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We consider an experiment to search for dark sector particles in dark photonkinetic mixing model by analyze invisible and semi-invisible decays of neutralmesons $M^0 = \pi^0$, $\eta$, $\eta'$, $\omega$, $f_2(1270)$, produced in theNA64 experiment at the CERN SPS. The approach proposed inRef.~\cite{Gninenko:2014sxa} is to use the charge-exchange reactions $\pi^- +(A, Z) \to M^0 + (A,Z-1); M^0 \to$ invisible or semi-invisible of high-energypions (or kaons) at a nuclei target as a source of $M^0$s, which subsequentlydecay invisibly into dark sector. This reaction chain would lead to a strikingsignature of the signal event - the complete disappearance of the beam energyin the setup. Using data obtained from the study of charge-exchange reactionsat IHEP (Protvino) and Fermilab (Batavia) we show that the integral crosssections $\sigma$ for production of the neutral mesons $M^0$ are slightlydeviate from phenomenological formula $\sigma \sim Z^{2/3}$, where $Z$ is thenuclei charge. In particular, we present the formulas for the differential andintegral sections that explicitly depend on the Mandelstam and $Z$ variables.Derived formulas are used to predict the cross sections as a function of beamenergy for several target nuclei, and to estimate the projection sensitivityfor the proposed search for the $M^0\to$ semi-invisible and $M^0\to$ invisibledecays through the vector portal to dark sector. Sensitivity to differentsemi-invisible decay modes of neutral pseudoscalar mesons is studied.

Test of vector portal with dark fermions in the charge-exchange reactions in the NA64 experiment at CERN SPS