Diffractive Production of Heavy Quarkonia at the Electron Ion Collider

Abstract

We study diffractive photo- and electroproduction of the $S$-wave heavy quarkonia $J/\psi$, $\psi (2S)$, and ${\rm Y}(nS)$ at energies relevant for the Electron-Ion Collider (EIC). The production amplitude is evaluated while retaining the full transverse-momentum (${\ell }_t$) dependence of the hard two-gluon kernel, that is, without expanding the impact-parameter Bessel kernel as is done in the small-size color-dipole limit. The quarkonia light-cone wave functions are built from Cornell-potential solutions of the Schrödinger equation, normalized to the measured leptonic widths, and combined with a modern collinear gluon distribution. After benchmarking the framework against the full set of HERA charmonium cross-section ratio data, we provide a consistent set of bottomonium cross-section ratio predictions in EIC kinematics. We find that the full ${\ell }_t$-resolved treatment systematically improves the description of the radially excited states relative to the leading dipole limit, and we identify the kinematic windows where this difference is largest.

Comments: 8 pages, 7 figures, 2 tables, includes supplemental material, accepted in Physical Review D as a Letter