Partial Wave Analysis of $e^{+}e^{-} \rightarrow π^{+}π^{-}J/ψ$ and Cross Section Measurement of $e^{+}e^{-} \rightarrow π^{\pm}Z_{c}(3900)^{\mp}$ from 4.1271 to 4.3583 GeV

Based on 12.0 $\mathrm{fb^{-1}}$ 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 $e^{+}e^{-} \rightarrow π^{+}π^{-}J/ψ$. The cross sections for the sub processes ${e^{+}e^{-}\rightarrowπ^{+}Z_{c}(3900)^{-}+c.c.\rightarrowπ^{+}π^{-}J/ψ}$, $f_{0}(980)(\rightarrowπ^{+}π^{-})J/ψ$, and $(π^{+}π^{-})_{\rm{S\mbox{-}wave}} J/ψ$ are measured for the first time. The mass and width of the $Z_{c}(3900)^{\pm}$ are determined to be $3884.6\pm0.7\pm3.3$ MeV/$c^{2}$ and $37.2\pm1.3\pm6.6$ MeV, respectively. The first errors are statistical and the second systematic. The final state $(π^{+}π^{-})_{\rm{S\mbox{-}wave}} J/ψ$ dominates the process $e^{+}e^{-} \rightarrow π^{+}π^{-}J/ψ$. By analyzing the cross sections of $π^{\pm}Z_{c}(3900)^{\mp}$ and $f_{0}(980)J/ψ$, $Y(4220)$ has been observed. Its mass and width are determined to be $4225.7\pm4.1\pm3.4$ MeV/$c^{2}$ and $57.5\pm9.4\pm12.1$ MeV, respectively.