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, ${\theta }_V$ and ${\theta }_A$, 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 ($K_{e3\mathrm{}}$) and axial-vector ($K_{\mu 2}, {\pi }_{\mu 2}$) decays of mesons, it can be shown that the angles ${\theta }_V$ and ${\theta }_A$ 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 ${\theta }_V=0.212\mathrm{}\pm 0.004$, ${\theta }_A=0.268\mathrm{}\pm 0.001$, $\alpha =0.665\mathrm{}\pm 0.018$, where the parameter $\alpha$ defines the relative content of $D$ coupling in the baryonic axial-vector current.