  We discuss new physics phenomenology of hidden scalar ($S$), pseudoscalar
($P$), vector ($V$) and axial-vector ($A$) particles coupled to nucleons and
leptons, which could give contributions to proton charge radius, $(g-2)_\mu$,
$^8$Be-$^4$He anomaly and electric dipole moment (EDM) of Standard Model (SM)
particles. In particular, we estimate sensitivity of NA64$\mu$ experiment to
observe muon missing energy events involving hidden scalar and vector
particles. That analysis is based on {\tt GEANT4} Monte Carlo simulation of the
signal process of muon scattering off target nuclei $\mu N \to \mu N S(V)$
followed by invisible boson decay into Dark Matter (DM) particles, $S(V)\to
\chi \chi$. The existence of light sub-GeV bosons could possibly explain the
muon $(g-2)$ anomaly observed. We also summarize existing bounds on ATOMKI
$X17(J^P=0^-, 1^\pm)$ boson coupling with neutron, proton and electron. We
implement these constraints to estimate the contribution of $P$, $V$ and $A$
particles to proton charge radius via direct 1-loop calculation of Sachs form
factors. The analysis reveals the corresponding contribution is negligible. We
also calculate bounds on dark axion portal couplings of dimension-five
operators, which contribute to the EDMs of leptons and neutron.
