Study of \pi^{-}p \to \eta n at low energies in a chiral constituent quark model

TL;DR

This study extends a chiral quark model to analyze low-energy  scattering, successfully describing cross sections near the  production threshold and clarifying the roles of various nucleon resonances.

Contribution

It introduces an extended chiral quark model to accurately describe  scattering at low energies, emphasizing resonance contributions and interference effects.

Findings

    near threshold is well described.

The (1535) resonance dominates near threshold, with destructive interference from (1650).

The (1520) and (1710) resonances are crucial for accurate cross section shapes.

Abstract

A chiral quark model approach is extended to the study of the $\pi N$ scattering at low energies. The process of $\pi^{-}p \to \eta n$ near threshold is investigated. The model is successful in describing the differential cross sections and total cross section near the $\eta$ production threshold. The roles of the resonances in $n\leq 2$ shells are clarified. Near threshold, the $S_{11}(1535)$ dominates the reactions, while the interferences from the $S_{11}(1650)$ turn out to be destructive around $W\lesssim 1.6$ GeV. The $D_{13}(1520)$ is crucial to give correct shapes of the differential cross sections. The nucleon pole term contributions are significant. The $P_{11}(1710)$ plays an important role around the c.m. energy $W=1.7$ GeV, it is crucial to produce an enhancement in the region of $W>1.6$ GeV as suggested by the data for total cross section. The $t$-channel is negligible in the reactions.