2014/12/03 by Véronique Bernard, Bernard, Véronique, Sébastien Descotes–Genon +3
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High-Energy Particle Collisions Research #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions
paper · doi:10.48550/arxiv.1412.1247
openalex publication_date 2014/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Isospin breaking in the Kℓ 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 Kℓ 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^±→π+π- e^± νe 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 ππ phase shifts studied theoretically (in the isospin limit). The dependence with respect to the two S-wave scattering lengths a00 and a02 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^±→π+π- e^± νe 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 a00 and a02.