Study of $e^+e^- rightarrow pi^{0}X(3872)gamma$ and search for $Z_c(4020)^{0}rightarrow X(3872)gamma$

Using data samples collected with the BESIII detector operating at the BEPCII storage ring at center-of-mass energies from 4.178 to 4.600 GeV, we study the process $e^+e^-rightarrowpi^{0}X(3872)gamma$ and search for $Z_c(4020)^{0}rightarrow X(3872)gamma$. We find no significant signal and set upper limits on $sigma(e^+e^-rightarrowpi^{0}X(3872)gamma)cdotmathcal{B}(X(3872)rightarrowpi^{+}pi^{-}J/psi)$ and $sigma(e^+e^-rightarrowpi^{0}Z_c(4020)^{0})cdotmathcal{B}(Z_c(4020)^{0}rightarrow X(3872)gamma)cdotmathcal{B}(X(3872)rightarrowpi^{+}pi^{-}J/psi)$ for each energy point at $90%$ confidence level, which is of the order of several tenths pb.