Radiative corrections to the Dalitz plot of K_{l3}^\pm decays: Contribution of the four-body region

TL;DR

This paper calculates radiative corrections to the Dalitz plot of K_{l3}^ decays focusing on the four-body region, providing analytical and numerical results to aid experimental analysis and understanding of decay rates.

Contribution

It offers the first detailed calculation of radiative corrections in the four-body region for K_{l3} decays, including analytical formulas and numerical estimates.

Findings

The four-body region contributes a small but significant correction to the decay rate.

Results are provided in both numerical and analytical forms for experimental use.

The correction impacts the interpretation of Dalitz plot analyses in kaon decays.

Abstract

We calculate the radiative corrections to the Dalitz plot of K_{l3}^\pm decays to order (alpha/pi)(q/M_1), where q is the momentum transfer and M_1 is the mass of the kaon. We restrict the analysis to the so-called four-body region, which arises when no discrimination of real photons is made either kinematically or experimentally. We present our results in two ways: the first one with the triple integration over the photon kinematical variables ready to be performed numerically and the second one in a fully analytical form. Our results can be useful in experimental analyses of the Dalitz plot, by evaluating the model-independent coefficients of the quadratic products of the form factors; we provide some numbers as a case example. We find a small, albeit non-negligible, contribution from the four-body region to the radiative correction to the total decay rate of K_{l3}^\pm decays.