Leptonic Decays of Hadrons

Abstract

The experimental data on leptonic decays of baryons have been re-examined in the light of a two-angle Cabibbo theory, where the two angles, ${\ensuremath{\theta}}_{V}$ and ${\ensuremath{\theta}}_{A}$, are characteristic of the vector and axial-vector baryon currents, respectively. With certain assumptions about the energy dependence of the form factors in the vector (${K}_{e3}$) and axial-vector (${K}_{\ensuremath{\mu}2}, {\ensuremath{\pi}}_{\ensuremath{\mu}2}$) decays of mesons, it can be shown that the angles ${\ensuremath{\theta}}_{V}$ and ${\ensuremath{\theta}}_{A}$ derived from baryon decays are compatible with the corresponding angles derived from meson decays, thus justifying our use of a two-angle theory. There is no discrepancy between the information from hyperon and meson decays and the information from the superallowed nuclear beta decays (${\mathrm{O}}^{14}$, ${\mathrm{Cl}}^{34}$, etc.). Using the assumptions about the meson form factors, a fit of all data on leptonic decays of hadrons gives the values ${\ensuremath{\theta}}_{V}=0.212\ifmmode\pm\else\textpm\fi{}0.004$, ${\ensuremath{\theta}}_{A}=0.268\ifmmode\pm\else\textpm\fi{}0.001$, $\ensuremath{\alpha}=0.665\ifmmode\pm\else\textpm\fi{}0.018$, where the parameter $\ensuremath{\alpha}$ defines the relative content of $D$ coupling in the baryonic axial-vector current.