Dominant spin-orbit effects in radiative decays {${\rm Y}(3S\to \gamma {\chi }_{bJ}(1P))$}}

Abstract

We show that there are two reasons why the partial width for the transition ${\Gamma }_1({\rm Y}(3S)\to \gamma {\chi }_{b1}(1P))$ is suppressed. Firstly, the spin-averaged matrix element (m.e.) $\overline{I(3S|r|1P_J)}$ is small, being equal to 0.023 GeV${}^{-1}$ in our relativistic calculations. Secondly, the spin-orbit splittings produce relatively large contributions, giving $I(3S|r|1P_2)=0.066$ GeV${}^{-1}$, while due to large cancellation the m.e. $I(3S|r|1P_1)=-0.020$ GeV${}^{-1}$ is small and negative; at the same time the magnitude of $I(3S|r|1P_0)=-0.063$ GeV${}^{-1}$ is relatively large. These m.e. give rise to the partial widths: ${\Gamma }_2({\rm Y}(3S)\to \gamma {\chi }_{b2}(1P))=212$ eV, ${\Gamma }_0({\rm Y}(3S)\to \gamma {\chi }_{b0}(1P))=54$ eV, which are in good agreement with the CLEO and BaBar data, and also to ${\Gamma }_1({\rm Y}(3S)\to \gamma {\chi }_{b1}(1P))=13$ eV, which satisfies the BaBar limit, ${\Gamma }_1(exp.)<22$ eV.

Comments: 8 pages