Predictions of ${\rm Y}(4S)\to h_b(1P,2P){\pi }^{+}{\pi }^{-}$ transitions

Abstract

In this work, we study the contributions of the intermediate bottomoniumlike $Z_b$ states and the bottom meson loops in the heavy quark spin flip transitions ${\rm Y}(4S)\to h_b(1P,2P){\pi }^{+}{\pi }^{-}$. Depending on the constructive or destructive interferences between the $Z_b$-exchange and the bottom meson loops mechanisms, we predict two possible branching ratios for each process: BR${}_{{\rm Y}(4S)\to h_b(1P){\pi }^{+}{\pi }^{-}}\simeq (1.2_{-0.4}^{+0.8}\times 10^{-6})$ or $(0.5_{-0.2}^{+0.5}\times 10^{-6})$, and BR${}_{{\rm Y}(4S)\to h_b(2P){\pi }^{+}{\pi }^{-}}\simeq (7.1_{-1.1}^{+1.7}\times 10^{-10})$ or $(2.4_{-0.1}^{+0.2}\times 10^{-10})$. The bottom meson loops contribution is found to be much larger than the $Z_b$-exchange contribution in the ${\rm Y}(4S)\to h_b(1P)\pi \pi$ transitions, while it can not produce decay rates comparable to the heavy quark spin conserved ${\rm Y}(4S)\to {\rm Y}(1S,2S)\pi \pi$ processes. We also predict the branch fractions of $\psi (3S,4S)\to h_c(1P){\pi }^{+}{\pi }^{-}$ contributed from the charm meson loops.

Comments: 17 pages, 4 figures; the direct gluon hadronization mechanism contribution within QCD multipole expansion discussed, the distributions of the $\pi \pi$ and $h_b\pi$ invariant mass spectra, and the angular distribution presented, the branch fractions of $\psi (3S,4S)\to h_c(1P){\pi }^{+}{\pi }^{-}$ estimated, more discussions added; version to appear in CPC