Scalar Resonance Contributions to the Dipion Transition Rates of ${\rm Y}(4S,5S)$ in the re-scattering model

Abstract

In order to explain the observed unusually large dipion transition rates of ${\rm Y}(10870)$, the scalar resonance contributions in the re-scattering model to the dipion transitions of ${\rm Y}(4S)$ and ${\rm Y}(5S)$ are studied. Since the imaginary part of the re-scattering amplitude is expected to be dominant, the large ratios of the transition rates of ${\rm Y}(10870)$, which is identified with ${\rm Y}(5S)$, to that of ${\rm Y}(4S)$ can be understood as mainly coming from the difference between the $p$-values in their decays into open bottom channels, and the ratios are estimated numerically to be about 200-600 with reasonable choices of parameters. The absolute and relative rates of ${\rm Y}(5S)\to {\rm Y}(1S,2S,3S){\pi }^{+}{\pi }^{-}$ and ${\rm Y}(5S)\to {\rm Y}(1S)K^{+}{K}^{-}$ are roughly consistent with data. We emphasize that the dipion transitions observed for some of the newly discovered $Y$ states associated with charmonia may have similar features to the dipion transitions of ${\rm Y}(5S)$. Measurements on the dipion transitions of ${\rm Y}(6S)$ could provide further test for this mechanism.

arXiv commentversion to appear in Phys. Rev. D, discussions and references added

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