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

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Summary

INTRODUCTION

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.

DETAILS OF THE LATTICE CALCULATION
MOMENTUM DEPENDENCE OF THE AMPLITUDE
CONTRIBUTION OF THE TWO-PION INTERMEDIATE STATE
SUMMARY AND CONCLUSIONS
Findings
Contribution from ππ intermediate states
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