Isospin breaking in pion and $K_{e4}$ form factors
Résumé
Isospin breaking in the Kℓ4form factors induced by the difference between charged and neutral pion masses is discussed within a framework built on suitably subtracted dispersion representations. The Kℓ4form 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±νechannel 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 a00and a20in the isospin limit is worked out in a general way, in contrast 0 0 to previous analyses based on one-loop chiralperturbation theory. The results on the phases of the K± → π+π−e±νeform factors obtained by the NA48/2 collaboration at the CERN SPS are reanalysed including isospin-breaking correction to extract values for the scattering lengths a00and a02
Mots clés
11.30.Rd
11.40.Ha
11.55.Fv
12.38.Qk
12.39.Fe
13.20.Eb
Form factors
Pions
Chiral symmetries
Perturbation theory
pi: mass
pi: form factor
K: form factor
perturbation theory: chiral
isospin: violation
pi: scattering length
pi pi: phase shift
analytic properties
intermediate state
dispersion relation
unitarity
CERN SPS
higher-order: 2
NA48