Study of the strong decays of $\varphi (2170)$ and the future charm-tau factory

The present data imply that $\varphi (2170)$ may not be an excited state of $\varphi$ but is a four-quark state with $ss\overline{s}\overline{s}$ constituents. Furthermore, there are no two mesons of $s\overline{s}$ available to form a molecule that fits the mass spectrum of $\varphi (2170)$; thus, we suggest it should be an $ss\overline{s}\overline{s}$ tetraquark state. In this scenario, we estimate its decay rates through the fall-apart mechanism. Our theoretical estimates indicate that its main decay modes should be $\varphi (2170)$ into $\varphi f_0(980)$, $h_1\eta$, $h_1{\eta }^{\prime }$, $K_1(1270)K$, and $K_1(1400)K$. Under this hypothesis, the modes $\varphi (2170)\to K^{*}(890{)}^0{\overline{K}}^{*}(890{)}^0$, $K^{+}{K}^{-}$, and $K_L^0{K}_S^0$ should be relatively suppressed. Since the width of $h_1$ is rather large, at present, it is hard to gain precise data on $\mathrm{BR}(\varphi (2170)\to h_1\eta )$ and $\mathrm{BR}(\varphi (2170)\to h_1{\eta }^{\prime })$, the measurements of which may be crucial for drawing a definite conclusion about the inner assignment of $\varphi (2170)$. We place our expectations on the proposed charm-tau factory, which will have much larger luminosity and better capacities.

Figure 1

The Feynman diagram for $ss\overline{s}\overline{s}\to \varphi f_0(980)$ transitions via the fall-apart mechanism.

Figure 2

The Feynman diagram for $ss\overline{s}\overline{s}\to K_1\overline{K}$ transitions.

Figure 3

The Feynman diagram for $ss\overline{s}\overline{s}\to \varphi f_0(980)$ transition as $f_0(980)$ is regarded as a multiquark state.