How to understand the underlying structures of $X(4140)$, $X(4274)$, $X(4500)$ and $X(4700)$

TL;DR

This paper explores whether certain exotic structures observed in particle physics are genuine resonances or artifacts of rescattering effects, providing insights into their underlying nature and possible classifications.

Contribution

It distinguishes between rescattering effects and genuine resonances for specific $X$ states, proposing that some are true particles while others may be effects.

Findings

Rescattering effects can mimic $X(4140)$ and $X(4700)$ structures.

$X(4274)$ and $X(4500)$ are likely genuine resonances.

$X(4274)$ may be an orbitally excited $ ext{chi}_{c1}(3P)$ state.

Abstract

We investigate the possible rescattering effects which may contribute to the process $B^+\to J/\psi\phi K^+$. It is shown that the $D_{s}^{*+}D_{s}^-$ rescattering via the open-charmed meson loops, and $\psi^\prime \phi$ rescattering via the $\psi^\prime K_1$ loops may simulate the structures of $X(4140)$ and $X(4700)$, respectively. However, if the quantum numbers of $X(4274)$ ($X(4500)$) are $1^{++}$ ($0^{++}$), it is hard to to ascribe the observation of $X(4274)$ and $X(4500)$ to the $P$-wave threshold rescattering effects, which implies that $X(4274)$ and $X(4500)$ could be genuine resonances. We also suggest that $X(4274)$ may be the conventional orbitally excited state $\chi_{c1}(3P)$.