Partial Wave Analysis of $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}J\mathrm{/}\psi$ and Cross Section Measurement of $e^{+}{e}^{-}\to {\pi }^{\pm }{Z}_c(3900{)}^{\mp }$ from 4.1271 to 4.3583 GeV

Based on 12.0 $\mathrm{f}{\mathrm{b}}^{-1}$ of $e^{+}{e}^{-}$ collision data samples collected by the BESIII detector at center-of-mass energies from 4.1271 to 4.3583 GeV, a partial wave analysis is performed for the process $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}J\mathrm{/}\psi$. The cross sections for the sub processes $e^{+}{e}^{-}\to {\pi }^{+}{Z}_c(3900{)}^{-}+c\mathrm{.}c\mathrm{.}\to {\pi }^{+}{\pi }^{-}J\mathrm{/}\psi$, $f_0(980)(\to {\pi }^{+}{\pi }^{-})J\mathrm{/}\psi$, and $({\pi }^{+}{\pi }^{-}{)}_{\mathrm{S}-\mathrm{w}\mathrm{a}\mathrm{v}\mathrm{e}}J\mathrm{/}\psi$ are measured for the first time. The mass and width of the $Z_c(3900{)}^{\pm }$ are determined to be $3884.6\pm 0.7\pm 3.3$ MeV/$c^2$ and $37.2\pm 1.3\pm 6.6$ MeV, respectively. The first errors are statistical and the second systematic. The final state $({\pi }^{+}{\pi }^{-}{)}_{\mathrm{S}-\mathrm{w}\mathrm{a}\mathrm{v}\mathrm{e}}J\mathrm{/}\psi$ dominates the process $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}J\mathrm{/}\psi$. By analyzing the cross sections of ${\pi }^{\pm }{Z}_c(3900{)}^{\mp }$ and $f_0(980)J\mathrm{/}\psi$, $Y(4220)$ has been observed. Its mass and width are determined to be $4225.7\pm 4.1\pm 3.4$ MeV/$c^2$ and $57.5\pm 9.4\pm 12.1$ MeV, respectively.