In this work, we investigate the possibility of interpreting two nucleon resonances, the $N(1875)$ and the $N(2100)$, as hadronic molecular states from the ${\mathrm{\Sigma }}^{*}K$ and $\mathrm{\Sigma }{K}^{*}$ interactions, respectively. With the help of effective Lagrangians in which coupling constants are determined by the SU(3) symmetry, the ${\mathrm{\Sigma }}^{*}K$ and $\mathrm{\Sigma }{K}^{*}$ interactions are described by the vector-meson and pseudoscalar-meson exchanges. With the one-boson-exchange potential obtained, bound states from the ${\mathrm{\Sigma }}^{*}K$ and $\mathrm{\Sigma }{K}^{*}$ interactions are searched for in a quasipotential Bethe-Saltpeter equation approach. A bound state with quantum number $I(J^P)=1/2(3/2^{-})$ is produced from the ${\mathrm{\Sigma }}^{*}K$ interaction, which can be identified as the $N(1875)$ listed in PDG. It can be seen as a strange partner of the LHCb pentaquark $P_c(4380)$ with the same quantum numbers in the molecular state picture. The $\mathrm{\Sigma }{K}^{*}$ interaction also produces a bound state with quantum number $I(J^P)=1/2(3/2^{-})$, which is related to experimentally observed $N(2100)$ in the $\varphi$ photoproduction. Our results suggest that the $N(2120)$ observed in the $K\mathrm{\Lambda }(1520)$ photoproduction and the $N(2100)$ observed in the $\varphi$ photoproduction have different origins. The former is a conventional three-quark state while the latter is a $\mathrm{\Sigma }{K}^{*}$ molecular state, which can be seen as a strange partner of the $P_c(4450)$ with different spin parity.

• Received 17 January 2017

DOI:https://doi.org/10.1103/PhysRevD.95.074031