On unitarity of the Coon amplitude

TL;DR

This paper investigates the unitarity of the Coon amplitude, a deformation of the Veneziano amplitude, demonstrating positivity in some regimes and unitarity violations in others using $q$-calculus and partial wave analysis.

Contribution

It provides the first detailed analysis of the unitarity properties of the Coon amplitude across different spacetime dimensions and deformation parameters.

Findings

Positivity on leading and sub-leading Regge trajectories in arbitrary dimensions.

Unitarity violation in certain $(q,D)$ regions at sub-sub-leading Regge order.

Numerical and analytic evidence for positivity in fixed spin and Regge asymptotics.

Abstract

The Coon amplitude is a one-parameter deformation of the Veneziano amplitude. We explore the unitarity of the Coon amplitude through its partial wave expansion using tools from $q$-calculus. Our analysis establishes manifest positivity on the leading and sub-leading Regge trajectories in arbitrary spacetime dimensions $D$, while revealing a violation of unitarity in a certain region of $(q,D)$ parameter space starting at the sub-sub-leading Regge order. A combination of numerical studies and analytic arguments allows us to argue for the manifest positivity of the partial wave coefficients in fixed spin and Regge asymptotics.