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

Abstract

We perform a theoretical analysis of the semileptonic decays ${\eta }^{(\prime )}\to {\pi }^0{\ell }^{+}{\ell }^{-}$ and ${\eta }^{\prime }\to \eta {\ell }^{+}{\ell }^{-}$, 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.

21 pages, 9 figures, 13 tables; C++ interface for Collier and Passarino-Veltman decompositions as ancillary files; v2 as published in Phys. Rev. D

References in corpus (23)

• FeynCalc 9.3: New features and improvements
• Scalar one-loop 4-point integrals
• Towards a data-driven analysis of hadronic light-by-light scattering
• Dispersive analysis of the pion transition form factor
• Extracting the chiral anomaly from gamma pi --> pi pi
• Precision tests of fundamental physics with $\eta$ and ${\eta }^{\prime }$ mesons
• Anomalous decay and scattering processes of the eta meson
• On the transition form factors of the axial-vector resonance $f_1(1285)$ and its decay into $e^{+}{e}^{-}$
• Hadronic vacuum polarization and vector-meson resonance parameters from $e^{+}{e}^{-}\to {\pi }^0\gamma$
• Radiative resonance couplings in $\gamma \pi \to \pi \pi$
• Updated measurement of the $e^{+}{e}^{-}\to \omega {\pi }^0\to {\pi }^0{\pi }^0\gamma$ cross section with the SND detector
• Dispersion relations for ${\gamma }^{\ast }{\gamma }^{\ast }\to \pi \pi$: helicity amplitudes, subtractions, and anomalous thresholds
• A new measurement of the rare decay eta -> pi^0 gamma gamma with the Crystal Ball/TAPS detectors at the Mainz Microtron
• Theoretical analysis of the $\gamma \gamma \to {\pi }^0\eta$ process
• The $\gamma \pi \to \pi \pi$ anomaly from lattice QCD and dispersion relations
• What can we learn about light-meson interactions at electron-positron colliders?
• Improved Standard-Model prediction for ${\pi }^0\to e^{+}{e}^{-}$
• A dispersive analysis of ${\eta }^{\prime }\to {\pi }^{+}{\pi }^{-}\gamma$ and ${\eta }^{\prime }\to {\ell }^{+}{\ell }^{-}\gamma$
• $\eta \to {\pi }^0\gamma \gamma$ decay within a chiral unitary approach revisited
• Width effects of broad new resonances in loop observables and application to $(g-2{)}_{\mu }$
• A theoretical analysis of the semileptonic decays ${\eta }^{(\prime )}\to {\pi }^0{l}^{+}{l}^{-}$ and ${\eta }^{\prime }\to \eta l^{+}{l}^{-}$
• $C$ and $CP$ violation in effective field theories
• New-physics signatures via $CP$ violation in ${\eta }^{(\prime )}\to {\pi }^0{\mu }^{+}{\mu }^{-}$ and ${\eta }^{\prime }\to \eta {\mu }^{+}{\mu }^{-}$ decays

Cited by in corpus (7)

• Dispersion relation for hadronic light-by-light scattering: subleading contributions
• Complete dispersive evaluation of the hadronic light-by-light contribution to muon $g-2$
• Hadronic light-by-light scattering in the anomalous magnetic moments of electron and $\tau$
• Polarizabilities from kaon Compton scattering
• Correlations of $C$ and $CP$ violation in $\eta \to {\pi }^0{\ell }^{+}{\ell }^{-}$ and ${\eta }^{\prime }\to \eta {\ell }^{+}{\ell }^{-}$
• Contributions of $\rho (770,1450)\to \omega \pi$ for the Cabibbo-favored $D\to h\omega \pi$ decays
• The virtual contributions from $K^{\ast }$ in the $B\to K^{\ast }\pi h$ and $B\to K\rho h$ decays