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

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 ($m_c^{\overline{\mathrm{MS}}}(\text{mbox}3GeV)=750$ 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.

Comments: 17 pages, 6 figures