Abstract
Standard lattice calculations in kaon physics are based on the evaluation of matrix elements of local operators between two single-hadron states or a single-hadron state and the vacuum. Recent progress in lattice QCD has gone beyond these standard observables. I will review the status and prospects of lattice kaon physics with an emphasis on non-leptonic K → ππ decay and long-distance processes including K0-K0 mixing and rare kaon decays.
Highlights
Since the discovery of kaons, the kaon physics plays a key role in the building of the Standard Model
Rare kaon decays including K → πννand K → π + − belong to this category. As these transitions proceed via the second-order weak interaction, the calculations would involve the construction of 4-point correlation function and the treatment of nonlocal matrix elements with two effective operator insertions
The worldwide lattice QCD community has developed a successful kaon physics program. It inspires the consideration of constructing a CKM unitarity triangle purely from kaon physics [76]
Summary
Since the discovery of kaons, the kaon physics plays a key role in the building of the Standard Model. Lattice QCD has been successful for the calculations of the observables such as the pion and kaon decay constants fK± π± , the K → π ν semileptonic form factor f+(0) and the neutral kaon mixing parameter BK. Rare kaon decays including K → πννand K → π + − belong to this category As these transitions proceed via the second-order weak interaction, the calculations would involve the construction of 4-point correlation function and the treatment of nonlocal matrix elements with two effective operator insertions. In the second part of this report, I will review the lattice calculations of non-standard observables such as K → ππ decay, K0-K0 mixing and rare kaon decays, presenting both recently-updated lattice results and the newlydeveloped lattice methodology
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