Analytic parametrisations of the scale dependence of proton parton distributions
Abstract
Parton distribution functions (PDFs) are non-perturbative inputs whose scale dependence is governed by the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) equations. Their numerical evaluation commonly relies on interpolation of tabulated grids. We discuss an analytic representation of collinear proton PDFs in (x,Q2), obtained by promoting the parameters of a standard x-space parametrisation to functions of the scale. The coefficients are reconstructed from the HERAPDF2.0 NLO set using machine-assisted fitting techniques, with sampling in 10−4≤ x≤ 0.65 and scales up to 1 TeV. The resulting ML-PDFs reproduce integrated distributions at the sub-percent level for most flavours, with deviations reaching about 1.5% for the strange quark at the highest scales. They satisfy valence and momentum sum rules at the percent level and reproduce representative pp→π and pp→γπ cross sections within approximately 2% and 5%, respectively, in the kinematic regions studied. Compared with grid interpolation through LHAPDF, direct evaluation of the analytic expressions reduces the total Monte Carlo run time by about 11% and 30% in these two applications.
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BibTeX
@misc{renteriaestrada2026analytic,
title = {{Analytic parametrisations of the scale dependence of proton parton distributions}},
author = {David F. Rentería-Estrada},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.08272},
eprint = {2611.08272},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.08272},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Analytic parametrisations of the scale dependence of proton parton distributions
AU - David F. Rentería-Estrada
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.08272
UR - https://arxiv.org/abs/2611.08272
AB - Parton distribution functions (PDFs) are non-perturbative inputs whose scale dependence is governed by the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) equations. Their numerical evaluation commonly relies on interpolation of tabulated grids. We discuss an analytic representation of collinear proton PDFs in (x,Q^2), obtained by promoting the parameters of a standard x-space parametrisation to functions of the scale. The coefficients are reconstructed from the HERAPDF2.0 NLO set using machine-assisted fitting techniques, with sampling in 10^−4≤ x≤ 0.65 and scales up to 1 TeV. The resulting ML-PDFs reproduce integrated distributions at the sub-percent level for most flavours, with deviations reaching about 1.5% for the strange quark at the highest scales. They satisfy valence and momentum sum rules at the percent level and reproduce representative pp→π and pp→γπ cross sections within approximately 2% and 5%, respectively, in the kinematic regions studied. Compared with grid interpolation through LHAPDF, direct evaluation of the analytic expressions reduces the total Monte Carlo run time by about 11% and 30% in these two applications.
ER -