Precision tests of fundamental physics with $\eta$ and $\eta'$ mesons

Abstract

Decays of the neutral and long-lived 𝜂 and 𝜂 ′ mesons provide a unique, flavor-conserving laboratory to test low-energy Quantum Chromodynamics and search for physics beyond the Standard Model. In these proceedings, we discuss recent progress in a dispersion-theoretical analysis of the 𝜂 and 𝜂 ′ transition form factors, which determine the corresponding pole contribution to hadronic lightby-light scattering in the anomalous magnetic moment of the muon. Subsequently, we consider discrete symmetry tests relevant for the search of potential new sources of 𝐶𝑃-violation. We point out how stringent constraints from electric dipole moment measurements strongly limit the realistic opportunities to observe 𝑃-and 𝐶𝑃-odd mechanisms in 𝜂 or 𝜂 ′ decays. For the far less investigated 𝐶-and 𝐶𝑃-odd processes, we introduce a dispersion-theoretical formalism to assess these from Dalitz plot asymmetries in a model-independent way. †