Roper resonances in chiral quark models

TL;DR

This paper develops a method to calculate meson-baryon scattering in chiral quark models, successfully reproducing low-lying resonance data and highlighting the importance of additional channels like $\sigma N$ for accurate width predictions.

Contribution

It introduces a new approach to compute multi-channel K matrices in chiral quark models, incorporating additional decay channels to improve resonance width predictions.

Findings

Good agreement with experimental scattering data achieved.

Including $\sigma N$ channels improves resonance width calculations.

Separable kernel approximation simplifies the integral equations.

Abstract

We derive a method to calculate the multi-channel K matrix applicable to a broad class of models in which mesons linearly couple to the quark core. The method is used to calculate pion scattering amplitudes in the energy region of low-lying P11 and P33 resonances. A good agreement with experimental data is achieved if in addition to the elastic channel we include the $\pi\Delta$ and $\sigma N$ ($\sigma\Delta$) channels where the $\sigma$-meson models the correlated two-pion decay. We solve the integral equation for the K matrix in the approximation of separable kernels; it yields a sizable increase of the widths of the $\Delta(1232)$ and the N(1440) resonances compared to the bare quark values.