Role of scalar dibaryon and $f_0(500)$ in the isovector channel of low-energy neutron-proton scattering

TL;DR

This study models low-energy neutron-proton scattering in the isovector channel using an extended Linear Sigma Model, highlighting the importance of the scalar dibaryon and $f_0(500)$ resonance for accurate data description.

Contribution

It introduces the inclusion of the scalar dibaryon and $f_0(500)$ resonance into the Linear Sigma Model to improve agreement with experimental scattering data.

Findings

The $f_0(500)$ resonance is essential for the correct shape of the differential cross section.

The scalar dibaryon explains the large cross section near threshold.

Model results agree well with SAID data analysis.

Abstract

We calculate the total and the differential cross section for $np$ scattering at low energies in the isospin $I=1$ channel within the so-called extended Linear Sigma Model. This model contains conventional (pseudo)scalar and (axial--)vector mesons, as well as the nucleon and its chiral partner within the mirror assignment. In order to obtain good agreement with experimental data analysis results we need to consider two additional resonances: the lightest scalar state $f_{0}(500)$ and a dibaryon state with quantum numbers $I=1,$ $J^{P}=0^{+}$ (also known as $^{1}S_{0}$ resonance). The resonance $f_{0}(500)$ is coupled to nucleons in a chirally invariant way through the mirror assignment and is crucial for a qualitatively correct description of the shape of the differential cross section. On the other hand, the dibaryon is exchanged in the $s$--channel and is responsible of the large cross section close to threshold. We compare our results to data analysis results performed by the SAID program of the CNS Data Analysis Center (in the following "SAID results").