Abstract
In the framework of chiral perturbation theory with photons and leptons, the one-loop isospin-breaking effects in \(K_{\ell 4}\) decays due to both the photonic contribution and the quark and meson mass differences are computed. A comparison with the isospin-breaking corrections applied by recent high statistics \(K_{e4}\) experiments is performed. The calculation can be used to correct the existing form factor measurements by isospin-breaking effects that have not yet been taken into account in the experimental analysis. Based on the present work, possible forthcoming experiments on \(K_{e4}\) decays could correct the isospin breaking effects in a more consistent way.
Highlights
High-precision hadron physics at low energies pursues mainly two aims: a better understanding of the strong interaction in its non-perturbative regime and the indirect search for new physics beyond the standard model
The physical region starts at the π π threshold, i.e. at lower energies than K π scattering, which gives access to the same low-energy constants. χ PT, being an expansion in the meson masses and momenta, should give a better description of K 4 than K π scattering
I neglect according to the softphoton approximation (SPA) terms with a q in the numerator, i.e. the q/ in Lμν and the qν in ν i insert the tree-level expressions for the form factors and consistently keep only terms that diverge as q−1, I find that the soft-photon amplitude factorises as Tγsoft = eTisLoO
Summary
High-precision hadron physics at low energies pursues mainly two aims: a better understanding of the strong interaction in its non-perturbative regime and the indirect search for new physics beyond the standard model. The mass effects on the phases at two-loop order have been recently studied in an elaborate dispersive framework [13], which confirms the previous results. In both works, the photonic effects are assumed to be treated consistently in the experimental analysis. 4, I present the strategy of extracting the isospin corrections and perform the phase space integration for the radiative decay. The cancellation of both infrared and mass divergences is demonstrated. It should be noted that large parts of this work assume a small lepton mass and are not applicable to the muonic mode of the process
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