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.

5 pages, 3 figures and 1 table

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• Observation of a resonant structure in $e^{+}{e}^{-}\to \omega \eta$ and another in $e^{+}{e}^{-}\to \omega {\pi }^0$ at center-of-mass energies between 2.00 and 3.08 GeV
• Observation of a structure in $e^{+}{e}^{-}\to \varphi {\eta }^{\prime }$ at $\sqrt{s}$ from 2.05 to 3.08 GeV
• Fully-strange tetraquark $ss\bar{s}\bar{s}$ spectrum and possible experimental evidence
• Mass spectrum and strong decays of strangeonium in a constituent quark model
• The $ss\bar{s}\bar{s}$ tetraquark states and the newly observed structure $X(2239)$ by BESIII Collaboration
• Is the $Y(2175)$ a Strangeonium Hybrid Meson?
• Study of the process $e^{+}{e}^{-}\to \varphi \eta$ at center-of-mass energies between 2.00 and 3.08 GeV
• Electromagnetic form factors of $\Lambda$ hyperon in the vector meson dominance model and a possible explanation of the near-threshold enhancement of the $e^{+}{e}^{-}\to \Lambda \bar{\Lambda }$ reaction
• The $\varphi (2170)$ production in the process $\gamma p\to \eta \varphi p$
• Cross section measurement of $e^{+}{e}^{-}\to K_S^0{K}_L^0$ at $\sqrt{s}=2.00-3.08\mathrm{GeV}$
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• The fully-light vector tetraquark states with explicit P-wave via the QCD sum rules
• The ground states and the first radially excited states of D-wave vector $\rho$ and $\varphi$ mesons
• Light tetraquark states with exotic quantum numbers $J^{PC}=2^{+-}$
• $\varphi (2170)$ decaying to $\varphi \pi \pi$ and $\varphi K\bar{K}$