Quark--hadron duality in inclusive electron--proton scattering at high $Q^{2}$: structure functions and truncated moments from CLAS12

Abstract

We present a high-precision study of quark--hadron duality in inclusive electron--proton scattering in the nucleon resonance region, extending to $Q^2\approx10~\mathrm{GeV}^2$, based on recent CLAS12 cross-section measurements at Jefferson Lab. The data, taken with a 10.6~GeV beam, span $2.55 \le Q^2 \le 10.4~\mathrm{GeV}^2$ and cover the full resonance region up to $W\approx2.5~\mathrm{GeV}$. To reach the CLAS12 kinematics, we develop a phenomenological high-$Q^2$ extension of the Argonne--Osaka (ANL-Osaka) dynamical coupled-channels framework, anchored to the original calculation at $Q_0^2=2.774~\mathrm{GeV}^2$ and constrained by the measured cross sections. This enables an ANL-Osaka-constrained longitudinal--transverse decomposition and determination of the proton structure function $F_2(W,Q^2)$, from which we evaluate $W$-truncated Cornwall--Norton moments $M_2(Q^2)$. Comparison with the CJ15 global QCD analysis, including target-mass and higher-twist corrections, shows consistency at the cross-section, structure-function, and truncated-moment levels, providing quantitative evidence for both local and global quark--hadron duality at substantially higher $Q^2$ than previously explored. We further identify a threshold effect in the partonic calculation: the finite-$Q^2$ corrections do not enforce the physical pion-production threshold, and the residual discrepancy in the first resonance region is consistent with this effect rather than a breakdown of duality. Within the coupled-channel description, the single-pion channel alone underestimates the inclusive resonance-region strength above the $\Delta(1232)$, which is carried predominantly by the multi-meson channels, as required for duality.