Speaker
Description
We present preliminary results for $K \to l \nu_l l'^+ l'^-$ decays, which are mediated by an off-shell $W$ boson and a virtual photon. These decays are suppressed in the Standard Model since their rates start at $\mathcal{O}(\alpha_{em}^2)$, making them very interesting in the search for new physics.
We compute the four form factors needed to describe the structure-dependent part of the decay amplitudes using the $N_f=2+1+1$ gauge ensembles generated by the Extended Twisted Mass Collaboration (ETMC) at the pion physical point.
We choose several values of both the momentum and the virtuality of the photon $k^2$ to cover all the allowed kinematic range. In the region above the two-pion threshold ($k^2 > 4 m_{\pi}^2$), where issues related to the analytic continuation are present, we reconstruct the form factors employing the so-called HLT method.
As a byproduct of our analysis, we reassess the form factors entering $K \to l \nu_l \gamma$.
