$K_{l3\gamma }^{+}$ decays revisited: branching ratios and T-odd momenta correlations

Abstract

We calculate the branching ratios of the $K^{+}\to {\pi }^0{l}^{+}{\nu }_l\gamma (l=e,\mu )$ decays, and the T-odd triple momenta correlations $\xi =\vec{q}\cdot [{\vec{p}}_l\times {\vec{p}}_{\pi }]/M_K^3$, due to the electromagnetic final state interaction, in these processes. The contributions on the order of ${\omega }^{-1}$ and ${\omega }^0$ to the corresponding amplitudes are treated exactly. For the branching ratios, the corrections on the order of $\omega$ are estimated and demonstrated to be small. We compare the results with those of other authors. In some cases our results differ considerably from the previous ones.

Comments: 13 pages, 11 figures; references added