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We study the energy distributions of dipion transitions $\Upsilon(5S)$ to$\Upsilon(1S,2S,3S)\pi^+\pi^-$ in the final state rescattering model. Since the$\Upsilon(5S)$ is well above the open bottom thresholds, the dipion transitionsare expected to mainly proceed through the real processes $\Upsilon(5S)\toB^{(*)}\bar{B}^{(*)}$ and $B^{(*)}\bar{B}^{(*)}\to\Upsilon(1S,2S,3S)\pi^+\pi^-$. We find that the energy distributions of$\Upsilon(1S,2S,3S)\pi^+\pi^-$ markedly differ from that of $\Upsilon(5S)\toB^{(*)}\bar{B}^{(*)}$. In particular, the resonance peak will be pushed up byabout 7-20 MeV for these dipion transitions relative to the main hadronic decaymodes. These predictions can be used to test the final state rescatteringmechanism in hadronic transitions for heavy quarkonia above the open flavorthresholds.

Peak shifts due to $B^{(*)}-\bar{B}^{(*)}$ rescattering in $\Upsilon(5S)$ dipion transitions

Peak shifts due to $B^{()}-\bar{B}^{()}$ rescattering in $\Upsilon(5S)$ dipion transitions