$K_{\mathrm{L}}\to {\mu }^{+}{\mu }^{-}$ from lattice QCD

Abstract

We propose a lattice-QCD-suitable framework for computing the two-photon long-distance contribution to the complex $K_{\mathrm{L}}\to {\mu }^{+}{\mu }^{-}$ decay amplitude, where QED is treated perturbatively in the continuum and infinite-volume. We provide preliminary numerical results on the quark-connected diagrams on one ensemble at physical pion mass from this method, with well-controlled systematic errors. The successful application of this method will allow the determination of the dispersive part of the aforementioned contribution from first-principles and enable a meaningful comparison between the Standard-Model prediction and experiment.

Comments: contribution to the 40th International Symposium on Lattice Field Theory, Lattice 2023, Fermi National Accelerator Laboratory; references added