On-Shell Current Algebra and the Radiative Leptonic Decay ofK+

Abstract

Dispersion relations and the hard-meson method of Schnitzer and Weinberg are used to study the radiative leptonic decay of the ${K}^{+}$. It is shown that in the pole-dominance approximation the relevant form factor in the axial-vector amplitude cannot be unsubtracted. Possible alterations of our results arising from relaxing a smoothness approximation are estimated to be small. We discuss and compare various symmetry-breaking schemes for the evaluation of necessary coupling constants. The branching ratio for ${K}^{+}\ensuremath{\rightarrow}\ensuremath{\gamma}{e}^{+}\ensuremath{\nu}$ is calculated to be \ensuremath{\sim}2.5\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}5}$ for interesting structure-dependent decays. This is comparable to that for $K\ensuremath{\rightarrow}e\ensuremath{\nu}$ and two orders of magnitude larger than one would expect from the usual estimates for electromagnetic decays. The feasibility of experimentally observing the decay is discussed, as are the possible effects of electromagnetic violations of time-reversal invariance. From these results, a soft-pion estimate of ${F}_{4}$, the vector form factor in ${K}_{l4}$, yields $|{F}_{4}|\ensuremath{\approx}6.9$.