Observation of the $\psi (4415)\to D{\overline{D}}_2^{*}(2460)$ Decay Using Initial-State Radiation

We report measurements of the exclusive cross section for $e^{+}{e}^{-}\to D^0{D}^{-}{\pi }^{+}$ over the center-of-mass energy range 4.0 GeV to 5.0 GeV with initial-state radiation and the first observation of the decay $\psi (4415)\to D^0{D}^{-}{\pi }^{+}$. From a study of the resonant substructure in $\psi (4415)$ decay we conclude that the $\psi (4415)\to D^0{D}^{-}{\pi }^{+}$ decay is dominated by $\psi (4415)\to D{\overline{D}}_2^{*}(2460)$. We obtain $\mathcal{B}\mathbf{(}\psi (4415)\to D^0{D}^{-}{\pi }_{\mathrm{nonresonant}}^{+}\mathbf{)}/\mathcal{B}\mathbf{(}\psi (4415)\to D{\overline{D}}_2^{*}(2460)\to D^0{D}^{-}{\pi }^{+}\mathbf{)}<0.22$ at 90% C.L. The analysis is based on a data sample collected with the Belle detector with an integrated luminosity of $673{\mathrm{fb}}^{-1}$.

Figure 1

The observed distributions of (a) $M_{\mathrm{rec}}^2(D^0{D}^{-}{\pi }^{+})$ and (b) $D^0{D}^{-}{\pi }^{+}$ polar angles. (c) The $D^0{D}^{-}{\pi }^{+}{\gamma }_{ISR}$ mass spectrum. (d) The resulting $M_{D^0{D}^{-}{\pi }^{+}}$ spectrum. Histograms show the normalized contributions from the $M_{D^0}$ and $M_{D^{-}}$ sidebands. The selected signal windows are indicated by vertical lines.

Figure 2

The exclusive cross section for $e^{+}{e}^{-}\to D^0{D}^{-}{\pi }^{+}$. The dotted line corresponds to the nominal mass of the $\psi (4415)$ [16].

Figure 3

(a) The scatter plot of $D^{-}{\pi }^{+}$ vs $D^0{\pi }^{+}$ for the signal region in the data for $|M_{D^0{D}^{-}{\pi }^{+}}-m_{\psi (4415)}|<100\mathrm{MeV}/c^2$. (b) $D^{-}{\pi }^{+}$ and (c) $D^0{\pi }^{+}$ mass projections. Histograms show the normalized contributions from the $M_{D^0}$ and $M_{D^{-}}$ sidebands. The selected mass windows are illustrated by vertical and horizontal lines.

Figure 4

(a) The $M_{D^0{D}^{-}{\pi }^{+}}$ spectrum for the $D{\overline{D}}_2^{*}(2460)$ signal region. The solid curve represents the result of the fit described in the text. The threshold function is shown by the dashed curve. (b) The $M_{D^0{D}^{-}{\pi }^{+}}$ spectrum outside the $D{\overline{D}}_2^{*}(2460)$ signal region. The solid curve is a fit with a second-order polynomial background function. The dashed curve shows the upper limit on the $\psi (4415)$ yield at 90% C.L. Histograms show the normalized contributions from $M_{D^0}$ and $M_{D^{-}}$ sidebands.