Study of the process $e^{+}{e}^{-}\to {\pi }^0{\pi }^{0}J/\psi$ and neutral charmonium-like state $Z_c(3900{)}^0$

Abstract

Cross sections of the process $e^{+}{e}^{-}\to {\pi }^0{\pi }^{0}J/\psi$ at center-of-mass energies between 3.808 and 4.600 GeV are measured with high precision by using 12.4 $f{b}^{-1}$ of data samples collected with the BESIII detector operating at the BEPCII collider facility. A fit to the measured energy-dependent cross sections confirms the existence of the charmonium-like state $Y(4220)$. The mass and width of the $Y(4220)$ are determined to be $(4220.4\pm 2.4\pm 2.3)$ $\mathrm{MeV}/c^2$ and $(46.2\pm 4.7\pm 2.1)$ MeV, respectively, where the first uncertainties are statistical and the second systematic. The mass and width are consistent with those measured in the process $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}J/\psi$. The neutral charmonium-like state $Z_c(3900{)}^0$ is observed prominently in the ${\pi }^{0}J/\psi$ invariant-mass spectrum, and, for the first time, an amplitude analysis is performed to study its properties. The spin-parity of $Z_c(3900{)}^0$ is determined to be $J^P=1^{+}$, and the pole position is $(3893.1\pm 2.2\pm 3.0)-i(22.2\pm 2.6\pm 7.0)$ $\mathrm{MeV}/c^2$, which is consistent with previous studies of electrically charged $Z_c(3900{)}^{\pm }$. In addition, cross sections of $e^{+}{e}^{-}\to {\pi }^0{Z}_c(3900{)}^0\to {\pi }^0{\pi }^{0}J/\psi$ are extracted, and the corresponding lineshape is found to agree with that of the $Y(4220)$.

8 pages, 3 figures

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