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

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.