# Exploratory Lattice QCD Study of the Rare Kaon Decay $K^+\to\pi^+\nu\bar{\nu}$

## TL;DR

This paper presents the first complete lattice QCD calculation of the long-distance contribution to the rare kaon decay $K^+ o \pi^+
u ar{
u}$ within the standard model, addressing key technical challenges.

## Contribution

It demonstrates that lattice methods can compute the long-distance effects in this decay, overcoming divergence, unphysical terms, and finite-volume issues.

## Key findings

- Long-distance contribution can be computed using lattice QCD.
- Technical difficulties such as divergence and unphysical terms can be addressed.
- Next-generation computing will enable calculations with physical quark masses.

## Abstract

We report a first, complete lattice QCD calculation of the long-distance contribution to the $K^+\to\pi^+\nu\bar{\nu}$ decay within the standard model. This is a second-order weak process involving two four-Fermi operators that is highly sensitive to new physics and being studied by the NA62 experiment at CERN. While much of this decay comes from perturbative, short-distance physics there is a long-distance part, perhaps as large as the planned experimental error, which involves nonperturbative phenomena. The calculation presented here, with unphysical quark masses, demonstrates that this contribution can be computed using lattice methods by overcoming three technical difficulties: (i) a short-distance divergence that results when the two weak operators approach each other, (ii) exponentially growing, unphysical terms that appear in Euclidean, second-order perturbation theory, and (iii) potentially large finite-volume effects. A follow-on calculation with physical quark masses and controlled systematic errors will be possible with the next generation of computers.