Measurement of $e^{+}e^{-}\rightarrowπ^{+}π^{-}D^{+}D^{-}$ cross sections at center-of-mass energies from 4.190 to 4.946 GeV
Using data samples collected with the BESIII detector operating at the BEPCII storage ring, we measure the cross sections of the $e^{+}e^{-}\rightarrowπ^{+}π^{-}D^{+}D^{-}$ process at center-of-mass energies from 4.190 to 4.946 GeV with a partial reconstruction method. Two resonance structures are seen and the resonance parameters are determined from a fit to the cross section line shape. The first resonance we observe has a mass of (4373.1 $\pm$ 4.0 $\pm$ 2.2) MeV/$c^2$ and a width of (146.5 $\pm$ 7.4 $\pm$ 1.3) MeV, in agreement with those of the $Y(4390)$ state; the other resonance has a mass of (4706 $\pm$ 11 $\pm$ 4) MeV/$c^2$, a width of (45 $\pm$ 28 $\pm$ 9) MeV, and a statistical significance of $4.1$ standard deviations ($σ$). This is the first evidence for a vector state at this mass value. The spin-$3$ $D$-wave charmonium state $X(3842)$ is searched for through the $e^{+}e^{-}\rightarrowπ^{+}π^{-}X(3842)\rightarrowπ^{+}π^{-}D^{+}D^{-}$ process, and evidence with a significance of $4.2σ$ is found in the data samples with center-of-mass energies from 4.600 to 4.700 GeV.