Study on the strong decays of $\phi(2170)$ and a grand expectation for the future charm-tau factory

The present data imply that $\phi(2170)$ may not be an excited state of $\phi$, but is a four quark state with $ss\bar s \bar s$ constituents. Furthermore, there are no two mesons of $s\bar s$ available to form a molecule which fits the mass spectrum of $\phi(2170)$, thus we suggest it should be an $ss\bar s \bar s$ 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 $\phi(2170)$ into $\phi f_0(980)$, $ h_1\eta$, $ h_1\eta'$, $K_1(1270)K$ and $K_1(1400)K$. Under this hypothesis the modes $\phi(2170)\to K^*(890)^0\bar K^*(890)^0$, $K^+K^-$ and $K^0_LK^0_S$ should be relatively suppressed. Since the width of $h_1$ is rather large, at present it is hard to gain precise data on $BR(\phi(2170)\to h_1\eta)$ and $BR(\phi(2170)\to h_1\eta')$ whose measurements may be crucial for drawing a definite conclusion about the inner assignment of $\phi(2170)$. We lay our expectation to the proposed charm-tau factory which will have much larger luminosity and better capacities.