Lattice QCD study of the rare kaon decay $K^+\to\pi^+\nu\bar{\nu}$ at a near-physical pion mass

TL;DR

This study uses lattice QCD to estimate the long-distance effects in the rare kaon decay $K^+ o ext{pi}^+ uar{ u}$ at near-physical pion mass, providing insights relevant for new physics searches.

Contribution

It presents the first lattice QCD calculation of the long-distance contribution to this decay at near-physical pion mass, analyzing momentum dependence and two-pion intermediate state effects.

Findings

The amplitude's momentum dependence is very mild.

Two-pion intermediate state contribution is less than 1%.

Finite-volume effects are negligible.

Abstract

The rare kaon decay $K^+\to\pi^+\nu\bar{\nu}$ is an ideal process in which to search for signs of new physics and is the primary goal of the NA62 experiment at CERN. In this paper we report on a lattice QCD calculation of the long-distance contribution to the $K^+\to\pi^+\nu\bar{\nu}$ decay amplitude at the near-physical pion mass $m_\pi=170$ MeV. The calculations are however, performed on a coarse lattice and hence with a lighter charm quark mass ($m_c^{\bar{\mathrm{MS}}}(\mbox{3 GeV})=750$ MeV) than the physical one. The main aims of this study are two-fold. Firstly we study the momentum dependence of the amplitude and conclude that it is very mild so that a computation at physical masses even at a single kinematic point would provide a good estimate of the long-distance contribution to the decay rate. Secondly we compute the contribution to the branching ratio from the two-pion intermediate state whose energy is below the kaon mass and find that it is less than 1% after its exponentially growing unphysical contribution has been removed and that the corresponding non-exponential finite-volume effects are negligibly small.