Enhanced breaking of heavy quark spin symmetry

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 $O({\Lambda }_{\mathrm{QCD}}/m_Q)$, with ${\Lambda }_{\mathrm{QCD}}$ 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 ${\rm Y}(10860)$ 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 ${\rm Y}(10860)$ 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 ${\rm Y}(10860)$. Prediction on the ratio $\Gamma ({\rm Y}(10860)\to {\chi }_{b0}\omega )/\Gamma ({\rm Y}(10860)\to {\chi }_{b2}\omega )$ is presented assuming that the decay of the $D$-wave component is dominated by the coupled-channel effects.

arXiv comment13 pages, 5 figures. Discussion extended, version to appear in Phys.Lett.B

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Cited by in corpus (18)

• Hadronic molecules
• Threshold cusps and triangle singularities in hadronic reactions
• How to reveal the exotic nature of the P_c(4450)
• Interplay of quark and meson degrees of freedom in near-threshold states: A practical parametrisation for line shapes
• Novel Method for Precisely Measuring the $X(3872)$ Mass
• A practical parametrization for line shapes of near-threshold states
• Dalitz plot distributions in presence of triangle singularities
• Bottomonium-like states: physics case for energy scan above the $B\bar{B}$ threshold at Belle-II
• How Large is the Contribution of Excited Mesons in Coupled-Channel Effects?
• Triangle singularity in the $B^{-}\to K^{-}{\pi }^{0}X(3872)$ reaction and sensitivity to the $X(3872)$ mass
• Observation of $e^{+}{e}^{-}\to \omega {\chi }_{bJ}(1P)$ and search for $X_b\to \omega {\rm Y}(1S)$ at $\sqrt{s}$ near 10.75 GeV
• Production of the spin partner of the X(3872) in e^+e^- collisions
• The impact of $S$-wave thresholds $D_{s1}{\bar{D}}_s+c.c.$ and $D_{s0}{\bar{D}}_s^{\ast }+c.c.$ on vector charmonium spectrum
• Observation of $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^0{\chi }_{b1,2}(1P)$ and search for $e^{+}{e}^{-}\to \varphi {\chi }_{b1,2}(1P)$ at $\sqrt{s}=$10.96---11.05 GeV
• Decays of ${\rm Y}(10860)$ and ${\rm Y}(10753)$ into $\omega {\chi }_{bJ}$
• Improved measurement of Born cross sections for ${\chi }_{bJ}\omega$ and ${\chi }_{bJ}({\pi }^{+}{\pi }^{-}{\pi }^0{)}_{\mathrm{non}-\omega }$ ($J$ = 0, 1, 2) at Belle and Belle II
• Exotic hadrons associated with $b$-quark
• Holographic Heavy Quark Symmetry