Predictions of $Υ(4S) \to h_b(1P,2P) π^+π^-$ transitions

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 $Υ(4S) \to h_b(1P,2P) π^+π^-$. 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$_{Υ(4S) \to h_b(1P)π^+π^-}\simeq\big(1.2^{+0.8}_{-0.4}\times10^{-6}\big)$ or $\big( 0.5^{+0.5}_{-0.2}\times10^{-6}\big)$, and BR$_{Υ(4S) \to h_b(2P)π^+π^-}\simeq \big(7.1^{+1.7}_{-1.1}\times10^{-10}\big)$ or $\big( 2.4^{+0.2}_{-0.1}\times10^{-10}\big)$. The bottom meson loops contribution is found to be much larger than the $Z_b$-exchange contribution in the $Υ(4S) \to h_b(1P) ππ$ transitions, while it can not produce decay rates comparable to the heavy quark spin conserved $Υ(4S) \to Υ(1S,2S) ππ$ processes. We also predict the branch fractions of $ψ(3S,4S) \to h_c(1P)π^+π^-$ contributed from the charm meson loops.

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