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At the high luminosity electron-positron circular colliders like FCC-ee inCERN and CEPC in China it will possible to measure very precisely $e^+e^-\toZ\gamma$ process with subsequent Z decay into particles invisible in thedetector, that is into three neutrina of the Standard Model and possibly intoother weakly coupled neutral particles. Apart from the measurement of the totalinvisible width (which is not the main subject of this work) this process maybe used as a source of $Z$ coupling to electron neutrino -- known very poorly.This is possible due to the presence of the $t$-channel $W$ exchange in the$e^+e^-\to \nu_e \bar\nu_e \gamma$ channel which deforms slightly spectrum ofthe photon. We are going to show experimental investigation of this effect, for$\sim 10$ inverse atobarn accumulated luminosity, which can provide measurementof the $Z-\nu_e$ coupling with statistical error of order 1\%. The estimationof the systematic experimental error will require more work, but most likely itwill be of similar size.

Precision measurement of the Z boson to electron neutrino coupling at the future circular colliders