Lattice determination of theK→(ππ)I=2decay amplitudeA2

Abstract

We describe the computation of the amplitude A 2 for a kaon to decay into two pions with isospin I = 2. The results presented in the letter [1] from an analysis of 63 gluon configurations are updated to 146 configurations giving Re A 2 = 1.381(46) stat (258) syst 10 −8 GeV and Im A 2 = −6.54(46) stat (120) syst 10 −13 GeV . Re A 2 is in good agreement with the experimental result, whereas the value of Im A 2 was hitherto unknown. We are also working towards a direct computation of the K → (ππ) I=0 amplitude A 0 but, within the standard model, our result for Im A 2 can be combined with the experimental results for Re A 0 , Re A 2 and ε /ε to give Im A 0 /Re A 0 = −1.61(28) × 10 −4 . Our result for Im A 2 implies that the electroweak penguin (EWP) contribution to ε /ε is Re(ε /ε) EWP = −(6.25 ± 0.44 stat ± 1.19 syst ) × 10 −4 . 2

K→ππΔI=3/2decay amplitude in the

“…Below we will confirm the feature found in our earlier work [1,2] that the dominant contribution to Re(A 2 ) comes from the (27,1) operator, while the dominant contribution to Im(A 2 ) in the MS scheme at 3 GeV comes from the (8, 8) mx operator. We can now write the expressions for the A 2 amplitude, which are…”

“…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:…”

“…(1) This was the first quantitative calculation of an amplitude for a realistic hadronic weak decay and hence extended the framework of lattice simulations into the important domain of nonleptonic weak decays. As explained in the Introduction of [2], in order to obtain the result in Eq. (1) it was necessary to overcome a number of theoretical problems and exploit recent improvements in algorithms and the opportunities provided by increases in computing resources.…”

“…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].…”

Anomalous triple gauge couplings from B-meson and kaon observables

“…While there is at present no reliable result for R 6 , lattice QCD calculations of R 8 have matured in recent years [59] and provide the value R 8 0.83 [60]. Anticipating further progress in the lattice QCD calculations of the hadronic parameters R 6 and R 8 , a full SM calculation of / with a total uncertainty of 20% may be possible in the near future (see section X.3.2.1 of [34]).…”