Enhanced breaking of heavy quark spin symmetry

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(ΛQCD/mQ)O(ΛQCD/mQ), with ΛQCDΛQCD the scale of QCD and mQmQ 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 View the MathML sourceϒ(10860) into the χbJωχbJω(J=0,1,2)(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 View the MathML sourceϒ(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 View the MathML sourceϒ(10860). Prediction on the ratio View the MathML sourceΓ(ϒ(10860)→χb0ω)/Γ(ϒ(10860)→χb2ω) is presented assuming that the decay of the D-wave component is dominated by the coupled-channel effects.A heavy quarkonium is a system consisting of a heavy quark and a heavy antiquark. The ground states and low-lying excited states below the open-flavor thresholds were well described in terms of potential quark models, e.g., the Godfrey–Isgur quark model [1], while the higher excited states are more complicated. The complexity comes from, e.g., the nearby strongly coupled thresholds, the existence of many new quarkonium-like states discovered in the last decade and so on. Because the heavy quark mass mQmQ is much larger than the scale of quantum chromodynamics (QCD), ΛQCDΛQCD, the amplitude of changing the spin orientation of a heavy quark by interacting with soft gluons is small, suppressed by O(ΛQCD/mQ)O(ΛQCD/mQ) relative to the spin-conserving case [2]. The resulting heavy quark spin symmetry (HQSS) [3] can lead to important observable consequences. On the one hand, heavy quarkonium states are organized into spin multiplets; on the other hand, the decay or production rate involving one heavy quarkonium can often be related to the one of its spin partners in the leading approximation. Breaking of HQSS is typically of the order of O(ΛQCD/mQ)O(ΛQCD/mQ) or even higher. In this paper, we will argue that the HQSS breaking could be much larger in certain processes. To be specific, we will show that a small mixing of S- and D-wave heavy quarkonia could result in a significant breaking of the spin symmetry relations when the decay amplitude of the D -wave component is enhanced. As an example, we will calculate the processes View the MathML sourceϒ(10860)→χbJω(J=0,1,2). Measurements for these transitions were done by the Belle Collaboration very recently, and the results for the branching fractions are [4