On The Pomeron at Large 't Hooft Coupling

TL;DR

This paper develops a framework for unitarizing the Pomeron at large 't Hooft coupling within conformal regimes, using eikonal approximation and complex J-plane analysis, with implications for QCD and confining theories.

Contribution

It introduces a generalized approach to Pomeron unitarization in conformal and confining theories, extending previous work on single and multiple graviton exchanges in AdS space.

Findings

Froissart bound is generally satisfied and saturated by the eikonal approximation.

Methods extend to confining theories, providing a broader applicability.

Analysis of unitarity and saturation effects in the conformal regime.

Abstract

We begin the process of unitarizing the Pomeron at large 't Hooft coupling. We do so first in the conformal regime, which applies to good accuracy to a number of real and toy problems in QCD. We rewrite the conformal Pomeron in the $J$-plane and transverse position space, and then work out the eikonal approximation to multiple Pomeron exchange. This is done in the context of a more general treatment of the complex $J$-plane and the geometric consequences of conformal invariance. The methods required are direct generalizations of our previous work on single Pomeron exchange and on multiple graviton exchange in AdS space, and should form a starting point for other investigations. We consider unitarity and saturation in the conformal regime, noting elastic and absorptive effects, and exploring where different processes dominate. Our methods extend to confining theories and we briefly consider the Pomeron kernel in this context. Though there is important model dependence that requires detailed consideration, the eikonal approximation indicates that the Froissart bound is generically both satisfied and saturated.