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, $(g-2{)}_{\mu }$, ${}^8\mathrm{Be}\text{−}{}^4\mathrm{He}$ anomaly and electric dipole moment (EDM) of Standard Model (SM) particles. In particular, we estimate sensitivity of $\mathrm{NA}64\mu$ experiment to observe muon missing energy events involving hidden scalar and vector particles. That analysis is based on geant4 Monte Carlo simulation of the signal process of muon scattering off target nuclei $\mu N\to \mu NS(V)$ 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.

We discuss constraints on soft CP-violating couplings of axion-like particles with photon and fermions by using data on electric dipole moments of standard model particles. In particular, for the axion-like particle (ALP) leptophilic scenario, we derive bounds on CP-odd ALP-photon-photon coupling from data of the ACME collaboration on electron EDM. We also discuss prospects of the storage ring experiment to constrain the ALP–photon–photon coupling from data on proton EDM for the simplified hadrophilic interactions of ALP. The resulting constraints from experimental bounds on the muon and neutron EDMs are weak. We set constraint on the CP-odd ALP coupling with electron and derive bounds on combinations of coupling constants, which involve soft CP-violating terms.

EPJ Web of Conferences, open-access proceedings in physics and astronomy

The current status of the muon g-2 problem is briefly discussed. We briefly discuss the latest results on the muon g-2 measured in experiment and obtained theoretically within the standard model. Special attention is for the hadronic corrections and in particular the corrections due to the light by light scattering mechanism. For latter we present the results found in the leading in 1/N_c approximation with the nonlocal chiral quark model.