Unpolarized quasi- and pseudo-distributions at one loop: gluon correlator decomposition, matching, and the region |x|>1
Abstract
We compute one-loop unpolarized quark and gluon quasi- and pseudo-distributions in MS̅ and match them to light-cone PDFs. Decomposing the gluon correlator into six covariant form factors, we derive the 6×6 renormalization mixing matrix: its eigenvectors classify multiplicatively renormalizable combinations, and any lattice operator choice projects onto our results without a further loop calculation. Evaluating all Fourier transforms in d dimensions, we resolve the structure of the exterior |x|>1 in quasi-distributions. The correlator carries a short-distance logarithm with a branch cut at ν=0. By the Paley-Wiener theorem, the analytic part transforms into |x|≤1, so the exterior is generated solely by this branch cut. At leading power, the exterior carries no independent non-perturbative physics: it is fixed by the light-cone PDF through the renormalization group. In the gluon channel, the matching kernel of Balitsky, Morris and Radyushkin differs from our MS̅ result by a finite polynomial, identical across index choices. We trace this to contracting an internal loop index over two instead of d−2 transverse directions, omitting an evanescent operator on the collinear pole. Using our basis, we show that the independent kernel of Yao, Ji and Zhang agrees with ours, separated from Balitsky et al. by the same polynomial. While the ratio scheme protects the momentum fraction ⟨ x⟩g, this kernel difference suppresses the extracted normalized second and third gluon moments by 11% and 13% at αs=0.3, so the true MS̅ gluon is systematically harder than reported.
Related
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BibTeX
@misc{monahan2026unpolarized,
title = {{Unpolarized quasi- and pseudo-distributions at one loop: gluon correlator decomposition, matching, and the region $|x|>1$}},
author = {Christopher Monahan and Tobias Neumann},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.40205},
eprint = {2609.40205},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.40205},
}
RIS
TY - UNPB
TI - Unpolarized quasi- and pseudo-distributions at one loop: gluon correlator decomposition, matching, and the region |x|>1
AU - Christopher Monahan
AU - Tobias Neumann
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2609.40205
UR - https://arxiv.org/abs/2609.40205
AB - We compute one-loop unpolarized quark and gluon quasi- and pseudo-distributions in MS̅ and match them to light-cone PDFs. Decomposing the gluon correlator into six covariant form factors, we derive the 6×6 renormalization mixing matrix: its eigenvectors classify multiplicatively renormalizable combinations, and any lattice operator choice projects onto our results without a further loop calculation. Evaluating all Fourier transforms in d dimensions, we resolve the structure of the exterior |x|>1 in quasi-distributions. The correlator carries a short-distance logarithm with a branch cut at ν=0. By the Paley-Wiener theorem, the analytic part transforms into |x|≤1, so the exterior is generated solely by this branch cut. At leading power, the exterior carries no independent non-perturbative physics: it is fixed by the light-cone PDF through the renormalization group. In the gluon channel, the matching kernel of Balitsky, Morris and Radyushkin differs from our MS̅ result by a finite polynomial, identical across index choices. We trace this to contracting an internal loop index over two instead of d−2 transverse directions, omitting an evanescent operator on the collinear pole. Using our basis, we show that the independent kernel of Yao, Ji and Zhang agrees with ours, separated from Balitsky et al. by the same polynomial. While the ratio scheme protects the momentum fraction ⟨ x⟩_g, this kernel difference suppresses the extracted normalized second and third gluon moments by 11% and 13% at α_s=0.3, so the true MS̅ gluon is systematically harder than reported.
ER -