  Isospin breaking in the Kl4 form factors induced by the difference between
charged and neutral pion masses is studied. Starting from suitably subtracted
dispersion representations, the 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 -> pi^+
pi^- e^\pm nu_e channel are given, 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 isospin-breaking correction consists of the sum of a
universal part, involving only pi-pi rescattering, and a process-dependent
contribution, involving the form factors in the coupled channels. The
dependence on 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 latter is used only to assess the
subtraction constants involved in the dispersive approach. The two-loop
universal and process-dependent contributions are estimated and cancel
partially to yield an isospin-breaking correction close to the one-loop case.
The recent results on the phases of K^\pm -> pi^+ pi^- e^\pm nu_e form factors
obtained by the NA48/2 collaboration at the CERN SPS are reanalysed including
this isospin-breaking correction to extract values for the scattering lengths
a_0^0 and a_0^2, as well as for low-energy constants and order parameters of
two-flavour ChPT.
