Toward a unified description of hadron scattering at all energies

The construction of general amplitudes satisfying symmetries and <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>S</a:mi></a:math>-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 parametrization, which can fulfill many expectations of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>S</c:mi></c:math>-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 <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>ρ</e:mi></e:math> and <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mrow><g:mi>σ</g:mi><g:mo>/</g:mo><g:msub><g:mrow><g:mi>f</g:mi></g:mrow><g:mrow><g:mn>0</g:mn></g:mrow></g:msub><g:mo stretchy="false">(</g:mo><g:mn>500</g:mn><g:mo stretchy="false">)</g:mo></g:mrow></g:math> mesons in <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>π</k:mi><k:mi>π</k:mi></k:math> scattering. Published by the American Physical Society 2024