Accepted 21 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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