A team of researchers has presented the first complete lattice Quantum Chromodynamics (QCD) calculation of the four structure-dependent form factors governing the rare charged kaon decay $K^- \to \ell^- \bar{\nu}_\ell \ell'^+ \ell'^-$. This breakthrough provides Standard Model (SM) predictions from first principles for the decay rates and differential observables of all four possible channels, enabling a direct comparison with existing and future experimental measurements. Kaon decay is a fundamental process in particle physics that offers a window to test the validity of the Standard Model and search for potential deviations that may indicate new physics.

The calculation is based on gauge ensembles generated by the Extended Twisted Mass Collaboration (ETMC) with $N_f = 2+1+1$ flavors of twisted-mass Wilson-clover fermions. Simulations were performed directly at physical light and strange quark mass values, and included an estimate of disconnected quark contributions, where the virtual photon couples to sea quarks. The four form factors were determined across the entire kinematic region explored by experiments. To overcome the problem of analytic continuation for dilepton invariant masses above the two-pion threshold, the Spectral Function Reconstruction (SFR) method was employed.

Finite volume effects were investigated using ensembles with spatial extents $L\simeq [3.8,7.6]~\mathrm{fm}$, while the continuum limit was obtained from three lattice spacings in the range $a\in[0.057, 0.08]~\mathrm{fm}$. The obtained results, with fully controlled statistical and systematic uncertainties, are crucial for the evaluation of decay rates and differential observables for all four channels: $K^- \to e^- \bar{\nu}_e e^+ e^-$, $K^- \to e^- \bar{\nu}_e \mu^+ \mu^-$, $K^- \to \mu^- \bar{\nu}_\mu e^+ e^-$ and $K^- \to \mu^- \bar{\nu}_\mu \mu^+ \mu^-$. This work lays the foundation for a detailed phenomenological analysis of these decays, presented in a companion paper, and is essential for the experimental program searching for new physics through rare kaon decays.