Diffractive $J/ψ$ photoproduction as a probe of the gluon density

Abstract

We use perturbative QCD, beyond the leading $\ln Q^2$ approximation, to show how measurements of diffractive $J/ψ$ production at HERA can provide a sensitive probe of the gluon density of the proton at small values of Bjorken $x$. We estimate both the effect of the relativistic motion of the $c$ and $\overline{c}$ within the $J/ψ$ and of the rescattering of the $c\overline{c}$ quark pair on the proton. We find that the available data for diffractive $J/ψ$ photoproduction can discriminate between the gluon distributions of the most recent sets of partons.

Figures (9)

• Figure 1: Schematic diagram for high energy diffractive $J/\psi$ photoproduction. The factorized form follows since, in the proton rest frame, the formation time $\tau_f \simeq 2 E_\gamma/(Q^2 + M_\psi^2)$ is much greater than the interaction time $\tau_{\rm int} \simeq R$ where $R$ is the radius of the proton.
• Figure 2: The points show the lowest-order estimate of the gluon density obtained from the available high energy $\sigma (\gamma p \rightarrow J/\psi \;p)$ data [5,6] using eq. (2). For comparison we also show the gluon of the GRV parton set [7], and of the MRS(A$^\prime$, G) partons of ref.[8] evolved back to $Q^2$ = 2.5 GeV$^2$.
• Figure 3: Lowest-order perturbative QCD diagrams for diffractive $J/\psi$ production. The particle four-momenta are shown; $z$ and $1-z$ denote the fractions of the longitudinal momentum of the photon that are carried by the $c$, $\overline{c}$ quarks. The small crosses indicate which quarks may be regarded as essentially on-mass-shell.
• Figure 4: One of the one-rung diagrams which give the $\alpha_S \ln (1/x)$ contribution to the BFKL gluon, $f_{\rm BFKL} (x, k_T^2)$. The emitted gluons have proton momentum fractions $x$ and $x^\prime$ with $|x^\prime| \ll x$.
• Figure 5: A typical diagram leading to a $c\overline{c}$ rescattering correction. In the text we compute the $n = 1$ contribution. All quark lines are on-shell except for that with momentum $r$, as in Fig. 3.