In this work we investigate the prospect of observing new-physics signatures via CP violation in η(′) → π0μ+μ− and η′ → ημ+μ− decays at the REDTOP experiment. We make use of the SMEFT to parametrise the new-physics CP-violating effects and find that the projected REDTOP statistics are not competitive with respect to nEDM experiments. This reasserts the η → μ+μ− process as the most promising channel to find CP-violation at this experimental facility.

A two mixing angle description of the pseudoscalar decay constants associated to the η-η system is used to parametrize the theoretical amplitudes of the radiative decays (η, η ) → γγ and the coupling constants g V (η,η )γ with V = ρ, ω, φ . The parametrization is performed in both the "octet-singlet" basis and the "quark-flavour" basis. An excellent agreement with the most recent experimental data is achieved. Our analysis reveals that at the present experimental accuracy the two mixing angles differ significantly in the former basis but not in the latter, in accordance with the expectations of large N c Chiral Perturbation Theory where the difference between the two mixing angles are due to a SU(3) f -breaking effect and a violation of the OZI rule respectively.

A consistent description of σ(500) meson effects in ρ 0 → π 0 π 0 γ and π + π − γ decays is proposed in terms of reasonably simple amplitudes which reproduce the expected chiral-loop behaviour for large m σ values. For the neutral case, in addition to the well known ω exchange, there is an important contribution from the σ(500) meson that is in agreement with recent experimental data. For the charged case, where the dominant contribution comes from bremsstrahlung, the effects of the σ(500) meson are relevant only at high values of the photon energy and compatible with present data. A combined analysis of both processes with moderately improved experimental information should contribute decisively to clarify the status of this controversial σ(500) meson.

The branching ratio of the electromagnetic rare decays η → π 0 γγ and η → (π 0 , η)γγ are analysed in terms of scalar and vector meson exchange contributions using the frameworks of the Linear Sigma Model and Vector Meson Dominance, respectively. The measured η → π 0 γγ process serves as a test of our approach while the non yet measured η → (π 0 , η)γγ reactions are predicted for the first time. Our prediction for the η → π 0 γγ decay agrees with recent experimental reported values, thus supporting the validity of our framework. Therefore, our predictions for the η → π 0 γγ and η → ηγγ decays should be taken as a first indication of the possible values of the associated branching ratios. We hope these predictions to be interesting and useful for experiments such as KLOE-2, Crystal Ball, WASA, and BES-III where these processes are expected to be measured in the next future.

The η and η transition form factors in the space-like region are analyzed at low and intermediate energies in a model-independent way through the use of rational approximants. The slope and curvature parameters of the form factors as well as their values at zero and infinity are extracted from experimental data. The impact of these results on the mixing parameters of the η-η system and the pseudoscalar-exchange contributions to the hadronic light-by-light scattering part of the anomalous magnetic moment aµ are also discussed.

The branching ratio of the η → π 0 γγ and η → ηγγ electromagnetic rare decays are calculated within the frameworks of the Linear Sigma Model and Vector Meson Dominance for the corresponding scalar and vector meson exchange contributions. The measured η → π 0 γγ process serves as a test of our approach while the non yet measured η → (π 0 , η)γγ reactions are predicted for the first time. Our prediction for the η → π 0 γγ decay agrees with recent experimental reported values, thus supporting the validity of our framework. Therefore, our predictions for the η → π 0 γγ and η → ηγγ decays should be taken as a first indication of the possible values of the associated branching ratios. We hope these predictions to be interesting and useful for experiments such as KLOE-2, Crystal Ball, WASA, and BES-III where these processes are expected to be measured in the next future.

Recently, we introduced several dispersive representations for the vector Kπ form factor and fitted them to the Belle spectrum of τ → Kπν τ. Here, we briefly present the model and discuss the results for the slope and curvature of F + (s) arising from the best fit. Furthermore, we compare the pole position of the charged K * (892) computed from our model with other results in the literature. Finally, we discuss the prospects of a simultaneous fit to τ → Kπν τ and K e3 spectra.

The sensitivity of the decays η → π0γγ and ηʹ → π0γγ to a leptophobic B boson in the sub-GeV mass range is summarised in this work. By adding an explicit B-boson resonance exchange to the dominant Standard Model contribution from vector meson exchanges, and employing experimental measurements of the associated branching ratios, the current constraints on the B-boson mass mB and coupling to Standard Model particles αB are significantly improved. From these constraints and the analysis of the available experimental γγ invariant mass distribution of η → π0γγ, we conclude that a B-boson signature in the resonant mass range mπ0 ≲ mB ≲ mη is strongly suppressed and would be very difficult to experimentally identified. The η΄ → π0γγ decay is not as powerful as the η → π0γγ at constraining B-boson parameters below mη but allow exploring larger B-boson masses. Yet, the task of identifying a B-boson with mB ∼ mω would be very challenging.