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We performed a search for a new generic $X$ boson, which could be a scalar($S$), pseudoscalar ($P$), vector ($V$) or an axial vector ($A$) particleproduced 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 forsuch process was found in the full NA64 data set of $2.84\times 10^{11}$electrons on target. We place new bounds on the $S, P, V, A$ coupling strengthsto electrons, and set constraints on their contributions to the electronanomalous magnetic moment $a_e$, $|\Delta a_{X}| \lesssim 10^{-15} - 10^{-13}$for the $X$ mass region $m_X\lesssim 1$ GeV. These results are an order ofmagnitude more sensitive compared to the current accuracy on $a_e$ from theelectron $g-2$ experiments and recent high-precision determination of the finestructure constant.

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