Coupled-Channel Effects for the Bottomonium with Realistic Wave Functions

TL;DR

This paper uses realistic wave functions via the Gaussian expansion method to analyze coupled-channel effects in bottomonium, revealing significant impacts on decay widths and mixing angles, and emphasizes the importance of accurate wave functions.

Contribution

It introduces the use of GEM for realistic wave functions in bottomonium coupled-channel calculations, improving accuracy over SHO approximations.

Findings

Both $S-D$ mixing and $B$ meson continuum affect decay width suppression.

GEM provides more accurate results than SHO approximation.

Results suggest the need for precise measurements of radiative decays.

Abstract

With Gaussian expansion method (GEM), realistic wave functions are used to calculate coupled-channel effects for the bottomonium under the framework of ${}^3P_0$ model. The simplicity and accuracy of GEM are explained. We calculate the mass shifts, probabilities of the $B$ meson continuum, $S-D$ mixing angles, strong and dielectric decay widths. Our calculation shows that both $S-D$ mixing and the $B$ meson continuum can contribute to the suppression of the vector meson's dielectric decay width. We suggest more precise measurements on the radiative decays of $\Upsilon(10580)$ and $\Upsilon(11020)$ to distinguish these two effects. The above quantities are also calculated with simple harmonic oscillator (SHO) wave function approximation for comparison. The deviation between GEM and SHO indicates that it is essential to treat the wave functions accurately for near threshold states.