Probing leptophobic dark sector with a pseudoscalar portal in the NA64 experiment at CERN

We propose the possibility of discovering a light pseudoscalar particle $a$, axion-like particle (ALP), interacting mainly with quarks using the electron and photon scattering reaction chain $e + Z \rightarrow e + \gamma + Z$; $\gamma + Z \rightarrow a + Z$ on nuclei in the NA64 experiment at the CERN SPS. We consider the mixing of ALP with light pseudoscalar mesons $P = \pi, \eta, \eta'$ with taking into account of the ALP mass explicitly breaking the Peccei-Quinn symmetry. It could open invisible channels of ALP decaying into dark fermion matter by analogy with $P$ mesons decays. New bounds on the coupling strengths of the ALP with quarks and of pseudoscalar mesons with dark fermions are obtained by using existing upper bounds on invisible decay modes of $P$s including those recently derived by NA64. We also study a scenario when the $a$ plays the role of a messenger in the communication between our world and the dark sector. New upper limits on axion couplings with quarks and its mixing parameters with $\pi, \eta, \eta'$ mesons are established.