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

## TL;DR

This paper explores the interpretation of nucleon resonances N(1875) and N(2100) as molecular states formed from $ ext{Sigma}^*K$ and $ ext{Sigma}K^*$ interactions, linking them to pentaquark states and experimental observations.

## Contribution

It introduces a molecular state model for N(1875) and N(2100), connecting them to pentaquark structures and providing a theoretical basis for their nature.

## Key findings

- N(1875) can be described as a $ ext{Sigma}^*K$ molecular state.
- N(2100) can be described as a $ ext{Sigma}K^*$ molecular state.
- N(2120) is likely a three-quark state, distinct from the molecular N(2100).

## 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.