How Large is the Contribution of Excited Mesons in Coupled-Channel Effects?

Abstract

We study the excited $B$ mesons' contributions to the coupled-channel effects under the framework of ${}^3{P}_0$ model for the bottomonium. Contrary to what has been widely accepted, the contributions of $P$ wave $B$ mesons are generally the largest and this result is independent of the potential parameters to some extent. We also push the calculation beyond $B(1P)$ and carefully analyze the contributions of $B(2S)$. A form factor is a key ingredient to suppress the contributions of $B(2S)$ for low lying bottomonia. However, this suppression mechanism is not efficient for highly excited bottomonia such as ${\rm Y}(5S)$ and ${\rm Y}(6S)$. We give explanations why this difficulty happens to ${}^3{P}_0$ model and suggest analyzing flux-tube breaking model for the full calculation of coupled-channel effects.

15 pages, 6 figures

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