Analytic Model of a Regge Trajectory in the Space-like and Time-like Regions

TL;DR

This paper presents an analytic model of a Regge trajectory that aligns with unitarity, asymptotic behavior, and experimental data, showing significant deviation from linearity in both space-like and time-like regions.

Contribution

The paper introduces a new analytic model of a Regge trajectory consistent with theoretical constraints and experimental observations, improving understanding of hadronic spectra.

Findings

Trajectory deviates from linearity in both regions

Model fits experimental data well

Matches between space-like and time-like regions are consistent

Abstract

A model for a Regge trajectory compatible with the threshold behavior required by unitarity and asymptotics in agreement with Mandelstam analyticity is analyzed and confronted with the experimental data on the spectrum of the $\rho$ trajectory as well as those on the $\pi^- p\to \pi^0 n$ charge-exchange reaction. The fitted trajectory deviates considerably from a linear one both in the space-like and time-like regions, matching nicely between the two.