Soft-momentum quark-model predictions for the pseudoscalar-meson decays into lepton pairs

Abstract

The pseudoscalar decays $P\ensuremath{\rightarrow}{l}^{+}{l}^{\ensuremath{-}}$ are driven by second-order electromagnetic loop diagrams which are rendered finite by use of appropriate off-shell $P\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}$ form factors determined in the quark model. The theoretical predictions using the soft-momentum limit are in reasonable agreement with the experimental rates and branching ratios, the latter being approximately twice the unitarity bounds for the decays ${\ensuremath{\pi}}^{0}\ensuremath{\rightarrow}{e}^{+}{e}^{\ensuremath{-}}$, $\ensuremath{\eta}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$, and ${K}_{L}^{0}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$. We also investigate the radiative decays ${\ensuremath{\pi}}^{0}\ensuremath{\rightarrow}{e}^{+}{e}^{\ensuremath{-}}\ensuremath{\gamma}$ and $\ensuremath{\eta}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}\ensuremath{\gamma}$ in the same model, and deduce that one cannot extract unambiguously the constituent quark masses from the experimental data.