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

TL;DR

This paper investigates the nature of the $ ext{phi}(2170)$ resonance, proposing it as an $ssar s ar s$ tetraquark, and predicts its decay modes, emphasizing the importance of future experiments at a charm-tau factory.

Contribution

It introduces the tetraquark interpretation of $ ext{phi}(2170)$ and estimates its decay rates, guiding future experimental searches.

Findings

Main decay modes are $ ext{phi}(2170)$ into $ ext{phi}f_0(980)$, $h_1 ext{eta}$, $h_1 ext{eta'}$, $K_1(1270)K$, and $K_1(1400)K$.

Suppressed modes include $K^*(890)^0ar K^*(890)^0$, $K^+K^-$, and $K^0_LK^0_S$.

Precise measurements of certain decay modes are crucial for confirming the tetraquark nature.

Abstract

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.