Dipion invariant mass distribution of the anomalous Υ(1S)π+ π- and Υ(2S)π+ π- production near the peak of Υ(10860)

Considering the defects of the previous work for estimating the anomalous production rates of e(+)e(-) -> Upsilon(1S)pi(+)pi(-), Upsilon(2S)pi(+)pi(-) near the peak of the Upsilon(5S) resonance at root s = 10.87 GeV [K. F. Chen et al. (Belle Collaboration), Phys. Rev. Lett. 100, 112001 (2008)], we suggest a new scenario where the contributions from the direct dipion transition and the final-state interactions interfere to result in not only the anomalously large production rates, but also line shapes of the differential widths consistent with experimental measurement when assuming the reactions are due to the dipion emission of Upsilon(5S). At the end, we raise a new puzzle that the predicted differential width d Gamma(Upsilon(5S) -> Upsilon(2S)pi(+)pi(-))/d cos0 has a discrepant trend from the data while other predictions are well in accord with the data. It should be further clarified by more accurate measurements carried by future experiments.