Radiative decays of Upsilon(nS) into S-wave and P-wave charmonium

TL;DR

This paper calculates the branching fractions of radiative bottomonium decays into S-wave and P-wave charmonium states using nonrelativistic QCD, including color-octet and relativistic effects, and compares predictions with recent experimental data.

Contribution

It provides analytical expressions for decay widths, incorporates color-octet and relativistic corrections, and systematically studies bottomonium radiative decays into charmonium states.

Findings

Predicted decay width for (1S) d7 (1S)+b3 is smaller than Belle measurement.

Analytical formulas for decay widths including color-octet contributions.

Relativistic corrections for (nS) d7 (nS)+b3 are obtained.

Abstract

Motivated by very recent measurement of the radiative decays of $\Upsilon(1S)$ to $\chi_{c1}$ at Belle, we use the nonrelativistic QCD factorization theory and calculate the branching fractions of the radiative decays of bottomonium into S-wave and P-wave charmonium, i.e. $\Upsilon(nS) \to \eta_c(nS)+\gamma$ and $\Upsilon(nS)\to \chi_{cJ}+\gamma$. We systematically studied the branching fractions of the radiative decays of bottomonium into charmonium. Compared to the previous calculation, we obtained the analytical expression for the decay widths and considered the color-octet contributions. For $\Upsilon(nS) \to \eta_c(nS)+\gamma$, the relativistic corrections are also obtained. Through the calculation, the theoretical prediction for $\Upsilon(1S)\to\chi_{c1}+\gamma$ is still smaller than the recent Belle measurement. Further theoretical work and experimental analysis are necessary to understand the $\chi_{c1}$ production mechanism in upsilon decays.