General amplitude of near-threshold hadron scattering for exotic hadrons

TL;DR

This paper introduces a new parametrization of near-threshold hadron scattering amplitudes that generalizes the Flatté model, accounts for background contributions, and explains possible dip structures in cross sections.

Contribution

It proposes a novel amplitude parametrization based on effective field theory that smoothly connects to the Flatté amplitude and includes background effects.

Findings

The new amplitude model reproduces the Flatté amplitude in the appropriate limit.

Background contributions can cause dip structures in cross sections.

Interference effects significantly influence near-threshold scattering features.

Abstract

We discuss the general behavior of the scattering amplitude with channel couplings near the two-body threshold. It is known that the Flatt\'{e} amplitude, which is often used in the analysis of experimental data involving exotic hadrons, has some constraint in the near-threshold energy region. While the M-matrix gives the general expression of the scattering amplitude, it is not smoothly connected to the Flatt\'{e} amplitude, due to the property of the determinant of the amplitude in channel space. In this paper, based on the effective field theory, we propose new parametrization of the scattering amplitude which gives the general expression near the threshold and has a well-defined limit reproducing the Flatt\'{e} amplitude. We show that the nonresonant background contribution exists in the general amplitude even in the first order in the momentum. Finally, we quantitatively evaluate the cross sections by changing the strength of the background contribution. We find that the interference with the background term may induce a dip structure of the cross section near the threshold, in addition to the peak and threshold cusp structures.