Diffractive Vector Meson Photoproduction from Dual String Theory

Abstract

We study diffractive vector meson photoproduction using string theory via AdS/CFT. The large $s$ behavior of the cross sections for the scattering of the vector meson $V$ on a proton is dominated by the soft Pomeron, $σ_V\sim s^{2ε-2α'_P/B}$, where from the string theory model of \cite{nastase2}, $ε$ is approximately 1/7 below 10 GeV, and 1/11 for higher, but still sub-Froissart, energies. This is due to the production of black holes in the dual gravity. In $ϕ$-photoproduction the mesonic Regge poles do not contribute, so that we deal with a pure Pomeron contribution. This allows for an experimental test. At the gauge theory "Planck scale" of about 1-2 GeV, the ratios of the soft Pomeron contributions to the photoproduction cross-sections of different vector mesons involve not only the obvious quark model factors, but also the Boltzmann factors $e^{-4 M_V/T_0}$, with $T_0$ the temperature of the dual black hole. The presence of these factors is confirmed in the experimental data for $ρ, ω, ϕ, J/ψ,$ and $ψ(2S)$ photoproduction and is compatible with the meager $Υ$ photoproduction data. Throughout, we use vector meson dominance, and from the data we obtain $T_0$ of about $1.3 GeV$, i.e. the gauge theory "Planck scale," as expected. The ratio of the experimental soft Pomeron onset scale $\hat{E}_R\sim 9$ GeV and of the gauge theory Planck scale, $T_0 \sim 1.3$ GeV conforms to the theoretical prediction of $N_c^2/N_c^{1/4}$.