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

Abstract

A combined analysis of the reactions $π^+p\to π^+p$, $π^-p\to π^-p$ and $π^-p\to π^0n$ is carried out with a chiral quark model. The observations are reasonably described from the $Δ(1232)$ resonance region up to the $N(1440)$ resonance region. Besides the $Δ(1232)P_{33}$, a confirmed role of $N(1440)P_{11}$ is found in the polarizations of the $π^-p\to π^-p$ and $π^-p\toπ^0n$ reactions. It is found that the $N(1440)Nπ$ and $Δ(1232)Nπ$ 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 $Δ(1232)P_{33}$. The $t$- and $u$-channel backgrounds have notable contributions to the $π^+ p\rightarrowπ^+ p$ reaction, while in the $π^-p\rightarrow π^- p,π^0 n$ reactions, the $s$-channel nucleon and $t$- and $u$-channel backgrounds play crucial roles.