Constraints on New Physics in the Electron g-2 from a Search for Invisible Decays of a Scalar, Pseudoscalar, Vector, and Axial Vector

We performed a search for a new generic $X$ boson, which could be a scalar ($S$), pseudoscalar ($P$), vector ($V$) or an axial vector ($A$) particle produced in the 100 GeV electron scattering off nuclei, $e^- Z to e^- Z X$, followed by its invisible decay in the NA64 experiment at CERN. No evidence for such process was found in the full NA64 data set of $2.84times 10^{11}$ electrons on target. We place new bounds on the $S, P, V, A$ coupling strengths to electrons, and set constraints on their contributions to the electron anomalous magnetic moment $a_e$, $|Delta a_{X}| lesssim 10^{-15} - 10^{-13}$ for the $X$ mass region $m_Xlesssim 1$ GeV. These results are an order of magnitude more sensitive compared to the current accuracy on $a_e$ from the electron $g-2$ experiments and recent high-precision determination of the fine structure constant.