$K_{l3\gamma }^0$ decays: branching ratios and T-odd momenta correlations

Abstract

The branching ratios of the $K^0\to {\pi }^{-}{l}^{+}{\nu }_l\gamma (l=e,\mu )$ 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 are calculated. The contributions on the order of ${\omega }^{-1}$ and ${\omega }^0$ to the corresponding amplitudes are treated exactly. For the branching ratios and T-odd correlation in $K^0\to {\pi }^{-}{e}^{+}{\nu }_e\gamma$ decay, the corrections on the order of $\omega$ are estimated and demonstrated to be small. The results for the branching ratios are in good agreement with the previous ones. The T-odd triple momenta correlations in $K_{l3\gamma }^0$ decays are calculated for the first time. The values of the \xi-odd asymmetry constitute $-1\times 10^{-4}$ and $-4.5\times 10^{-4}$ in the $K^0\to {\pi }^{-}{\mu }^{+}{\nu }_{\mu }\gamma$ and $K^0\to {\pi }^{-}{e}^{+}{\nu }_e\gamma$ decays, respectively.

Comments: 24 pages, 10 figures; computational mistake corrected, results change considerably. arXiv admin note: substantial text overlap with arXiv:1012.0147