Mixing of pseudoscalar-baryon and vector-baryon in the $J^P=1/2^{-}$ sector and the $N^{*}$ (1535) and $N^{*}$ (1650) resonances

We study the meson-baryon interaction with $J^P=1/2^{-}$ using the hidden-gauge Lagrangians and mixing pseudoscalar meson-baryon with the vector meson-baryon states in a coupled channels scheme with $\pi N,\eta N,K\Lambda ,K\Sigma ,\rho N$, and $\pi \Delta (d$ wave). We fit the subtraction constants of each channel to the $S_{11}$ partial wave amplitude of the $\pi N$ scattering data extracted from the partial wave analysis of the George Washington group. We find two poles that we associate to the $N^{*}\left(1535\right)$ and the $N^{*}\left(1650\right)$ resonances, with negative subtraction constants of natural size, and compare the results with empirical determinations of these pole positions. We calculate the branching ratios for the different channels of each resonance and we find a good agreement with the experimental data. The cross section for the ${\pi }^{-}p\to \eta n$ scattering is also evaluated and compared with experiment.

Figure 1

Vector meson-baryon interaction: (a) with vector meson exchange and (b) contact term.

Figure 2

Diagrams of the channels involved in the calculation for $N^{*}\left(1520\right)$ and $N^{*}\left(1700\right)$.

Figure 3

Diagrams of $s\text{−}$ and $u\text{−}$ channel exchanges with the nucleon propagator.

Figure 4

Fit to the $S_{11} \pi N$ partial wave amplitude extracted from Ref. [1]. We show the real part (circles) and imaginary part (crosses) of the data and the result of our fit of ${\tilde{T}}_{\pi N}$ for the real (solid) and imaginary (dashed) parts.

Figure 5

Results of the ${\left|T\right|}^2$ matrix for the diagonal channels.

Figure 6

Comparison of the cross section of ${\pi }^{-}p\to \eta n$ scattering (solid) and the result for the cross section of Ref. [6] (dashed).