Measurement of ${e}^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{D}^{+}{D}^{-}$ 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 ${e}^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{D}^{+}{D}^{-}$ process at center-of-mass energies from 4.190 to 4.946 GeV with a partial reconstruction method. Resonance structures are seen and the cross section line shape can be described by the coherent sum of either two Breit-Wigner functions or a Breit-Wigner function and a phase space term. The mass and width of the resonance at about 4.4 GeV are determined to be $\left(4371.6±2.5±9.2\right)\text{}\mathrm{MeV}/{c}^{2}$ and $\left(167±4±29\right)\text{}\mathrm{MeV}$, respectively, which are in agreement with those of the $\psi \left(4360\right)$ or $Y\left(4390\right)$ state. The spin-$3D$-wave charmonium state $X\left(3842\right)$ is searched for through the ${e}^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}X\left(3842\right)\to {\pi }^{+}{\pi }^{-}{D}^{+}{D}^{-}$ process, and evidence with a significance of $4.2\sigma $ is found in the data samples with center-of-mass energies from 4.6 to 4.7 GeV.