Internal structures of the nucleon resonances $N\left(1875\right)$ and $N\left(2120\right)$

A nucleon resonance with spin-parity $J^P=3/2^{-}$ and mass about 2.1 GeV is essential to reproducing the photoproduction cross sections for $\Lambda \left(1520\right)$ released by the LEPS and CLAS collaborations. It can be explained as the third nucleon resonance state ${[3/2^{-}]}_3$ in the constituent quark model so that there is no position to settle the $N\left(1875\right)$ which is listed by the Particle Data Group as the third $N3/2^{-}$ nucleon resonance. An interpretation is proposed that the $N\left(1875\right)$ is from the interaction of a decuplet baryon $\Sigma \left(1385\right)$ and an octet meson $K$, which is favored by the calculation of binding energy and decay pattern in a Bethe-Salpeter approach.

Figure 1

Change of ${\chi }^2$ in the mass scan. The solid and dashed lines are for the results with assuming the $N\left(2120\right)$ as state ${[N3/2^{-}]}_3$ and as state ${[N3/2^{-}]}_4$, respectively.

Figure 2

Decays of the ${\Sigma }^{*}K$ bound state. (a) $N\sigma$ channel with $K$ exchange. (b) $N\rho$ channel with $K$ exchange. (c) $N\omega$ channel with $K$ exchange. (d) $K\Lambda /\Sigma$ channel with $\rho$ exchange. (e) and (f) are for the $N\pi$ decay channel with $K^{*}$ exchange and with $\Lambda /\Sigma$ exchange, respectively.