Target-mass corrections in the OPE sum-rule approach to quarkonium–nucleon interactions with global-fit PDFs: An x-resolved analysis

We derive an exact all-orders treatment of target-mass corrections (TMCs) within the leading-twist Coulombic OPE for the absorptive quarkonium–nucleon spectral baseline. Resumming the complete trace series before analytic continuation yields a closed spectral kernel, a shifted-convolution expression, and a moment representation that preserves the on-shell incoming domain 0 < y ≤ 1, with y=mN/λ and λ the nucleon energy in the quarkonium rest frame. Using native ABMP16, MSHT20, CT18, and NNPDF4.0 grids, we find at Q=10 GeV and ϵ0=0.16 GeV that the TMC/no-TMC moment ratio decreases from about 0.85 at n=4 to 0.42–0.48 at n=12. At the first tabulated energies above the incoming two-body endpoint, the leading-twist cross-section ratio is strongly suppressed but rapidly approaches unity with increasing energy. The strict endpoint has an integrable inverse-velocity behaviour, whose hadronic-threshold interpretation lies outside the leading-twist construction.