K*andKMeson Pole Contributions to LeptonicΛDecay

Abstract

An attempt is made to calculate the leptonic $\Lambda$ decay rate on the basis of the known $K_{e3\mathrm{}}$ and $K_{\mu 2}$ decay rates. Unsubtracted dispersion relations are written for the relevant matrix elements of the strangeness-changing vector weak current and the absorptive parts are approximated by retaining only the contribution from the $K^{*}$. In this way the vector current contribution to the $\Lambda$ decay is related to the known $K_{e3\mathrm{}}$ rate, the known effective $\pi -K-K^{*}$ coupling constant, and the as yet unknown $\Lambda -p-K^{*}$ coupling constant. The latter coupling constant will hopefully be determined soon from extrapolation of the associated production data. The axial vector contribution to $\Lambda$ decay is related to the $K_{\mu 2}$ decay rate by writing unsubtracted dispersion relations for the divergence of this current and approximating the absorptive parts by keeping only the contribution of the $K$ meson. The numerical consequences of this calculation can only be evaluated once the $\Lambda -p-K^{*}$ is determined, but a crude estimate suggested by "unitary symmetry" yields a leptonic $\Lambda$ decay rate a few times smaller than is now suggested experimentally.