Branching ratio ofϒ(1D)→ϒ(1S)ππ

We consider the branching ratio of $\Upsilon \mathrm{}\left(1D\right)\mathrm{}\to \Upsilon \mathrm{}\left(1S\right)\mathrm{}\pi \pi$, which is related to the $\pi \pi$ spectrum in $\Upsilon \mathrm{}\left(2S\right)\mathrm{}\to \Upsilon \mathrm{}\left(1S\right)\mathrm{}\pi \pi$. Fixing the gluonic contribution to $\Upsilon \mathrm{}\left(2S\right)\mathrm{}\to \Upsilon \mathrm{}\left(1S\right)\mathrm{}\pi \pi$ from the $\pi \pi$ spectrum in $\Upsilon \mathrm{}\left(2S\right)\mathrm{}\to \Upsilon \mathrm{}\left(1S\right)\mathrm{}\pi \pi$, we find that the decay rate of $\Upsilon \mathrm{}\left(1D\right)\mathrm{}\to \Upsilon \mathrm{}\left(1S\right)\mathrm{}\pi \pi$ can be an order of magnitude larger than the previous calculations. Then, we can have 70 to 90 events of $\Upsilon \mathrm{}\left(1D\right)\mathrm{}\to \Upsilon \mathrm{}\left(1S\right)\mathrm{}\pi \pi$ in ${10}^6\Upsilon \mathrm{}\left(3S\right)\mathrm{}$ decays, which is at the limit of detectability.