Strong decays of the $X(2500)$ newly observed by the BESIII Collaboration

Basing on the observation of a new $J^{PC}=0^{-+}$ state, $X(2500)$, in the partial wave analysis of the decay $J/\psi \to \gamma X\to \gamma \varphi \varphi$ performed by the BESIII Collaboration, we have evaluated the strong decays of the $X(2500)$ as the $4^1{S}_0$ and $5^1{S}_0$ $s\overline{s}$ states in the ${}^3{P}_0$ model of meson decay. The predicted total decay width for the $4^1{S}_0$ $s\overline{s}$ is about 894.5 MeV, and the one for the $5^1{S}_0$ $s\overline{s}$ is about 271.1 MeV, which is in agreement with the experimental data ${\mathrm{\Gamma }}_{X(2500)}=230_{-35-33}^{+64+56}\mathrm{MeV}$. By considering the mass and the total strong decay width of the $X(2500)$, we propose that the $X(2500)$ state can be interpreted as a candidate of the $5^1{S}_0$ $s\overline{s}$ state.

Figure 1

The Regge trajectories for the $n{{}^{1}S}_0$ meson mass spectrum with $M^2=M_0^2+(n-1){\mu }^2({\mu }^2=1.31,1.32,1.36{\mathrm{GeV}}^2$ for the ${\eta }^{\prime }$, $\eta$, and $\pi$ trajectories, respectively. The masses of $\eta (2100)$, $\eta (2225)$, and $X(2500)$ are from the BESIII results [1], the $X(2370)$ mass is from the BESIII results [11]. All the other states masses are taken from PDG [2].

Figure 2

The two possible diagrams contributing to $A\to BC$ in the ${}^3{P}_0$ model: (a) the quark within the meson $A$ combines with the created antiquark to form the meson $B$, the antiquark within the meson $A$ combines with the created quark to form the meson $C$; (b) the quark within the meson $A$ combines with the created antiquark to form the meson $C$, the antiquark within the meson $A$ combines with the created quark to form the meson $B$.

Figure 3

The dependence of the total widths of the $5^1{S}_0$ and $4^1{S}_0$ $s\overline{s}$ states on the initial state mass in the ${}^3{P}_0$ decay model. The dashed line with a green band denotes the BESIII data.

Figure 4

The dependence of the partial widths of the $5^1{S}_0$ (left panels) and $4^1{S}_0$ (right panels) $s\overline{s}$ states on the initial state mass in the ${}^3{P}_0$ model. The curves labeled “$\mathrm{ch}i$” stand for the results of the $i$ decay channels of Table 1.