Radiative K e3 decays revisited

Motivated by recent experimental results and ongoing measurements, we review the chiral perturbation theory prediction for \(K_{\mathrm {L}}\to\pi^{\mp} e^{\pm} \nu_e\gamma\) decays. Special emphasis is given to the stability of the inner bremsstrahlung-dominated relative branching ratio versus the K e3 form factors, and on the separation of the structure-dependent amplitude in differential distributions over the phase space. For the structure-dependent terms, an assessment of the order p 6 corrections is given, in particular, a full next-to-leading order calculation of the axial component is performed. The experimental analysis of the photon energy spectrum is discussed, and other potentially useful distributions are introduced.