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

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 the 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 interpreted, at least partly, 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.

Figure 1

Spin half $\pi N$ amplitudes for the isospin $1/2$ (left panel) and $3/2$ (right panel) configurations. The dotted (dash-dotted) lines represent experimental data from Ref. 35 on the real (imaginary) part of the $\pi N$ amplitudes. The corresponding amplitudes obtained in our work [renormalized through Eq. (11)], using the subtraction constants given in Table , are shown as the solid and dashed lines.

Figure 2

Total cross sections for the ${\pi }^{-}p\to \eta n$ (left panel) and ${\pi }^{-}p\to K^0\Lambda$ (right panel) reactions as a function of the beam momentum (${\mathrm{P}}_{\mathrm{Lab}}$). The experimental data have been taken from Refs. 46, 47, 48, 49, 50.

Figure 3

Double pole structure related to $N^{*}(1650)$.

Figure 4

Total cross section on the pion induced omega (left panel) and phi (right panel) production on a nucleon. The left panel shows the cross section as a function of the center of mass momentum in the final state, while on the right side we show the cross section as a function of the beam momentum. This is done to show our results in comparison with the experimental data as available from Refs. 51, 52.