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

Abstract: We consider an experiment to search for dark sector particles in dark photon kinetic mixing model by analyze invisible and semi-invisible decays of neutral mesons $M^0 = \pi^0$, $\eta$, $\eta'$, $\omega$, $f_2(1270)$, produced in the NA64 experiment at the CERN SPS. The approach proposed in Ref.~\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-energy pions (or kaons) at a nuclei target as a source of $M^0$s, which subsequently decay invisibly into dark sector. This reaction chain would lead to a striking signature of the signal event - the complete disappearance of the beam energy in the setup. Using data obtained from the study of charge-exchange reactions at IHEP (Protvino) and Fermilab (Batavia) we show that the integral cross sections $\sigma$ for production of the neutral mesons $M^0$ are slightly deviate from phenomenological formula $\sigma \sim Z^{2/3}$, where $Z$ is the nuclei charge. In particular, we present the formulas for the differential and integral sections that explicitly depend on the Mandelstam and $Z$ variables. Derived formulas are used to predict the cross sections as a function of beam energy for several target nuclei, and to estimate the projection sensitivity for the proposed search for the $M^0\to$ semi-invisible and $M^0\to$ invisible decays through the vector portal to dark sector. Sensitivity to different semi-invisible decay modes of neutral pseudoscalar mesons is studied.