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Study of $e^{+}e^{-} \to D^{+} D^{-} π^{+} π^{-} $ at center-of-mass energies from 4.36 to 4.60 GeV

We report a study of the $e^{+}e^{-} \to D^{+} D^{-} π^{+} π^{-}$ process using $e^{+}e^{-}$ collision data samples with an integrated luminosity of $2.5\,\rm{fb}^{-1}$ at center-of-mass energies from 4.36 to $4.60 \rm{GeV}$, collected with the BESIII detector at the BEPCII storage ring. The $D_{1}(2420)^+$ is observed in the $D^{+} π^{+} π^{-}$ mass spectrum. The mass and width of the $D_{1}(2420)^+$ are measured to be $(2427.2\pm 1.0_{\rm stat.}\pm 1.2_{\rm syst.}) \rm{MeV}/c^2$ and $(23.2\pm 2.3_{\rm stat.} \pm2.3_{\rm syst.}) \rm{MeV}$, respectively. The first errors are statistical and the second ones are systematic. In addition, the Born cross sections of the $e^{+}e^{-} \to D_{1}(2420)^+D^- + c.c. \to D^{+} D^{-} π^{+} π^{-}$ and $e^{+}e^{-} \to ψ(3770) π^{+} π^{-} \to D^{+} D^{-} π^{+} π^{-}$ processes are measured as a function of the center-of-mass energy.