T-odd correlation in theKl3γdecay

The dependence of the $K^{+}\to {\pi }^0{l}^{+}{\nu }_l\gamma$ decay width on the T-odd kinematical variable $\xi =\overrightarrow{q}\cdot [p_l\times p_{\pi }]{/M}^3$ is studied at the tree and one-loop levels of the standard model (SM). It is shown that at the tree level this decay width is an even function of $\xi ,$ while the odd contribution arises due to the electromagnetic final state interaction. This contribution is determined by the imaginary parts of the one-loop diagrams. The calculations performed show that the ξ-odd contribution to the $K^{+}\to {\pi }^0{e}^{+}{\nu }_e\gamma$ and $K^{+}\to {\pi }^0{\mu }^{+}{\nu }_{\mu }\gamma$ decay widths is four orders of magnitude smaller than the even contribution coming from the tree level of the SM.