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

Abstract

The present data imply that $\varphi (2170)$ may not be an excited state of $\varphi$, 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 $\varphi (2170)$, 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 $\varphi (2170)$ 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 $\varphi (2170)\to K^{\ast }(890{)}^0{\bar{K}}^{\ast }(890{)}^0$, $K^{+}{K}^{-}$ 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 $BR(\varphi (2170)\to h_1\eta )$ and $BR(\varphi (2170)\to h_1{\eta }^{\prime })$ whose measurements may be crucial for drawing a definite conclusion about the inner assignment of $\varphi (2170)$. We lay our expectation to the proposed charm-tau factory which will have much larger luminosity and better capacities.

Comments: 5 pages, 3 figures and 1 table