Central production of η and η′ via double Pomeron exchange in the Sakai-Sugimoto model

Abstract

We construct a string-inspired model for the central production of $\ensuremath{\eta}$ and ${\ensuremath{\eta}}^{\ensuremath{'}}$ mesons in proton-proton collisions via double Pomeron exchange. Using general symmetry considerations, we construct a low-energy differential cross section for double glueball exchange in terms of some undetermined coupling constants and form factors. We extend this model to the Regge regime, replacing the glueball propagators with Pomeron trajectories and modifying the interaction term by a factor derived from the five-string scattering amplitude in flat space. We then fix the couplings which remain undetermined, using the Sakai--Sugimoto framework to model low-energy QCD. Finally, we generate a simulation of the scattering process at $\sqrt{s}=29.1\text{ }\text{ }\mathrm{GeV}$, where double Pomeron exchange should play a role (secondary to double Reggeon exchange). We focus on the dependence of the scattering cross section on ${\ensuremath{\theta}}_{34}$, the angle between the scattered protons in the transverse plane. The results exhibit a definite deviation from the pure ${\mathrm{sin}}^{2}{\ensuremath{\theta}}_{34}$ dependence that arises as a consequence of natural parity violation alone. The amount of deviation is primarily determined by couplings that come from the Chern--Simons action of the anti-de Sitter/QCD supergravity dual, which is directly related to the QCD gravitational anomaly, and thus constitutes a universal part of any five-dimensional string/gravity dual theory of QCD. We argue that this makes the high-energy central production of pseudoscalar mesons an interesting probe of anti-de Sitter/QCD models.