Revisiting relativistic corrections to inclusive J/ψ production at B factories: complete expansion for three-body quarkonium production

A bstract We revisit the calculations of relativistic corrections to inclusive J/ψ production at B factories. For quark-level subprocesses with three-body final states, we carry out a full expansion of the final-state kinematic parameters. The resulting cross sections are theoretically self-consistent and independent of the choice of integration variables. In the high-energy limit, both cross-section magnitudes and the line shapes of correction curves for energy and momentum distributions agree remarkably well with fragmentation-function calculations. We find that 𝒪( v 2 ) corrections suppress the cross section by roughly 14 . 55% in the J/ψ +Xcc̄ J / ψ + X c c ¯ channel and enhance it by approximately 11 . 54% for the J/ψ +Xnon-cc̄ J / ψ + X non - c c ¯ channel. After incorporating published 𝒪( α s ) corrections, color-octet contributions, two-photon production channels, and feed-down effects, tension persists between theoretical predictions and experimental measurements. This indicates that complete prompt-quarkonium calculations through 𝒪( α s , v 2 ), or evaluations incorporating higher-order corrections, are required to resolve this tension.