On the positivity of Coon amplitude in D=4

TL;DR

This paper demonstrates that the Coon amplitude in four dimensions maintains positivity of partial wave coefficients, supporting its unitarity, by explicit computation of leading Regge trajectory coefficients.

Contribution

It provides the first explicit verification of partial wave coefficient positivity for the Coon amplitude in D=4, suggesting its unitarity without a formal proof.

Findings

Partial wave coefficients on the leading Regge trajectory are positive.

Coefficients decrease in magnitude with increasing spin.

Full amplitude likely maintains positivity, indicating unitarity.

Abstract

The Coon amplitude is the unique solution to duality constraints with logarithmic Regge trajectories. A striking feature of this solution is that it interpolates between the Veneziano amplitude and a scalar particle amplitude. However, an analytic proof of unitarity of the amplitude is not yet known. In this short note, we explicitly compute the partial wave coefficients on the leading Regge trajectory in D=4. We find that these coefficients always remain positive, even though their magnitude decreases with spin. Since the coefficients on the subleading trajectories are observed to be larger than those on the leading ones, our result indicates the positivity of the full Coon amplitude in D=4.