  We present a preliminary non-perturbative lattice calculation of the form
factors entering the processes $K\to \ell\,\nu_\ell\,\ell'^+\,\ell'^-$ and of
the corresponding branching ratios. These form factors describe the interaction
between the mediating virtual photon and the internal hadronic structure of the
meson. By separating them from the point-like contribution to the matrix
element we are able to isolate and reconstruct the structure-dependent
contribution to the decay width. Our numerical analysis employs only one gauge
ensemble and so it is affected by systematic uncertainties due to the missing
continuum and physical point extrapolation. Despite this, we already find a
reasonable agreement with the experimental data and with the next to leading
order Chiral Perturbation Theory predictions. The method is general and can be
applied to any pseudoscalar meson, though for heavier mesons the possibility of
internal lighter states becomes problematic and still needs a proper study. A
non-perturbative, model-independent lattice evaluation of these processes would
allow further progress in the theoretical predictions of SM hadronic quantities
and in the search of New Physics.
