Evidence of Two Resonant Structures in $e^+ e^- \to \pi^+ \pi^- h_c$

The cross sections of $e^{+}e^{-}\to\pi^{+}\pi^{-}h_c$ at center-of-mass energies from 3.896 to 4.600 GeV are measured using data samples collected with the BESIII detector operating at the Beijing Electron Positron Collider. The cross sections are found to be of the same order of magnitude as those of $e^{+}e^{-}\to\pi^{+}\pi^{-}J/\psi$ and $e^{+}e^{-}\to\pi^{+}\pi^{-}\psi(2S)$, but the line shape is inconsistent with the $Y$ states observed in the latter two modes. Two structures are observed in the $e^{+}e^{-}\to\pi^{+}\pi^{-}h_c$ cross sections around 4.22 and 4.39 GeV/$c^{2}$, which we call $Y(4220)$ and $Y(4390)$, respectively. A fit with a coherent sum of two Breit-Wigner functions results in a mass of $(4218.4^{+5.5}_{-4.5}\pm0.9)$ MeV/$c^{2}$ and a width of $(66.0^{+12.3}_{-8.3}\pm0.4)$ MeV for the $Y(4220)$, and a mass of $(4391.6^{+6.3}_{-6.8}\pm1.0)$ MeV/$c^{2}$ and a width of $(139.5^{+16.2}_{-20.6}\pm0.6)$ MeV for the $Y(4390)$, where the first uncertainties are statistical and the second ones systematic. The statistical significance of $Y(4220)$ and $Y(4390)$ is 10$\sigma$ over one structure assumption.