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.

8 pages

References in corpus (8)

• Heavy quarkonium: progress, puzzles, and opportunities
• Quarkonia and their transitions
• Observation of a new chi_b state in radiative transitions to Upsilon(1S) and Upsilon(2S) at ATLAS
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• On the possibility to observe higher $n^3{D}_1$ bottomonium states in the $e^{+}{e}^{-}$ processes
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• Study of radiative bottomonium transitions using converted photons
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Cited by in corpus (3)

• Spectrum and electromagnetic transitions of bottomonium
• Bottomonium spectroscopy and radiative transitions involving the chi_bJ(1P,2P) states at BABAR
• Predictions for Bottomonium from a Relativistic Screened Potential Model