Study of → 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 $2.5\phantom{\rule{0.2em}{0ex}}{\text{fb}}^{-1}$ at center-of-mass energies from 4.36 to 4.60GeV, collected with the BESIII detector at the BEPCII storage ring. The ${D}_{1}{\left(2420\right)}^{+}$ is observed in the ${D}^{+}{\pi }^{+}{\pi }^{-}$ mass spectrum. The mass and width of the ${D}_{1}{\left(2420\right)}^{+}$ are measured to be $\left(2427.2±{1.0}_{\mathrm{stat}.}±{1.2}_{\mathrm{syst}.}\right)$MeV/${c}^{2}$ and $\left(23.2±{2.3}_{\mathrm{stat}.}±{2.3}_{\mathrm{syst}.}\right)$MeV, respectively. In addition, the Born cross sections of the ${e}^{+}{e}^{-}\to {D}_{1}{\left(2420\right)}^{+}{D}^{-}+c.c.\to {D}^{+}{D}^{-}{\pi }^{+}{\pi }^{-}$ and ${e}^{+}{e}^{-}\to \psi \left(3770\right){\pi }^{+}{\pi }^{-}\to {D}^{+}{D}^{-}{\pi }^{+}{\pi }^{-}$ processes are measured as a function of the center-of-mass energy.