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 ${S}^{\ensuremath{'}}$. In particular, the measured decays $\mathrm{\ensuremath{\Upsilon}}(10860)\ensuremath{\rightarrow}\ensuremath{\pi}{Z}_{b}^{(\ensuremath{'})}\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}\mathrm{\ensuremath{\Upsilon}}(nS)$ ($n=1$, 2, 3) and $\mathrm{\ensuremath{\Upsilon}}(10860)\ensuremath{\rightarrow}\ensuremath{\pi}{Z}_{b}^{(\ensuremath{'})}\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}{h}_{b}(mP)$ ($m=1$, 2) appear to have nearly equal strengths, which is conventionally explained by a simultaneous presence of both ${S}_{b\overline{b}}=0$ and ${S}_{b\overline{b}}=1$ components in the wave functions of the ${Z}_{b}\mathrm{s}$ in equal shares. Meanwhile, the destructive interference between the contributions of the ${Z}_{b}$ and ${Z}_{b}^{\ensuremath{'}}$ to the decay amplitude for a $\ensuremath{\pi}\ensuremath{\pi}{h}_{b}$ 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 ${Z}_{b}^{(\ensuremath{'})}$ 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 $\ensuremath{\pi}\ensuremath{\pi}{h}_{b}$ and $\ensuremath{\pi}\ensuremath{\pi}\mathrm{\ensuremath{\Upsilon}}$ can be obtained and how the mentioned HQSS breaking can be reconciled with the dispersive approach to the $\ensuremath{\pi}\ensuremath{\pi}/K\overline{K}$ interaction in the final state and matched with the low-energy chiral dynamics in both final states.