$K_{\rm L}\rightarrow\mu^+\mu^-$ from lattice QCD

TL;DR

This paper introduces a lattice QCD framework to compute the long-distance two-photon contribution to the rare decay $K_L ightarrow \mu^+\mu^-$, aiming to improve theoretical predictions and compare with experimental results.

Contribution

It presents a novel lattice-QCD approach for calculating the long-distance effects in $K_L$ decay, with preliminary results at physical pion mass and controlled systematic errors.

Findings

Preliminary numerical results on quark-connected diagrams.

Method shows promise for first-principles determination of dispersive contributions.

Framework enables comparison between Standard Model predictions and experimental data.

Abstract

We propose a lattice-QCD-suitable framework for computing the two-photon long-distance contribution to the complex $K_{\rm L}\rightarrow\mu^+\mu^-$ 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.