T-odd correlation in the $K_{l3\gamma }$-decay

Abstract

The dependence of the $K^{+}\to {\pi }^0{l}^{+}{\nu }_l\gamma$ decay width on the $T$-odd kinematical variable, $\xi =\vec{q}\cdot [{\vec{p}}_l\times {\vec{p}}_{\pi }]/M^3$, 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 $\xi$, 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 $\xi$-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 even contribution coming from the tree level of SM.

Comments: 20 pages, 5 figures