$4\pi$ Decay Modes of the $f_0(1500)$ Resonance

Abstract

We investigate the two-body decay modes $\rho \rho ,\pi {\pi }^{\ast }(1300)$ and $\sigma \sigma$ of the $f_0(1500)$, all leading to the $4\pi$ decay channel, in a three-state mixing scheme, where the $f_0(1500)$ is a mixture of the lowest-lying scalar glueball with the nearby isoscalar states of the $0^{++}Q\bar{Q}$ nonet. In the leading order of this scheme, the decay mechanism of the $f_0(1500)$ proceeds dominantly via its quarkonia components, which can be described in the framework of the ${}^3{P}_0$ $Q\bar{Q}$ pair creation model. We predict the hierarchy of decay branching ratios B with $B(\rho \rho {)}_{\sim }^{>}B(\pi \pi {)}_{\sim }^{>}B(\sigma \sigma )>B(\pi {\pi }^{\ast })$, providing a key signature for the proposed mixing scheme in this leading order approach.

Comments: 11 pages, 1 figure