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We report the first observation of the $\psi(4415)$ resonance in the reaction$\e^+e^-\to D^0 D^-\pi^+$ and a measurement of its cross section in thecenter-of-mass energy range $4.0\mathrm{GeV}$ to $5.0\mathrm{GeV}$ with initialstate radiation. From a study of resonant structure in $\psi(4415)$ decay weconclude that the $\psi(4415)\to D^0 D^-\pi^+$ decay is dominated by$\psi(4415)\to D \bar D{}^{*}_2(2460)$. We obtain $\mathcal{B}(\psi(4415)\toD^0 D^-\pi^+_{\mathrm {non-resonant}})/\mathcal{B}(\psi(4415)\to D \barD{}^{*}_2(2460)\to D^0 D^-\pi^+)<0.22$ at 90% C.L. The analysis is based on adata sample collected with the Belle detector with an integrated luminosity of673 $\mathrm{fb}^{-1}$.

Observation of $\psi(4415)\to D \bar D{}^{*}_2(2460)$ decay using initial-state radiation