Precision computation of the kaon bag parameter

Indirect CP violation in K rightarrow {pi}{pi} decays plays a central role in constraining the flavor structure of the Standard Model (SM) and in the search for new physics. For many years the leading uncertainty in the SM prediction of this phenomenon was the one associated with the nonperturbative strong interaction dynamics in this process. Here we present a fully controlled lattice QCD calculation of these effects, which are described by the neutral kaon mixing parameter B_K . We use a two step HEX smeared clover-improved Wilson action, with four lattice spacings from aapprox0.054 fm to aapprox0.093 fm and pion masses at and even below the physical value. Nonperturbative renormalization is performed in the RI-MOM scheme, where we find that operator mixing induced by chiral symmetry breaking is very small. Using fully nonperturbative continuum running, we obtain our main result B_K^{RI}(3.5GeV)=0.531(6)_{stat}(2)_{sys}. A perturbative 2-loop conversion yields B_K^{MSbar-NDR}(2GeV)=0.564(6)_{stat}(3)_{sys}(6)_{PT}, which is in good agreement with current results from fits to experimental data.

The Kaon Bag Parameter at Physical Mass

We present preliminary results for the calculation of the Kaon Bag parameter $B_K$ in $N_f=2+1$ lattice QCD, using Mobius 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.

Kaon $B$-parameters for Generic $Delta S=2$ Four-Quark Operators in Quenched Domain Wall QCD

We present a study of $B$-parameters for generic $Delta S=2$ four-quark operators in domain wall QCD. Our calculation covers all the $B$-parameters required to study the neutral kaon mixing in the standard model (SM) and beyond it. We evaluate one-loop renormalization factors of the operators employing the plaquette and Iwasaki gauge actions. Numerical simulations are carried out in quenched QCD with both gauge actions on $16^3times 32times 16$ and $24^3times 32times 16$ at the lattice spacing $1/aapprox 2$GeV. We investigate the relative magnitudes of the non-SM $B$-parameters to the SM one, which are compared with the previous results obtained with the overlap and the clover quark actions.

Lattice QCD Calculation of the Kaon B-parameter with the Wilson Quark Action

The kaon B parameter is calculated in quenched lattice QCD with the Wilson quark action. The mixing problem of the Delta s=2 four-quark operators is solved non-perturbatively with full use of chiral Ward identities, and this method enables us to construct the weak four-quark operators exhibiting good chiral behavior. We find B_K(NDR, 2GeV)=0.562(64) in the continuum limit, which agrees with the value obtained with the Kogut-Susskind quark action.

The Kaon B-parameter with the Wilson Quark Action using Chiral Ward Identities

A lattice QCD calculation of the kaon $B$ parameter $B_K$ is carried out with the Wilson quark action in the quenched approximation at $beta=6/g^2=5.9-6.5$. The mixing problem of the $Delta s=2$ four-quark operators is solved non-perturbatively with full use of chiral Ward identities employing four external quarks with an equal off-shell momentum in the Landau gauge. This method, without invoking any effective theory, enables us to construct the weak four-quark operators exhibiting good chiral behavior. Our results for $B_K$ with the non-perturbative mixing coefficients show small scaling violation beyond the lattice cut-off $a^{-1}sim 2.5 $GeV. Our estimate concludes $B_K(NDR, 2 GeV)=0.69(7)$ at $a^{-1}=2.7-4.3$GeV, which agrees with the value obtained with the Kogut-Susskind quark action. For comparison we also calculate $B_K$ with one-loop perturbative mixing coefficients. While this yields incorrect values at finite lattice spacing, a linear extrapolation to the continuum limit as a function of $a$ leads to a result consistent with those obtained with the Ward identity method.