$K^+_{l3\gamma}$ decays revisited: branching ratios and T-odd momenta correlations

TL;DR

This paper recalculates the branching ratios and T-odd momentum correlations in $K^+_{l3\gamma}$ decays, considering electromagnetic final state interactions and providing updated, sometimes significantly different, results from previous studies.

Contribution

It provides exact calculations of certain amplitude contributions and estimates small corrections, offering new insights into decay processes and discrepancies with prior work.

Findings

Calculated branching ratios for $K^+ o \pi^0 l^+ u_l\gamma$ decays.

Analyzed T-odd momentum correlations due to electromagnetic interactions.

Found some results differ significantly from previous studies.

Abstract

We calculate the branching ratios of the $K^+ \to \pi^0 l^+ \nu_l\gamma (l = e, \mu)$ decays, and the T-odd triple momenta correlations $\xi=\vec{q}\cdot[\vec{p}_l \times \vec{p}_\pi]/M^3_K$, due to the electromagnetic final state interaction, in these processes. The contributions on the order of $\omega^{-1}$ and $\omega^0$ to the corresponding amplitudes are treated exactly. For the branching ratios, the corrections on the order of $\omega$ are estimated and demonstrated to be small. We compare the results with those of other authors. In some cases our results differ considerably from the previous ones.