Lattice QCD calculation of $K\to \ell\nu_\ell \ell'^+ \ell'^-$ decay width

Understand

We develop a methodology for the computation of the $K\to \ell\nu_\ell \ell'^+ \ell'^-$ decay width using lattice QCD and present an exploratory study here.

• We use a scalar function method to account for the momentum dependence of the decay amplitude and adopt the infinite volume reconstruction method to reduce the systematic errors such as the temporal truncation effects and the finite-volume effects.
• We then perform a four-body phase-space integral to obtain the decay width.
• The only remaining technical problem is the possible power-law finite-volume effects associated with the process of $K\to\pi\pi \ell\nu_\ell\to \ell\nu_\ell \ell'^+ \ell'^-$, where the intermediate state involves multiple hadrons.