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Renormalization of the gluon distribution function in the background field formalism

Tolga Altinoluk1, Guillaume Beuf1, and Jamal Jalilian-Marian1,2,3

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Phys. Rev. D 112, 034021 – Published 21 August, 2025

DOI: https://doi.org/10.1103/mxtj-vblf

Abstract

We derive the leading order Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution of gluon distribution function in the target light cone gauge starting from its standard operator definition. The derivation is performed using the background field formalism also employed in the color glass condensate effective theory of small x QCD. We adopt Mandelstam-Leibbrandt prescription to regulate in an unambiguous way the spurious singularity appearing in the light-cone gauge Feynman propagator. UV divergences are regulated via dimensional regularization. The methods introduced in this paper represent the first steps in the construction of a unified framework for QCD evolution, which could address collinear physics as well as small x physics and gluon saturation.

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Phys. Rev. D 112, 034021– Published 21 August, 2025
  • Received 28 May 2025
  • Accepted 19 July 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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