Scalar Resonance Contributions to the Dipion Transition Rates of $Υ(4S,5S)$ in the re-scattering model

Details Scalar Resonance Contributions to the Dipion Transition Rates of $Υ(4S,5S)$ in the re-scattering model Scalar Resonance Contributions to the Dipion Transition Rates of $Υ(4S,5S)$ in the re-scattering model

2007-12-20

arxiv.org/abs/0712.3595v2

Phys.Rev.D77:074003,2008

Physics

High Energy Physics

High Energy Physics - Phenomenology

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

Scientific paper

10.1103/PhysRevD.77.074003

In order to explain the observed unusually large dipion transition rates of $\Upsilon(10870)$, the scalar resonance contributions in the re-scattering model to the dipion transitions of $\Upsilon(4S)$ and $\Upsilon(5S)$ are studied. Since the imaginary part of the re-scattering amplitude is expected to be dominant, the large ratios of the transition rates of $\Upsilon(10870)$, which is identified with $\Upsilon(5S)$, to that of $\Upsilon(4S)$ 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 $\Upsilon(5S)\to\Upsilon(1S,2S,3S)\pi^+\pi^-$ and $\Upsilon(5S)\to\Upsilon(1S)K^+K^-$ 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 $\Upsilon(5S)$. Measurements on the dipion transitions of $\Upsilon(6S)$ could provide further test for this mechanism.

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