# Quark model study of the $\pi N\to \pi N$ reactions up to the $N(1440)$ resonance region

## TL;DR

This study uses a chiral quark model to analyze pion-nucleon reactions up to the N(1440) resonance, revealing enhanced couplings and the significance of specific resonances and background contributions.

## Contribution

It provides a detailed analysis of pion-nucleon reactions with a chiral quark model, highlighting the roles of N(1440) and Delta(1232) resonances and their couplings, which differ from simple quark model expectations.

## Key findings

- N(1440)P_{11}$ plays a confirmed role in polarization observables.
- Couplings of N(1440)Nπ and Δ(1232)Nπ are significantly larger than simple quark model predictions.
- Background contributions vary among different reaction channels, affecting the reaction mechanisms.

## Abstract

A combined analysis of the reactions $\pi^+p\to \pi^+p$, $\pi^-p\to \pi^-p$ and $\pi^-p\to \pi^0n$ is carried out with a chiral quark model. The observations are reasonably described from the $\Delta(1232)$ resonance region up to the $N(1440)$ resonance region. Besides the $\Delta(1232)P_{33}$, a confirmed role of $N(1440)P_{11}$ is found in the polarizations of the $\pi^-p\to \pi^-p$ and $\pi^-p\to\pi^0n$ reactions. It is found that the $N(1440)N\pi$ and $\Delta(1232)N\pi$ couplings are about $1.7$ and $4.8$ times larger than the expectations from the simple quark model, respectively, which may suggest the unusual property of $N(1440)P_{11}$ and deficiency of the simple quark model in the description of $N(1440)P_{11}$ and $\Delta(1232)P_{33}$. The $t$- and $u$-channel backgrounds have notable contributions to the $\pi^+ p\rightarrow\pi^+ p$ reaction, while in the $\pi^-p\rightarrow \pi^- p,\pi^0 n$ reactions, the $s$-channel nucleon and $t$- and $u$-channel backgrounds play crucial roles.