Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2004-08-08
Eur.Phys.J.C40:367-382,2005
Physics
High Energy Physics
High Energy Physics - Phenomenology
29 pages, LaTeX, 7 postscript figures
Scientific paper
10.1140/epjc/s2005-02149-5
We evaluate the size of isospin breaking corrections to form factors $f$ and $g$ of the $K_{\ell 4}$ decay process $K^+\to\pi^+\pi^-\ell^+\nu_{\ell}$ which is actually measured by the extended NA48 setup at CERN. We found that, keeping apart the effect of Coulomb interaction, isospin breaking does not affect modules. This is due to the cancelation between corrections of electromagnetic origin and those generated by the difference between up and down quark masses. On the other hand, electromagnetism affects considerably phases if the infrared divergence is dropped out using a minimal subtraction scheme. Consequently, the greatest care must be taken in the extraction of $\pi\pi$ phase shifts from experiment.
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