$K^0_{l3γ}$ decays: branching ratios and T-odd momenta correlations

Abstract

The branching ratios of the $K^0 \to π^- l^+ ν_l γ(l = e, μ)$ decays, and the T-odd triple momenta correlations $ξ=\vec{q}\cdot[\vec{p}_l \times \vec{p}_π]/M^3_K$, due to the electromagnetic final state interaction, in these processes are calculated. The contributions on the order of $ω^{-1}$ and $ω^0$ to the corresponding amplitudes are treated exactly. For the branching ratios and T-odd correlation in $K^0 \to π^- e^+ ν_e γ$ decay, the corrections on the order of $ω$ 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 $K^0_{l3γ}$ decays are calculated for the first time. The values of the ξ-odd asymmetry constitute $-1\times10^{-4}$ and $-4.5\times10^{-4}$ in the $K^0 \to π^- μ^+ ν_μγ$ and $K^0 \to π^- e^+ ν_eγ$ decays, respectively.