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

TL;DR

This paper investigates the contributions of excited B mesons to coupled-channel effects in bottomonium, revealing that P-wave B mesons are the dominant contributors and discussing limitations of the ${}^3P_0$ model for highly excited states.

Contribution

It challenges the common assumption by showing P-wave B mesons dominate coupled-channel effects and explores the limitations of the ${}^3P_0$ model for excited bottomonia.

Findings

P-wave B mesons are the largest contributors to coupled-channel effects.

Form factor suppression is ineffective for highly excited bottomonia.

The ${}^3P_0$ model has limitations for states like $S$ and $S$.

Abstract

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. However, this suppression mechanism is not efficient for highly excited bottomonia such as $\Upsilon(5S)$ and $\Upsilon(6S)$. We give explanations why this difficulty happens to ${}^3P_0$ model and suggest analyzing flux-tube breaking model for the full calculation of coupled-channel effects.