Prospects for a lattice computation of rare kaon decay amplitudes II $K\to\pi\nu\bar{\nu}$ decays

TL;DR

This paper explores the potential of lattice QCD to accurately compute long-distance contributions to the rare kaon decay $K^+ o ext{ extmu}^+ uar{ ext{ extmu}}$, aiming to improve standard model predictions for these suppressed processes.

Contribution

It demonstrates a methodology for calculating long-distance effects in $K o ext{ extmu} uar{ ext{ extmu}}$ decays using lattice QCD, including $W$-$W$ and $Z$-exchange diagrams, with strategies to combine with short-distance calculations.

Findings

Feasibility of lattice QCD for long-distance contributions shown

Methods to estimate finite-volume and power-law corrections developed

Framework for combining lattice and perturbative results established

Abstract

The rare kaon decays $K\to\pi\nu\bar{\nu}$ are strongly suppressed in the standard model and widely regarded as processes in which new phenomena, not predicted by the standard model, may be observed. Recognizing such new phenomena requires precise standard model prediction for the braching ratio of $K\to\pi\nu\bar{\nu}$ with controlled uncertainty for both short-distance and long-distance contributions. In this work we demonstrate the feasibility of lattice QCD calculation of the long-distance contribution to rare kaon decays with the emphasis on $K^+\to\pi^+\nu\bar{\nu}$. Our methodology covers the calculation of both $W$-$W$ and $Z$-exchange diagrams. We discuss the estimation of the power-law, finite-volume corrections and two methods to consistently combine the long distance contribution determined by the lattice methods outlined here with the short distance parts that can be reliably determined using perturbation theory. It is a subsequent work of our first methodology paper on $K\to\pi\ell^+\ell^-$, where the focus was made on the $\gamma$-exchange diagrams.