Isospin breaking effects in <math><msub><mi>K</mi><mrow><mi>ℓ</mi><mn>4</mn></mrow></msub></math> decays

In the framework of chiral perturbation theory with photons and leptons, the one-loop isospin-breaking effects in <math><msub><mi>K</mi><mrow><mi>ℓ</mi><mn>4</mn></mrow></msub></math> 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 <math><msub><mi>K</mi><mrow><mi>e</mi><mn>4</mn></mrow></msub></math> 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 <math><msub><mi>K</mi><mrow><mi>e</mi><mn>4</mn></mrow></msub></math> decays could correct the isospin breaking effects in a more consistent way