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

Abstract

A combined analysis of the reactions ${\pi }^{+}p\to {\pi }^{+}p$, ${\pi }^{-}p\to {\pi }^{-}p$ and ${\pi }^{-}p\to {\pi }^{0}n$ 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 ${\pi }^{-}p\to {\pi }^{0}n$ 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 ${\pi }^{+}p\to {\pi }^{+}p$ reaction, while in the ${\pi }^{-}p\to {\pi }^{-}p,{\pi }^{0}n$ reactions, the $s$-channel nucleon and $t$- and $u$-channel backgrounds play crucial roles.

Comments: 15 pages, 11 figures, submitted to PRC. arXiv admin note: text overlap with arXiv:1602.04455