We develop a methodology for the computation of the K→ℓνℓℓ′+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→ππℓνℓ→ℓνℓℓ′+ℓ′−, where the intermediate state involves multiple hadrons. In this work, we use a gauge ensemble of twisted mass fermion with a pion mass mπ=352 MeV and a nearly-physical kaon mass. At this kinematics, the ππ in the intermediate state cannot be on shell simultaneously as 2mπ>mK and the finite-volume effects associated with ππ state are exponentially suppressed. Using the developed methods mentioned above, we calculate the branching ratios for four channels of K→ℓνℓℓ′+ℓ′−, and obtain the results comparable to the experimental measurements and ChPT predictions. Our work demonstrates the capability of lattice QCD to improve Standard Model prediction in K→ℓνℓℓ′+ℓ′− decay width.
@article{arxiv.2103.11331,
title = {Lattice QCD calculation of $K\to \ell\nu_\ell \ell'^+ \ell'^-$ decay width},
author = {Xin-Yu Tuo and Xu Feng and Lu-Chang Jin and Teng Wang},
journal= {arXiv preprint arXiv:2103.11331},
year = {2022}
}