A data-driven approach to ${{\rm{\pi }}}^{0},{\rm{\eta }}$ and ${{\rm{\eta }}}^{\prime}$ single and double Dalitz decays

Abstract

The dilepton invariant mass spectra and integrated branching ratios of the single and double Dalitz decays P → + − γ and P → + − + − (P = π 0 , η, η ; = e or µ) are predicted by means of a data-driven approach based on the use of rational approximants applied to π 0 , η and η transition form factor experimental data in the space-like region.

Radiative corrections to double-Dalitz decays revisited

“…[4,7,8,10]. In the following, we comment briefly on some aspects that, we believe, could be tested at future experiments.…”

Dalitz decays of $\pi^0$, $\eta$ and $\eta’$ mesons

“…[7] are found in Ref. [1]. The predictions for the integrated branching ratios of π 0 → e + e − γ and π 0 → e + e − e + e − together with their experimental values are shown in Table 1.…”

“…For the η case, our approach is limited to some point in the neighbourhood of the pole (see details in Ref. [1]), thus making mandatory to use a model, for instance VMD, to describe the TFF in the resonance region. Again, the predictions for the integrated branching ratios of the η and η single and double Dalitz decays together with their experimental values are found in Table 1.…”

“…The main goal of the analysis in which this contribution is based on was predict the time-like region of the π 0 , η and η TFFs from the corresponding fits to existing and precise experimental data on their space-like counterparts using Padé approximants (PAs) [1]. As a byproduct, we were able to calculate the invariant mass spectra and the integrated branching ratios of the so-called single Dalitz decays π 0 → e + e − γ and η ( ) → + − γ, with = e or µ, and the double Dalitz decays π 0 → e + e − e + e − and η ( ) → + − + − .…”

The radiative corrections to double-Dalitz decays revisited

“…Still, it would be desirable to gather complementary measurements at lower energies in order to test the most compelling frameworks devised for describing such TFFs in the region relevant to (g − 2) µ [5,10], and also to compare against the recent lattice results [11]. Experimentally, such a possibility can be brought by the double-Dalitz decays, P → γ + − + − , especially for the η and η cases due to their larger phase space [12,13,14,15,16,17,18]. 1 Notoriously, the required statistics for such measurements would be at hand at the proposed REDTOP facility [21].…”