Kaon to Two Pion decay from Lattice QCD and CP violation

Abstract

Kaon to Two Pion decay from Lattice QCD and CP violation Daiqian Zhang We report a direct lattice calculation of the K to ππ (∆I = 1/2) decay amplitude A0 on a 32 × 64 ensemble, with 2+1 flavor Mobius Domain Wall Fermion, with a−1 = 1.379(9) GeV. This is a complete and physical calculation: chiral symmetry breaking is controlled by the Mobius Domain Wall formalism; pion and kaon masses are simulated at their nearphysical values, mK ≈ 490 MeV and mπ ≈ 140 MeV. G-parity boundary conditions are used to realize correct kinematics for the final two-pion state and give Eππ(I=0) ≈ 498 MeV, while keeping isospin symmetry; all 10 ∆S = 1 operators are considered, each of which involve the notorious disconnected diagrams. With this setup, we are able to resolve, for the first time, the physical decay amplitudes Re(A0) and Im(A0) from 0. The Re(A0) amplitude agrees with its experimental value, The result for Im(A0) is used, in combination with the lattice calculated decay amplitude A2, to compute Re( ′/ ), which evaluates to 1.38(5.08) × 10−4 and agrees at the 2σ level with the experimental value 1.66(0.23) × 10−3. This is a major step towards understanding and testing CP violation in the standard model. Several measurement techniques are used to increase computational efficiency. We use all-to-all propagators to construct finite sized mesons, which have a better overlap with the meson ground state and reducing statistical noise from the vacuum graphs. This also saves matrix-inversion overhead when constructing mesons with different momenta. The other technical improvements include the mixed-precision conjugate gradient algorithm, and optimized fast Fourier transformation. We also discuss the cross-checks on the use of G-parity boundary conditions, and estimate several important systematic errors.