The semileptonic decays $\eta^{(\prime)} \to \pi^0 \ell^+ \ell^-$ and $\eta' \to \eta \ell^+ \ell^-$ in the standard model

TL;DR

This paper provides a theoretical analysis of specific semileptonic eta decays within the Standard Model, modeling form factors with vector-meson dominance and considering rescattering effects, predicting branching ratios below current experimental limits.

Contribution

It introduces a detailed modeling of form factors using vector-meson dominance and assesses rescattering effects, offering more accurate decay predictions.

Findings

Form factors significantly affect decay rates.

Branching ratios are below experimental limits.

Rescattering contributions are non-negligible.

Abstract

We perform a theoretical analysis of the semileptonic decays $\eta^{(\prime)} \to \pi^0 \ell^+ \ell^-$ and $\eta' \to \eta \ell^+ \ell^-$, where $\ell = e, \mu$, via a charge-conjugation-conserving two-photon mechanism. The underlying form factors are modeled using vector-meson dominance, phenomenological input, and $\mathrm{U}(3)$ flavor symmetry. We consider both a monopole and a dipole model, the latter tailored such that the expected high-energy behavior is ensured. Furthermore, we benchmark the effect of $S$-wave rescattering contributions to the decays. We infer significant effects of the form factors neglected in the literature so far, still finding branching ratios of the various decays well below the current experimental upper limits.