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

Abstract

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 $0<y\leq1$, with $y=m_N/λ$ 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 $ε_0=0.16$~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.