Search for the $Y(4140)$ via $e^{+} e^{-} to gamma phi J/psi$ at $sqrt{s}=$ 4.23, 4.26 and 4.36 GeV

Using data samples collected at center-of-mass energies $sqrt{s} = 4.23$, 4.26, and 4.36 GeV with the BESIII detector operating at the BEPCII storage ring, we search for the production of the charmoniumlike state $Y(4140)$ through a radiative transition followed by its decay to $phi J/psi$. No significant signal is observed and upper limits on $sigma[e^{+} e^{-} rightarrow gamma Y(4140)] cdot mathcal{B}(Y(4140)rightarrow phi J/psi)$ at the $90%$ confidence level are estimated as 0.35, 0.28, and 0.33 pb at $sqrt{s} = 4.23$, 4.26, and 4.36 GeV, respectively.