T-odd correlation in the K13 decay

The dependence of the ${K}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{l}^{+}{\ensuremath{\nu}}_{l}\ensuremath{\gamma}$ decay width on the T-odd kinematical variable $\ensuremath{\xi}=\stackrel{\ensuremath{\rightarrow}}{q}\ensuremath{\cdot}[{p}_{l}\ifmmode\times\else\texttimes\fi{}{p}_{\ensuremath{\pi}}]{/M}^{3}$ 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 $\ensuremath{\xi},$ 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 \ensuremath{\xi}-odd contribution to the ${K}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{e}^{+}{\ensuremath{\nu}}_{e}\ensuremath{\gamma}$ and ${K}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{\ensuremath{\mu}}^{+}{\ensuremath{\nu}}_{\ensuremath{\mu}}\ensuremath{\gamma}$ decay widths is four orders of magnitude smaller than the even contribution coming from the tree level of the SM.