The Kaon Bag Parameter at Physical Mass

Abstract

We present preliminary results for the calculation of the Kaon Bag parameter B K in N f = 2 + 1 lattice QCD, using Möbius Domain Wall Fermion ensembles generated by the RBC-UKQCD collaboration. This computation is done directly at physical meson masses, so that we do not have to rely on chiral perturbation theory or any other mass extrapolation. In parallel, the four-quark operator is renormalised through the Rome-Southampton technique. Finally, we compare our value with previous results and draw some conclusions about the remaining dominant contributions in our error budget.

Upper bounds on ε′/ε parameters B 6 (1/2) and B 8 (3/2) from large N QCD and other news

“…See also the recent analyses in [30,31]. While this result violates the bound in (8), it should be noted that a number of lattice groups among [24][25][26][27][28][29] published results with central values satisfying the bound in (8) but the errors did not allow for a clear cut conclusion.…”

“…Had the ∆S = 2 matrix element in (5) been normalized relative to its large N value, the most preciseB K parameter extracted from lattice QCD in (10) would readB K = 1.021 ± 0.013 nowadays and our result in (9)B K = 0.97 ± 0.03. In [34,41], B 6 and B 8 were also normalized with respect to the VIA as in (30).…”

Heavy Flavour Physics Review

“…Four results [22, 99 -101] enter the FLAG-2 average for N f = 2 + 1, which is quoted with an uncertainty of 1.3%, while one result [102] enters the average for N f = 2. Three new results were reported at this conference, two for N f = 2 + 1 [103,104] and one for N f = 2 + 1 + 1 [105]. The first result from physical-mass ensembles was obtained by the BMW collaboration [101].…”

“…It is the most precise result forB K to date with a quoted uncertainty of 1.5% and therefore dominates the N f = 2 + 1 FLAG-2 average. A calculation ofB K on RBC/UKQCD's new physical mass ensembles was presented at this conference [104] with a 2.1% uncertainty. The effort of the lattice community to calculateB K has already paid off, since its contribution to the ε K error budget ranks third, behind the parametric V cb uncertainty and also behind the uncertainty on the short-distance Wilson coefficient (η cc ) calculated at NNLO in perturbative QCD.…”

“…The first results with physical-mass sea pions were presented by the PACS-CS collaboration [19] with N f = 2 + 1 nonperturbatively improved Wilson flavors on a relatively small (L 2 fm) spatial volume. Since then the BMW [20], MILC [21], and the RBC/UKQCD [22,104] collaborations have generated ensembles with N f ≥ 2 + 1 with physical-mass sea pions on large spatial volumes. Other collaborations also have plans for (or are in the process of) generating ensembles at the physical point.…”