On the emergence of heavy quark spin symmetry breaking in heavy quarkonium decays

Abstract

Heavy-quark spin symmetry (HQSS) implies that in the direct decay of a heavy quarkonium with spin $S$, only lower lying heavy quarkonia with the same spin $S$ can be produced. However, this selection rule, expected to work very well in the $b$-quark sector, can be overcome if multiquark intermediate states are involved in the decay chain, allowing for transitions to the final-state heavy quarkonia with a different spin $S^{\prime }$. In particular, the measured decays ${\rm Y}(10860)\to \pi Z_b^{(\prime )}\to \pi \pi {\rm Y}(nS)$ $(n=1,2,3)$ and ${\rm Y}(10860)\to \pi Z_b^{(\prime )}\to \pi \pi h_b(mP)$ ($m=1,2$) appear to have nearly equal strengths which is conventionally explained by a simultaneous presence of both $S_{b\bar{b}}=0$ and $S_{b\bar{b}}=1$ components in the wave functions of the $Z_b$'s in equal shares. Meanwhile, the destructive interference between the contributions of the $Z_b$ and $Z_b^{\prime }$ to the decay amplitude for a $\pi \pi h_b$ final state kills the signal to zero in the strict HQSS limit. In this paper, we discuss how the HQSS violation needs to be balanced by the narrowness of the $Z_b^{(\prime )}$ states in the physical case, to allow for equal transition strengths into final states with different total heavy quark spins, and how spin symmetry is restored as a result of a subtle interplay of the scales involved, when the mass of a heavy quark becomes infinite. Moreover, we demonstrate how similar branching fractions of the decays into $\pi \pi h_b$ and $\pi \pi {\rm Y}$ can be obtained and how the mentioned HQSS breaking can be reconciled with the dispersive approach to the $\pi \pi /K\bar{K}$ interaction in the final state and matched with the low-energy chiral dynamics in both final states.

11 pages, 5 figures

References in corpus (11)

• Multiquark Resonances
• Pentaquark and Tetraquark states
• Exotics: Heavy Pentaquarks and Tetraquarks
• Observation of a resonance-like structure in the pi^+- psi' mass distribution in exclusive B-->K pi^+- psi' decays
• The pion-pion scattering amplitude. IV: Improved analysis with once subtracted Roy-like equations up to 1100 MeV
• Observation of the resonant character of the $Z(4430{)}^{-}$ state
• The Z(4430) and a New Paradigm for Spin Interactions in Tetraquarks
• Comprehensive Amplitude Analysis of $\gamma \gamma \to {\pi }^{+}{\pi }^{-},{\pi }^0{\pi }^0$ and $\overline{K}K$ below 1.5 GeV
• Effects of $Z_b$ states and bottom meson loops on ${\rm Y}(4S)\to {\rm Y}(1S,2S){\pi }^{+}{\pi }^{-}$ transitions
• Spin partners $W_{bJ}$ from the line shapes of the $Z_b(10610)$ and $Z_b(10650)$
• Insights into $Z_b(10610)$ and $Z_b(10650)$ from dipion transitions from ${\rm Y}(10860)$

Cited by in corpus (4)

• Heavy-Quark spin symmetry breaking in the Born-Oppenheimer approximation
• Global coupled-channel analysis of $e^{+}{e}^{-}\to c\bar{c}$ processes in $\sqrt{s}=3.75-4.7$ GeV
• Two-pion exchange for coupled-channel scattering of two heavy mesons
• Exotic hadrons associated with $b$-quark