T-odd correlation in the $K_{l 3 γ}$-decay

Abstract

The dependence of the $K^+ \to π^0 l^+ ν_l γ$ decay width on the $T$-odd kinematical variable, $ ξ= {\vec q \cdot [\vec p_l \times \vec p_π]} / {M^3}$, is studied at the tree and one-loop levels of Standard Model. It is shown that at the tree level this decay width is the even function of $ξ$, while the odd contribution arises due to the electromagnetic final state interaction. This contribution is determined by imaginary parts of one-loop diagrams. The calculations performed show that the $ξ$-odd contribution to the $K^+ \to π^0 e^+ ν_e γ$ and $K^+ \to π^0 μ^+ ν_μγ$ decay widths is four orders of magnitude smaller than even contribution coming from the tree level of SM.