Observation of the $\mathit{{\rm Y}}(1^3{D}_J)$ bottomonium state through decays to ${\pi }^{+}{\pi }^{-}\mathit{{\rm Y}}(1S)$

Based on $122\times {10}^6\mathit{{\rm Y}}(3S)$ events collected with the BABAR detector, we have observed the $\mathit{{\rm Y}}(1^3{D}_J)$ bottomonium state through the $\mathit{{\rm Y}}(3S)\to \gamma \gamma \mathit{{\rm Y}}(1^3{D}_J)\to \gamma \gamma {\pi }^{+}{\pi }^{-}\mathit{{\rm Y}}(1S)$ decay chain. The significance for the $J=2$ member of the $\mathit{{\rm Y}}(1^3{D}_J)$ triplet is 5.8 standard deviations including systematic uncertainties. The mass of the $J=2$ state is determined to be $10164.5\pm 0.8(\mathrm{stat})\pm 0.5(\mathrm{syst})\mathrm{MeV}/c^2$. We use the ${\pi }^{+}{\pi }^{-}$ invariant mass distribution to confirm the consistency of the observed state with the orbital angular momentum assignment of the $\mathit{{\rm Y}}(1^3{D}_J)$.

Figure 1

The ${\pi }^{+}{\pi }^{-}{\ell }^{+}{\ell }^{-}$ mass spectrum and fit results. The two peaks near $10.25\mathrm{GeV}/c^2$ arise from ${\chi }_{b{J}^{\prime }}(2P)\to \omega \mathit{{\rm Y}}(1S)$ background events with $\omega \to {\pi }^{+}{\pi }^{-}$.

Figure 2

The ${\pi }^{+}{\pi }^{-}{\ell }^{+}{\ell }^{-}$ mass spectra for the separated (a) $\mathit{{\rm Y}}(1S)\to e^{+}{e}^{-}$ and (b) $\mathit{{\rm Y}}(1S)\to {\mu }^{+}{\mu }^{-}$ channels. The results of the fit are shown. The legend is given in Fig. 1.

Figure 3

(a) The ${\pi }^{+}{\pi }^{-}$ mass spectrum in the $\mathit{{\rm Y}}(1^3{D}_2)$ signal region. The area under each curve equals the number of events. (b),(c) Distributions in the $\mathit{{\rm Y}}(1^3{D}_2)$ signal region of (b) the angle $\chi$ between the ${\pi }^{+}{\pi }^{-}$ and ${\ell }^{+}{\ell }^{-}$ planes and (c) the ${\pi }^{+}$ helicity angle. The uncertainties include both statistical and systematic terms.