K→(ππ)I=2Decay Amplitude from Lattice QCD

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 ǫ ′ /ǫ, 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 ǫ ′ (the so-called Electroweak Penguin, EWP, contribution) is Re(ǫ ′ /ǫ)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.

K→ππΔI=3/2decay amplitude in the

“…These results were obtained from two ensembles generated at physical quark masses (in the isospin limit) with inverse lattice spacings a −1 = 1.728(4) GeV and 2.358(7) GeV. We are therefore able to perform a continuum extrapolation and hence largely to remove the dominant systematic uncertainty from our earlier results [1,2], that due to lattice artifacts. The only previous lattice computation of K → ππ decays at physical kinematics was performed using an ensemble at a single, rather coarse, value of the lattice spacing [a −1 ≃ 1.37(1) GeV].…”

“…In [1,2] we reported on the first results from a lattice determination of the amplitude A 2 for K → (ππ) I=2 decays, where I is the total isospin of the two-pion final state:…”

Kenneth Wilson and Lattice QCD

“…The RBC Collaboration has developed applications of the domain-wall formulation of QCD having chiral symmetry. It has succeeded in calculating the I = 2 amplitude for the physical pion mass [105]. Their result, obtained at a lattice spacing of a ≈ 0.14 fm, is given by…”

Multi-Hadron Observables from Lattice Quantum Chromodynamics

“…8 A full-error-budget calculation is now being implemented by the RBC/UKQCD collaboration [88,89,90]. The methodology is fully in place, results for the I = 2 final state with a complete error budget are available [91], and complete results for the more challenging I = 0 final states should become available in the next few years. At that stage we will finally learn whether and in what manner QCD can explain the ∆I = 1/2 rule and the observed CP-violation 9 rate in K → ππ decays.…”

“…See Refs. [193,194,195,88] for recent examples of the implementation of this formalism on LQCD calculations of the K → ππ decay amplitude. 4 .…”