Diffractive Heavy Quarkonium Photo- and Electroproduction in QCD

TL;DR

This work develops a QCD-based framework for hard diffractive photo- and electroproduction of heavy vector mesons, emphasizing the leading role of the quark–antiquark light-cone wave function and the gluon distribution in the target. It extends prior longitudinal-only analyses to transverse polarizations, deriving explicit corrections T(Q^2) and R(Q^2) and a Q_eff^2 rescaling that connects transverse sizes to the effective hard scale. Through a critical examination of non-relativistic quarkonium wave functions and a constructed hybrid light-cone wave function, the authors achieve improved predictions for J/ψ and Υ production that are broadly consistent with HERA data and highlight the sensitivity to the gluon density and wave-function structure. The study also updates ρ^0 electroproduction and argues that these hard diffractive processes offer a precise laboratory for exploring color distributions and short-distance QCD dynamics in bound states.

Abstract

Hard diffractive photo- and electroproduction of heavy vector mesons ($J/ψ$ and $Υ$) is evaluated within the leading $α_s\ln{Q^2 \overΛ_{QCD}^2}$ approximation of QCD. In difference from our earlier work on that subject, also the production of transversely polarized vector mesons is calculated. Special emphasis is placed on the role of the vector meson's $q\bar q$ light-cone wave function. In that context, conventional non-relativistic quarkonium models and a light-front QCD bound state calculation are critically examined and confronted with QCD expectations. Our numerical analysis finds a significant high momentum tail in the latter wave functions and a deviation from the expected asymptotic behavior of $φ_V(z,b=0)\propto z(1-z)$. We then design an interpolation to match the quarkonium models at large inter-quark separations with QCD expectations at small distances. We use these results to compare our predictions for the forward differential cross section of $J/ψ$ photo- and electroproduction with recent experimental results from HERA. In addition, our earlier discussion of $ρ^o$ electroproduction is updated in light of recent experimental and theoretical enhancements.

Figures (14)

• Figure 1: Feynman diagrams relevant for the evaluation of the amplitude for diffractive production of vector mesons, i.e., the $\gamma^{(*)}+N \rightarrow V + N$ process, in leading $\alpha_s\ln{Q^2\over\Lambda_{QCD}^2}$ approximation.
• Figure 2: Average transverse distances effective in the evaluation of the longitudinal structure function as well as for diffractive production of longitudinally polarized $\rho^o$, $J/\psi$ and $\Upsilon$ mesons. Also shown are the resulting effective scales, $Q_{eff}^2$, for diffractive vector meson production.
• Figure 3: The contribution of the hard blob to the $t$-slope of diffractive electroproduction of longitudinally polarized $\rho^o$ and $J/\psi$ vector mesons.
• Figure 4: The $t$-dependence of the diffractive vector meson production cross section, i.e., $\left.{d\sigma \over dt}\right|_{screen}/\left.{d\sigma \over dt}\right|_{t=0}$ of Eq. (\ref{['slope']}), and the change of the $t$-slope with energy, i.e., $\alpha^{\prime}(t)$ of Eq. (\ref{['alprim']}). Results are shown for $\rho^o$ electroproduction at $Q^2=10$ GeV$^2$.
• Figure 5: The non-relativistic quarkonium wave functions for the heavy ground state mesons $J/\psi$ and $\Upsilon$ from various potential models charmlogcharmqcdcharmpowcharmcor and a light-front QCD bound state calculation perry. In the lower part of the figure, we also show a Gaussian fit adjusted to reproduce $\phi_V(k)$ at small $k$ (dotted lines).