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

We report a study of the $e^{+}e^{-} to D^{+} D^{-} pi^{+} pi^{-}$ 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 $D^{+} pi^{+} pi^{-}$ mass spectrum. The mass and width of the $D_{1}(2420)^+$ are measured to be $(2427.2pm 1.0_{rm stat.}pm 1.2_{rm syst.}) rm{MeV}/c^2$ and $(23.2pm 2.3_{rm stat.} pm2.3_{rm syst.}) rm{MeV}$, respectively. The first errors are statistical and the second ones are systematic. In addition, the Born cross sections of the $e^{+}e^{-} to D_{1}(2420)^+D^- + c.c. to D^{+} D^{-} pi^{+} pi^{-}$ and $e^{+}e^{-} to psi(3770) pi^{+} pi^{-} to D^{+} D^{-} pi^{+} pi^{-}$ processes are measured as a function of the center-of-mass energy.