Anomalous dipion invariant mass distribution of the $\Upsilon(4S)$ decays into $\Upsilon(1S) \pi^{+} \pi^{-}$ and $\Upsilon(2S) \pi^{+} \pi^{-}$

TL;DR

This paper investigates the anomalous dipion mass distributions in $5S$ decays to $5S$ and $2S$ states, proposing an additional B-meson loop contribution that, when combined with direct decay, explains experimental data.

Contribution

It introduces a new mechanism involving B-meson loops and their interference with direct decay to better match experimental observations of $5S$ dipion decays.

Findings

The combined contribution reproduces the observed partial widths and lineshapes.

The interference effect is significant in explaining the data.

Predictions for unmeasured angular distributions are provided.

Abstract

To solve the discrepancy between the experimental data on the partial widths and lineshapes of the dipion emission of $\Upsilon(4S)$ and the theoretical predictions, we suggest that there is an additional contribution which was not taken into account in previous calculations. Noticing that the mass of $\Upsilon(4S)$ is above the production threshold of $B\bar B$, the contribution of the sequential process $\Upsilon(4S)\to B\bar B\to \Upsilon(nS)+S\to \Upsilon(nS)+\pi^+\pi^-$ ($n=1,2$) may be sizable, and its interference with that from the direct production would be important. The goal of this work is to investigate if a sum of the two contributions with a relative phase indeed reproduces the data. Our numerical results on the partial widths and the lineshapes $d\Gamma(\Upsilon(4S)\to \Upsilon(2S,1S)\pi^+\pi^-)/d(m_{\pi^+\pi^-})$ are satisfactorily consistent with the measurements, thus the role of this mechanism is confirmed. Moreover, with the parameters obtained by fitting the data of the Belle and Babar collaborations, we predict the distributions $d\Gamma(\Upsilon(4S)\to \Upsilon(2S,1S)\pi^+\pi^-)/d\cos\theta$ which have not been measured yet.