A theoretical analysis of the semileptonic decays ${\eta }^{(\prime )}\to {\pi }^0{l}^{+}{l}^{-}$ and ${\eta }^{\prime }\to \eta l^{+}{l}^{-}$

Abstract

A complete theoretical analysis of the $C$-conserving semileptonic decays ${\eta }^{(\prime )}\to {\pi }^0{l}^{+}{l}^{-}$ and ${\eta }^{\prime }\to \eta l^{+}{l}^{-}$ ($l=e$ or $\mu$) is carried out within the framework of the Vector Meson Dominance (VMD) model. An existing phenomenological model is used to parametrise the VMD coupling constants and the associated numerical values are obtained from an optimisation fit to $V\to P\gamma$ and $P\to V\gamma$ radiative decays ($V={\rho }^0$, $\omega$, $\varphi$ and $P={\pi }^0$, $\eta$, ${\eta }^{\prime }$). The decay widths and dilepton energy spectra for the two $\eta \to {\pi }^0{l}^{+}{l}^{-}$ processes obtained using this approach are compared and found to be in good agreement with other results available in the published literature. Theoretical predictions for the four ${\eta }^{\prime }\to {\pi }^0{l}^{+}{l}^{-}$ and ${\eta }^{\prime }\to \eta l^{+}{l}^{-}$ decay widths and dilepton energy spectra are calculated and presented for the first time in this work.

arXiv comment11 pages, 2 figures, 1 table; v2 includes estimated errors coming from the dependence on the model and a detailed explanation of the structure of the $VP\gamma$ vertex; v3 corrects eqs. (6) and (15), includes discussions on the Feynman integral numerical computations and the use of the energy-dependent width for the $\rho$ propagator, as well as corrected numerical results in Table I and Fig. 2

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• New-physics signatures via $CP$ violation in ${\eta }^{(\prime )}\to {\pi }^0{\mu }^{+}{\mu }^{-}$ and ${\eta }^{\prime }\to \eta {\mu }^{+}{\mu }^{-}$ decays
• Measurement of the absolute branching fractions of Jpsi to gamma eta and eta decay modes
• Sensitivity of the ${\eta }^{(\prime )}\to {\pi }^0\gamma \gamma$ and ${\eta }^{\prime }\to \eta \gamma \gamma$ decays to a sub-GeV leptophobic $U(1{)}_B$ boson