No 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.

We present physical results for a variety of light hadronic quantities obtained via a combined analysis of three 2+1 flavour domain wall fermion ensemble sets. For two of our ensemble sets we used the Iwasaki gauge action with β = 2.13 (a −1 = 1.75(4) GeV) and β = 2.25 (a −1 = 2.31(4) We also obtain values for the SU(2) chiral perturbation theory effective couplings,l 3 = 2.91(23) stat (7) sys andl 4 = 3.99(16) stat (9) sys .GeV3

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

We determine the charm and strange quark masses in the MS scheme, using n f = 2 + 1 + 1 lattice QCD calculations with highly improved staggered quarks (HISQ) and the RI-SMOM intermediate scheme to connect the bare lattice quark masses to continuum renormalisation schemes. Our study covers analysis of systematic uncertainties from this method, including nonperturbative artefacts and the impact of the non-zero physical sea quark masses. We find m MS c (3 GeV) = 0.9896(61) GeV and m MS s (3 GeV) = 0.08536(85) GeV, where the uncertainties are dominated by the tuning of the bare lattice quark masses. These results are consistent with, and of similar accuracy to, those using the current-current correlator approach coupled to high-order continuum QCD perturbation theory, implemented in the same quark formalism and on the same gauge field configurations. This provides a strong test of the consistency of methods for determining the quark masses to high precision from lattice QCD. We also give updated lattice QCD world averages for c and s quark masses.arXiv:1805.06225v1 [hep-lat]