Chromopolarizability of charm-beauty quarkonium from $B_c(2S) \rightarrow B_c\pi\pi$ transition

TL;DR

This paper determines the chromopolarizability of the charm-beauty quarkonium $B_c(2S)$ using a dispersion theory analysis of the $B_c(2S) ightarrow B_c\, ext{pi}\, ext{pi}$ decay, revealing its interaction strength with soft gluonic fields.

Contribution

The study introduces a model-independent dispersion theory approach to extract the chromopolarizability of $B_c(2S)$, providing new quantitative insights into charm-beauty quarkonium interactions.

Findings

Chromopolarizability of $B_c(2S)$ is $(0.66\, ext{±}\,0.25)$ GeV$^{-3}$.

Parameter $\, ext{kappa}$ is $-0.02\, ext{±}\,0.13$.

Charm-beauty quarkonium interacts with light hadrons at a level between charmonium and bottomonium.

Abstract

The chromopolarizability of a charm-beauty quarkonium characterizes its interaction with soft gluonic fields and can be probed through heavy quarkonium decays. Using the dispersion theory which considers the $\pi\pi$ final state interaction model-independently, we analyze the transition $B_c(2S) \rightarrow B_c\pi^+\pi^-$ and determine the chromopolarizability $\alpha_{B_c(2S) B_c}=(0.66\pm 0.25)$ GeV$^{-3}$ and the parameter $\kappa =-0.02\pm 0.13$. Our results indicate that the transitional chromopolarizability of the $c\bar{b}$ state lies between the transitional chromopolarizabilities of the $c\bar{c}$ and $b\bar{b}$ states. These findings provide valuable insights into the interactions of charm-beauty quarkonium with light hadrons.