Nucleon resonances $N(1875)$ and $N(2100)$ as strange partners of LHCb pentaquarks

Abstract

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 $\Sigma^*K$ and $\Sigma K^*$ interactions, respectively. With the help of effective Lagrangians in which coupling constants are determined by the SU(3) symmetry, the $\Sigma^*K$ and $\Sigma K^*$ interactions are described by the vector-meson and pseudoscalar-meson exchanges. With the one-boson-exchange potential obtained, bound states from the $\Sigma^*K$ and $\Sigma K^*$ 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 $\Sigma^*K$ 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 $\Sigma K^*$ 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 $\phi$ photoproduction. Our results suggest that the $N(2120)$ observed in the $K\Lambda(1520)$ photoproduction and the $N(2100)$ observed in the $\phi$ photoproduction have different origins. The former is a conventional three-quark state while the latter is a $\Sigma K^*$ molecular state, which can be seen as a strange partner of the $P_c(4450)$ with different spin parity.