Role of vector and pseudoscalar mesons in understanding $1/2^-$ $N^*$ and $\Delta$ resonances

TL;DR

This paper investigates the role of vector and pseudoscalar mesons in understanding low-lying $1/2^-$ $N^*$ and $\Delta$ resonances through a coupled channels approach based on chiral Lagrangians and hidden local symmetry.

Contribution

It introduces a combined formalism for pseudoscalar and vector mesons in meson-baryon interactions to dynamically generate and analyze $N^*$ and $\Delta$ resonances.

Findings

Resonances related to $N^*(1535)$, $N^*(1650)$, $N^*(1895)$, and $\Delta(1620)$ were identified.

Vector mesons significantly influence the dynamical origin of these resonances.

Some resonances can be interpreted as dynamically generated states.

Abstract

A study of nonstrange meson-baryon systems has been made with the idea of understanding the properties of the low-lying $1/2^-$ $N^*$ and $\Delta$ resonances. The coupled channels are built by considering the pseudoscalar and vector mesons together with the octet baryons. The formalism is based on obtaining the interactions from the lowest order chiral Lagrangian when dealing with pseudoscalar mesons and relying on the hidden local symmetry in case of the vector mesons. The transition between the two systems is obtained by replacing the photon by a vector meson in the Kroll-Ruderman theorem for the photoproduction of pseudoscalar mesons. The subtraction constants, required to calculate the loop-function in the scattering equations, are constrained by fitting the available experimental data on some of the reactions with pseudoscalar meson-baryon final states. As a consequence, we find resonances which can be related to $N^*(1535)$, $N^*(1650)$ (with a double pole structure), $N^*(1895)$ and $\Delta(1620)$. We conclude that these resonances can be, at least partly, interpreted as dynamically generated resonances and that the vector mesons play an important role in determining the dynamical origin of the low-lying $N^*$ and $\Delta$ states.