Partial wave analysis of $ {e}^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}J/\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\text{}\text{}{\mathrm{fb}}^{-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/\psi $. The cross sections for the subprocesses $ {e}^{+}{e}^{-}\to {\pi }^{+}{Z}_{c}(3900{)}^{-}+\mathrm{c}.\mathrm{c}.\to {\pi }^{+}{\pi }^{-}J/\psi $, $ {f}_{0}(980)(\to {\pi }^{+}{\pi }^{-})J/\psi $, and $ ({\pi }^{+}{\pi }^{-}{)}_{\mathrm{S}\text{−}\mathrm{wave}}J/\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\text{}\text{}\mathrm{MeV}/{c}^{2}$ and $ 37.2\pm 1.3\pm 6.6\text{}\text{}\mathrm{MeV}$, respectively. The first errors are statistical and the second systematic. The final state $ ({\pi }^{+}{\pi }^{-}{)}_{\mathrm{S}\text{−}\mathrm{wave}}J/\psi $ dominates the process $ {e}^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}J/\psi $. By analyzing the cross sections of $ {\pi }^{\pm }{Z}_{c}(3900{)}^{\mp }$ and $ {f}_{0}(980)J/\psi $, $ Y(4220)$ has been observed. Its mass and width are determined to be $ 4225.7\pm 4.1\pm 3.4\text{}\text{}\mathrm{MeV}/{c}^{2}$ and $ 57.5\pm 9.4\pm 12.1\text{}\text{}\mathrm{MeV}$, respectively.