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

17 pages, 6 figures

References in corpus (2)

• Two-Loop Electroweak Corrections for the K -> pi nu anti-nu Decays
• Electroweak Corrections to the Charm Quark Contribution to K+ -> pi+ nu nu-bar

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