Study of $\chi_{c0}(1P) --> J/\psi \gamma $ and $\chi_{b0}(1P) --> \Upsilon(1S) \gamma $ decays via QCD sum rules

TL;DR

This paper calculates the form factors and decay properties of certain quarkonium states using QCD sum rules, providing theoretical predictions consistent with experimental data.

Contribution

First theoretical calculation of form factors for these decays using QCD sum rules, including branching ratios and total decay width estimates.

Findings

Branching ratio for $ ext{chi}_{c0}(1P) o J/ ext{psi} \gamma$ matches experimental data.

Estimated total decay width of $ ext{chi}_{b0}(1P)$ is 5.5 MeV, within experimental bounds.

Form factors calculated for the first time in this context.

Abstract

In this study we present the first theoretical calculation of the form factor of the $\chi_{c0}(1P) \rar J/\psi \gamma $ and $\chi_{b0}(1P) \rightarrow \Upsilon(1S) \gamma $ decays in the frame work of QCD sum rules. We also find branching ratio ${\cal B}_r(\chi_{c0}(1P) \rightarrow J/\psi \gamma)=(1.07\times \pm 0.14) \times 10^{(-2)} $ which is in agreement with the experimental data. Furthermore, we estimate the $\Gamma_{tot}(\chi_{b0}(1P)) =5.5\pm 0.5 $ MeV, where experimental bound for full width of $\chi_{b0}$ is $\Gamma_{tot}(\chi_{b0}(1P)) <6 $ MeV.