Four-body Dalitz plot contribution to the radiative corrections in K_{l3}^0 decays and its role in the determination of |V_{us}|

TL;DR

This paper calculates four-body radiative corrections to neutral kaon semileptonic decays' Dalitz plot, providing analytical and numerical forms, to improve precision in determining the CKM matrix element |V_{us}|.

Contribution

It introduces a comprehensive calculation of four-body radiative corrections to kaon decays, enhancing the accuracy of |V_{us}| extraction without fixing form factors.

Findings

Analytical and numerical expressions for radiative corrections are provided.

The study yields a precise value for the product f_+^{K^0 o\pi^-}|V_{us}| = 0.2168(3).

The work improves the reliability of kaon decay analysis in precision experiments.

Abstract

The four-body contribution of the model-independent radiative corrections to the Dalitz plot of the semileptonic decays of neutral kaons are computed to order (\alpha/\pi)(q/M_1), where q is the momentum transfer and M_1 is the kaon mass. The final result is presented in two forms. The first one is given in terms of the triple integration of the bremsstrahlung photon ready to be performed numerically; the second one is a fully analytical expression. This paper is organized to make it accessible and reliable in the analysis of the Dalitz plot of precision experiments involving kaons and is not compromised to fixing the form factors at predetermined values. As a byproduct, gathering together three- and four-body contributions of radiative corrections yields, through a least-squares fit to the measured kaon decay rates, the value f_+^{K^0\pi^-}|V_{us}| = 0.2168(3).