Lattice QCD calculation of K → lνll′+l′- decay width

We develop a methodology for the computation of the K -> l nu(l)l '(+)l '(-) 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 -> pi pi l nu(l)( )-> l nu(l)l '(+)l '(-) , where the intermediate state involves multiple hadrons. In this work, we use a gauge ensemble of a twisted-mass fermion with a pion mass m(pi) = 352 MeV and a nearly physical kaon mass. At this kinematics, the pi pi in the intermediate state cannot be on shell simultaneously, as 2m(pi) > m(K), and the finite-volume effects associated with the pi pi state are exponentially suppressed. Using the developed methods mentioned above, we calculate the branching ratios for four channels of K -> l nu(l)l '(+)l '(-) , and obtain the results comparable to the experimental measurements and ChPT predictions. Our work demonstrates the capability of lattice QCD to improve the Standard Model prediction in the K -> l nu(l)l '(+)l '(-) decay width.

Automated summary

We develop a methodology using lattice QCD to compute the decay width of K -> l nu(l)l '(+)l '(-) and present an exploratory study. By employing the scalar function method and the infinite-volume reconstruction method, we consider the momentum dependence of the decay amplitude and reduce systematic errors. Our results show the potential of lattice QCD in improving the Standard Model prediction for the K -> l nu(l)l '(+)l '(-) decay width.