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

Understand

We study the excited $B$ mesons' contributions to the coupled-channel effects under the framework of ${}^3P_0$ 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.