A case in favor of the $N^*(1700)(3/2^-)$

TL;DR

This paper uses a coupled channel approach with hidden gauge Lagrangians to dynamically generate and analyze the $N^*(1700)(3/2^-)$ resonance, explaining its elusive experimental signature and confirming its theoretical existence.

Contribution

It demonstrates the dynamical generation of the $N^*(1700)(3/2^-)$ resonance using a unitarized coupled channel model based on hidden gauge interactions, providing a theoretical basis for its existence.

Findings

The $N^*(1700)(3/2^-)$ appears as a pole in the complex plane.

The resonance's signal is weak in $ ho N$ and $ ext{d-wave} ext{ } ext{π}N$ channels.

The approach explains the resonance's elusive experimental detection.

Abstract

Using an interaction extracted from the local hidden gauge Lagrangians, which brings together vector and pseudoscalar mesons, and the coupled channels $\rho N$ (s-wave), $\pi N$ (d-wave), $\pi \Delta$ (s-wave) and $\pi \Delta$ (d-wave), we look in the region of $\sqrt s =1400-1850$ MeV and we find two resonances dynamically generated by the interaction of these channels, which are naturally associated to the $N^*(1520) (3/2^-)$ and $N^*(1700) (3/2^-)$. The $N^*(1700) (3/2^-)$ appears neatly as a pole in the complex plane. The free parameters of the theory are chosen to fit the $\pi N$ (d-wave) data. Both the real and imaginary parts of the $\pi N$ amplitude vanish in our approach in the vicinity of this resonance, similarly to what happens in experimental determinations, what makes this signal very weak in this channel. This feature could explain why this resonance does not show up in some experimental analyses, but the situation is analogous to that of the $f_0(980)$ resonance, the second scalar meson after the $\sigma (f_0(500))$ in the $\pi \pi$(d-wave) amplitude. The unitary coupled channel approach followed here, in connection with the experimental data, leads automatically to a pole in the 1700 MeV region and makes this second $3/2^-$ resonance unavoidable.