K → (ππ)_I=2 decay amplitude from lattice QCD

Blum, T., Boyle, P., Christ, N., Garron, N., Goode, E., Izubuchi, T., Jung, C., Kelly, C., Lehner, C., Lightman, M., Liu, Q., Lytle, A., Mawhinney, R., Sachrajda, C., Soni, A. and Sturm, C. (2012) K → (ππ)_I=2 decay amplitude from lattice QCD. Physical Review Letters, 108 (14), 141601-1-141601-5. (doi:10.1103/PhysRevLett.108.141601).

Abstract

We report on the first realistic ab initio calculation of a hadronic weak decay, that of the amplitude A₂ for a kaon to decay into two π mesons with isospin 2. We find Re A₂ = (1.436±0.063_stat±0.258_syst)10^-8 GeV in good agreement with the experimental result and for the hitherto unknown imaginary part we find Im A₂ = -(6.83±0.51_stat±1.30_syst)10^-13 GeV. Moreover combining our result for Im A₂ with experimental values of Re A₂, Re A₀, and ε'/ε, we obtain the following value for the unknown ratio Im A₀/Re A₀ within the standard model: Im A₀/Re A₀ = -1.63(19)_stat(20)_syst×10^-4. One consequence of these results is that the contribution from Im A₂ to the direct CP violation parameter ε' (the so-called Electroweak Penguin contribution) is Re(ε'/ε)_EWP = -(6.52±0.49_stat±1.24_syst)×10^-4. We explain why this calculation of A₂ represents a major milestone for lattice QCD and discuss the exciting prospects for a full quantitative understanding of CP violation in kaon decays.

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