Target-Mass Corrections in the OPE Sum-Rule Approach to Quarkonium-Nucleon Interactions with Global-Fit PDFs: an $x$-Resolved Analysis

TL;DR

This paper revisits the operator-product-expansion sum-rule approach to quarkonium-nucleon interactions, analyzing the impact of target mass corrections and the detailed gluon distribution across different x-regions using modern global-fit PDFs.

Contribution

It introduces an x-resolved analysis of target mass corrections and directly computes the cross section, improving the understanding of gluon contributions in quarkonium-nucleon interactions.

Findings

Target mass corrections depend on the gluon distribution's support across x-regions.

The cross section is accurately computed via partonic convolution, avoiding unphysical threshold ansatz.

The analysis clarifies the role of current PDFs in predicting quarkonium-nucleon cross sections.

Abstract

We revisit the operator-product-expansion sum-rule approach to inelastic quarkonium-nucleon interactions using global-fit parton distribution functions ABMP16, MSHT20, CT18 and NNPDF4.0. In contrast to the original analyses, our goal is not limited to updating the PDF input, but is to resolve the full chain from the gluon distribution $g(x,Q)$ to the Mellin moments $A_n(Q)$, the corresponding sum rules, and the resulting cross section $\sigma_{\Phi N}(s)$. We perform an $x$-resolved analysis of the TMC effect by studying the weighted moment densities entering the sum rules and their decomposition into different $x$-regions. This allows us to determine which parts of the gluon distribution dominate individual Mellin moments and how the finite target mass suppresses their contributions. We show that the magnitude of the TMC effect is controlled not only by the universal kinematic weight appearing in the modified sum rules, but also by the way in which a given global-fit PDF redistributes the support of the moments between the small-, intermediate- and large-$x$ regions. The cross section is computed directly via the partonic convolution integral, bypassing the two-parameter threshold ansatz that develops unphysically large exponents with modern PDFs. The resulting framework provides a transparent reanalysis of quarkonium-nucleon sum rules and clarifies the role of current PDF information in predictions for $\sigma_{\Phi N}(s)$.