On some aspects of isospin breaking in the decay $K^pm$ $\to$ $\pi^0 \pi^0 e^\pm$ $\stackrel{_{(-)}}{\nu_e}$

Understand

Two aspects of isospin breaking in the decay $K^\pm \to \pi^0 \pi^0 e^\pm \stackrel{_{(-)}}{\nu_e}$ are studied and discussed.

• The first addresses the possible influence of the phenomenological description of the unitarity cusp on the extraction of the normalization of the form factor from data.
• Using the scalar form factor of the pion as a theoretical laboratory, we find that this determination is robust under variations of the phenomenological parameterizations of the form factor.
• The second aspect concerns the issue of radiative corrections.