Study of the $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}\omega$ process at center-of-mass energies between 4.0 and 4.6 GeV

Using $15.6$ $\mathrm{f}{\mathrm{b}}^{-1}$ of $e^{+}{e}^{-}$ collision data collected at twenty-four center-of-mass energies from $4.0$ to $4.6$ GeV with the BESIII detector, the helicity amplitudes of the process $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}\omega$ are analyzed for the first time. Born cross section measurements of two-body intermediate resonance states with statistical significance greater than 5$\sigma$ are presented, such as $f_0(500)$, $f_0(980)$, $f_2(1270)$, $f_0(1370)$, $b_1(1235{)}^{\pm }$, and $\rho (1450{)}^{\pm }$. In addition, evidence of a resonance state in $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}\omega$ production is found. The mass of this state obtained by line shape fitting is about 4.2 GeV/$c^2$, which is consistent with the production of $\psi (4160)$ or $Y(4220)$.