On the number of Regge trajectories for dual amplitudes

TL;DR

This paper investigates the number of Regge trajectories in dual amplitudes, proving that finite numbers cannot produce reggeizing amplitudes and developing a bootstrap method to exclude such models.

Contribution

It provides a theoretical proof that finite Regge trajectories cannot generate reggeization and introduces a linear programming bootstrap approach to exclude these models.

Findings

Finite Regge trajectories cannot produce reggeizing amplitudes.

Meromorphic amplitudes with finite trajectories are excluded by crossing symmetry and unitarity.

A bootstrap method is developed to exclude finite Regge trajectory models in momentum space.

Abstract

Regge poles connect the analytic structure of scattering amplitudes, analytically continued in spin, to the high-energy limit in momentum space. Dual models are expected to have only Regge poles, and string theory suggests there should be an infinite number of them. In this study, we investigate the number of Regge trajectories these models may have. We prove, based solely on crossing symmetry and unitarity, that meromorphic amplitudes, with or without subtractions, cannot produce a reggeizing amplitude if they contain any finite number of Regge trajectories. We argue that this should exclude the existence of such amplitudes altogether. Additionally, we develop and apply a linear programming dual bootstrap method to exclude these amplitudes directly in momentum space.