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.
Highlights
The rare kaon decays K → πννhave attracted increasing interest during the past few decades
In this paper we report on a lattice QCD calculation of the long-distance contribution to the Kþ → πþννdecay amplitude at the near-physical pion mass mπ 1⁄4 170 MeV
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
Summary
The rare kaon decays K → πννhave attracted increasing interest during the past few decades. The current experimental value of the branching ratio, BrðKþ → πþννÞ 1⁄4 ð1.73þ−11..0155Þ × 10−10 [3], is a combined result based on the seven events collected by the E787 experiment at the Brookhaven National Laboratory [4,5,6,7] and its successor experiment E949 [3,8] This result can be compared to SM theoretical predictions such as that in Ref. Because of the small phase space available with these masses, the allowed momenta for the final-state particles are constrained to lie in a narrow region and provide little information on the momentum dependence of the decay amplitude. For this reason, we computed the amplitude in.
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