Towards a unified description of hadron scattering at all energies

TL;DR

This paper introduces a new parameterization for hadron scattering amplitudes that unifies descriptions across all energies, connecting resonance and asymptotic regimes through Regge trajectories.

Contribution

It presents a novel amplitude parameterization satisfying symmetries and S-matrix constraints, linking resonance and high-energy physics via generalized Regge trajectories.

Findings

Successfully models $ ho$ and $\sigma/f_0(500)$ mesons in $\pi\pi$ scattering

Connects resonance region physics with asymptotic limits

Provides a framework consistent with Regge theory and dispersive approaches

Abstract

The construction of general amplitudes satisfying symmetries and $S$-matrix constraints has been the primary tool in studying the spectrum of hadrons for over half a century. In this work, we present a new parameterization, which can fulfill many expectations of $S$-matrix and Regge theory and connects the essential physics of hadron scattering in the resonance region and in asymptotic limits. In this construction, dynamical information is entirely contained in Regge trajectories that generalize resonance poles in the complex energy plane to moving poles in the angular momentum plane. We highlight the salient features of the model, compare with existing literature on dispersive and dual amplitudes, and benchmark the formalism with an initial numerical application to the $\rho$ and $\sigma/f_0(500)$ mesons in $\pi\pi$ scattering.