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

TL;DR

This paper provides a comprehensive theoretical analysis of specific semileptonic decays of eta and eta prime mesons using the Vector Meson Dominance model, including new predictions for decay widths and spectra.

Contribution

It introduces the first theoretical predictions for certain eta prime decay widths and dilepton spectra, utilizing an optimized VMD model based on radiative decay data.

Findings

Decay widths and spectra for eta decays agree with existing literature.

New predictions for eta prime decay widths and spectra are presented.

The VMD model effectively describes the semileptonic decay processes.

Abstract

A complete theoretical analysis of the $C$-conserving semileptonic decays $\eta^{(\prime)}\to\pi^0l^+l^-$ 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 ($V=\rho^0$, $\omega$, $\phi$ and $P=\pi^0$, $\eta$, $\eta^{\prime}$). The decay widths and dilepton energy spectra for the two $\eta\to\pi^0l^+l^-$ 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 $\eta^{\prime}\to\pi^0l^+l^-$ and $\eta^\prime\to\eta l^+l^-$ decay widths and dilepton energy spectra are calculated and presented for the first time in this work.