Enhanced breaking of heavy quark spin symmetry

TL;DR

This paper demonstrates that small S- and D-wave mixing in heavy quarkonium wave functions can cause significant deviations from expected heavy quark spin symmetry ratios, explaining recent experimental anomalies in bottomonium decays.

Contribution

It introduces the idea that wave function mixing can significantly break heavy quark spin symmetry predictions, supported by analysis of $$psilon(10860) decay data.

Findings

Large breaking of spin symmetry ratios observed in $$psilon(10860) decays.

S- and D-wave mixing can account for experimental deviations.

Predicted ratio of decay widths assuming D-wave dominance.

Abstract

Heavy quark spin symmetry is useful to make predictions on ratios of decay or production rates of systems involving heavy quarks. The breaking of spin symmetry is generally of the order of $O({\Lambda_{\rm QCD}/m_Q})$, with $\Lambda_{\rm QCD}$ the scale of QCD and $m_Q$ the heavy quark mass. In this paper, we will show that a small $S$- and $D$-wave mixing in the wave function of the heavy quarkonium could induce a large breaking in the ratios of partial decay widths. As an example, we consider the decays of the $\Upsilon(10860)$ into the $\chi_{bJ}\omega\, (J=0,1,2)$, which were recently measured by the Belle Collaboration. These decays exhibit a huge breaking of the spin symmetry relation were the $\Upsilon(10860)$ a pure $5S$ bottomonium state. We propose that this could be a consequence of a mixing of the $S$-wave and $D$-wave components in the $\Upsilon(10860)$. Prediction on the ratio $\Gamma(\Upsilon(10860)\to\chi_{b0}\omega)/\Gamma(\Upsilon(10860)\to\chi_{b2}\omega)$ is presented assuming that the decay of the $D$-wave component is dominated by the coupled-channel effects.