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

Abstract

We investigate the possible rescattering effects which may contribute to the process $B^{+}\to J/\psi \varphi K^{+}$. It is shown that the $D_s^{\ast +}{D}_s^{-}$ rescattering via the open-charmed meson loops, and ${\psi }^{\prime }\varphi$ 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 ${\chi }_{c1}(3P)$.

Comments: 14 pages, 5 figures, 1 table