Observation of $e^+e^-to pi^0pi^0 h_c$ and a neutral charmoniumlike structure $Z_c(4020)^0$

Using data collected with the BESIII detector operating at the Beijing Electron Positron Collider at center-of-mass energies of $sqrt{s}=4.23$, 4.26, and 4.36~GeV, we observe $EEto pphc$ for the first time. The Born cross sections are measured and found to be about half of those of $EEto pi^+pi^-h_c$ within less than 2$sigma$. In the $pi^0h_c$ mass spectrum, a structure at 4.02~GeV/$c^2$ is found. It is most likely to be the neutral isospin partner of the $zcp^{pm}$ observed in the process of $EEto pi^+pi^-h_c$ is found. A fit to the $pi^0 h_c$ invariant mass spectrum, with the width of the $zcpn$ fixed to that of its charged isospin partner and possible interferences with non-$zcpn$ amplitudes neglected, gives a mass of ($4023.9pm 2.2 pm 3.8$)~MeV/$c^2$ for the $zcpn$, where the first error is statistical and the second systematic.