Threshold Cusp Structures in the Presence of Isospin Symmetry Breaking

Abstract

We study the behavior of the cusp structures focusing on the isospin-breaking effects. The properties of the near-threshold exotic hadrons are encoded in the shapes of the cusp structures. In hadron scattering, it is often the case that the thresholds of isospin partner channels are located within a narrow energy region. To analyze the scattering in such systems, it is therefore essential to study the cusp structures that emerge at two closely separated thresholds with isospin symmetry breaking. In this study, we propose a practical representation of the scattering amplitude and show that the two neighboring cusp structures are related through the isospin symmetry.

Figures (2)

• Figure 1: The normalized $\Lambda p$ elastic cross section $\sigma_{\rm el}(E)$ in Eq. \ref{['eq: csec norm']} with the scattering length $a_{\Sigma N}=-1.0-i0.8\ {\rm fm}$. The solid line corresponds to the isospin-broken cross section and the dotted line represents the isospin-symmetric one. The dotted vertical lines represent the thresholds of channel $\Sigma^+ n$, $\Sigma N$ and $\Sigma^0 p$.
• Figure 2: Same as Fig. \ref{['fig: Flatte']} but the scattering lengths are fixed as Eq. \ref{['eq: cp a3 H']} with $C_1=2.0\ {\rm fm}$.