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

Abstract

A complete theoretical analysis of the C- conserving semileptonic decays eta ^{(prime )}rightarrow pi ^0l^+l^- and eta ^prime rightarrow 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 Vrightarrow Pgamma and Prightarrow Vgamma 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 rightarrow 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 }rightarrow pi ^0l^+l^- and eta ^prime rightarrow eta l^+l^- decay widths and dilepton energy spectra are calculated and presented for the first time in this work.