$K_{l3\gamma }^{+}$ 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.

13 pages, 11 figures; references added

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