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

Abstract

A combined analysis of the reactions ${\ensuremath{\pi}}^{+}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}p, {\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}p$, and ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}n$ is carried out with a chiral quark model. The observations are reasonably described from the $\mathrm{\ensuremath{\Delta}}(1232)$ resonance region up to the $N(1440)$ resonance region. Besides the $\mathrm{\ensuremath{\Delta}}(1232){P}_{33}$, a confirmed role of $N(1440){P}_{11}$ is found in the polarizations of the ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}p$ and ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}n$ reactions. It is found that the $N(1440)N\ensuremath{\pi}$ and $\mathrm{\ensuremath{\Delta}}(1232)N\ensuremath{\pi}$ 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 $\mathrm{\ensuremath{\Delta}}(1232){P}_{33}$. The $t$- and $u$-channel backgrounds have notable contributions to the ${\ensuremath{\pi}}^{+}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}p$ reaction, while in the ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}p,\phantom{\rule{0.16em}{0ex}}{\ensuremath{\pi}}^{0}n$ reactions, the $s$-channel nucleon and $t$- and $u$-channel backgrounds play crucial roles.