Partial wave analysis of $K^+N$ scattering and the possibility of pentaquark $\Theta^+(1540)$

TL;DR

This paper performs a partial wave analysis of $K^+N$ scattering to explore the potential existence of the exotic $ heta^+(1540)$ pentaquark resonance, providing phase shifts and examining experimental data for resonance signals.

Contribution

It introduces two phase shift solutions for $K^+N$ scattering and assesses the evidence for the $ heta^+(1540)$ pentaquark resonance using polarization and differential cross section data.

Findings

Two phase shift sets obtained from data fitting.

Polarization data helps validate the phase shift solutions.

Evidence suggests a possible resonance near 1.54 GeV.

Abstract

Elastic $K^+ n\to K^+ n$ and charge exchange $K^+n\to K^0p$ reactions at low momenta are investigated using the partial wave analysis. Isospin relation gives constrains for the partial $s$- and $p$-waves among elastic $K^+p$, $K^+n$ and charge exchange $K^+n\to K^0p$ amplitudes. Two sets of the phase shift for these partial waves in the isoscalar channel are obtained from the fit of experimental data on total and differential cross sections. Polarization observable leads to a good criterion to decide which set is valid. Differential cross section data near $P_{\rm Lab}=434$ MeV/$c$ suggests a possibility of a resonance, e.g., the exotic $\Theta^+(1540)$ baryon around $\sqrt{s}\simeq$ 1.54GeV.