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Isospin breaking in pion and $K_{e4}$ form factors
- Publication Year :
- 2014
-
Abstract
- Isospin breaking in the $K_{\ell 4}$ form factors induced by the difference between charged and neutral pion masses is discussed within a framework built on suitably subtracted dispersion representations. The $K_{\ell 4}$ form factors are constructed in an iterative way up to two loops in the low-energy expansion by implementing analyticity, crossing, and unitarity due to two-meson intermediate states. Analytical expressions for the phases of the two-loop form factors of the $K^\pm\to\pi^+\pi^- e^\pm \nu_e$ channel are presented, allowing one to connect the difference of form-factor phase shifts measured experimentally (out of the isospin limit) and the difference of $S$- and $P$-wave $\pi\pi$ phase shifts studied theoretically (in the isospin limit). The dependence with respect to the two $S$-wave scattering lengths $a_0^0$ and $a_0^2$ in the isospin limit is worked out in a general way, in contrast to previous analyses based on one-loop chiral perturbation theory. The results on the phases of the $K^\pm\to\pi^+\pi^- e^\pm \nu_e$ form factors obtained by the NA48/2 collaboration at the CERN SPS are reanalysed including isospin-breaking correction to extract values for the scattering lengths $a_0^0$ and $a_0^2$.<br />Comment: 15 pages, 3 figures, prepared for the proceedings of the XIth Confinement and Hadron Spectrum Conference, Saint-Petersburg, Sept. 8-12, 2014
- Subjects :
- High Energy Physics - Phenomenology
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1412.1247
- Document Type :
- Working Paper