We present high statistics results for the isovector charges g u−dA , g u−dS and g u−dT of the nucleon. Calculations were carried out on eleven ensembles of gauge configurations generated by the MILC collaboration using highly improved staggered quarks action with 2 þ 1 þ 1 dynamical flavors. These ensembles span four lattice spacings a ≈ 0.06, 0.09, 0.12 and 0.15 fm and light-quark masses corresponding to M π ≈ 135, 225 and 315 MeV. Excited-state contamination in the nucleon three-point correlation functions is controlled by including up to three-states in the spectral decomposition. Remaining systematic uncertainties associated with lattice discretization, lattice volume and light-quark masses are controlled using a simultaneous fit in these three variables. Our final estimates of the isovector charges in the MS scheme at 2 GeV are T with precision low-energy nuclear experiments, and find them comparable to those from the ATLAS and the CMS experiments at the LHC.

We report the Standard Model evaluation of the indirect CP violation parameter εK using inputs determined from lattice QCD: the kaon bag parameterBK , ξ0, |Vus| from the K 3 and Kµ2 decays, and |V cb | from the axial current form factor for the exclusive decayB → D * ν at zero-recoil. The theoretical expression for εK is thoroughly reviewed to give an estimate of the size of the neglected corrections, including long distance effects. The Wolfenstein parametrization (|V cb |, λ,ρ,η) is adopted for CKM matrix elements which enter through the short distance contribution of the box diagrams. For the central value, we take the Unitarity Triangle apex (ρ,η) from the angle-only fit of the UTfit collaboration and use Vus as an independent input to fix λ. We find that the Standard Model prediction of εK with exclusive V cb (lattice QCD results) is lower than the experimental value by 3.4σ. However, with inclusive V cb (results of the heavy quark expansion), there is no gap between the Standard Model prediction of εK and its experimental value. For the calculation of εK , we perform the renormalization group running to obtain ηcc at next-to-next-to-leading-order; we find η NNLO cc = 1.72(27).

We present results for the form factors of the isovector axial vector current in the nucleon state using large scale simulations of lattice QCD. The calculations were done using eight ensembles of gauge configurations generated by the MILC collaboration using the HISQ action with 2+1+1 dynamical flavors. These ensembles span three lattice spacings a ≈ 0.06, 0.09 and 0.12 fm and light-quark masses corresponding to the pion masses Mπ ≈ 135, 225 and 310 MeV. High-statistics estimates allow us to quantify systematic uncertainties in the extraction of GA(Q 2 ) and the induced pseudoscalar form factorGP (Q 2 ). We perform a simultaneous extrapolation in the lattice spacing, lattice volume and light-quark masses of the axial charge radius rA data to obtain physical estimates. Using the dipole ansatz to fit the Q 2 behavior we obtain rA| dipole = 0.49(3) fm, which corresponds to MA = 1.39(9) GeV, and is consistent with MA = 1.35(17) GeV obtained by the miniBooNE collaboration. The estimate obtained using the z-expansion is rA|z−expansion = 0.46(6) fm, and the combined result is rA| combined = 0.48(4) fm. Analysis of the induced pseudoscalar form factor GP (Q 2 ) yields low estimates for g * P and gπNN compared to their phenomenological values. To understand these, we analyze the partially conserved axial current (PCAC) relation by also calculating the pseudoscalar form factor. We find that these low values are due to large deviations in the PCAC relation between the three form factors and from the pion-pole dominance hypothesis.

Previous lattice QCD calculations of axial vector and pseudoscalar form factors show significant deviation from the partially conserved axial current (PCAC) relation between them. Since the original correlation functions satisfy PCAC, the observed deviations from the operator identity cast doubt on whether all of the systematics in the extraction of form factors from the correlation functions are under control. We identify the problematic systematic as a missed excited state, whose energy as a function of the momentum transfer squared Q 2 is determined from the analysis of the three-point functions themselves. Its energy is much smaller than those of the excited states previously considered, and including it impacts the extraction of all of the ground state matrix elements. The form factors extracted using these mass and energy gaps satisfy PCAC and another consistency condition, and they validate the pion-pole dominance hypothesis. We also show that the extraction of the axial charge g A is very sensitive to the value of the mass gaps of the excited states used, and current lattice data do not provide an unambiguous determination of these, unlike the Q 2 ≠ 0 case. To highlight the differences and improvement between the conventional vs the new analysis strategy, we present a comparison of results obtained on a physical pion mass ensemble at a ≈ 0.0871 fm. With the new strategy, we find g A ¼ 1.30ð6Þ and axial charge radius r A ¼ 0.74ð6Þ fm, both extracted using the z expansion to parametrize the Q 2 behavior of G A ðQ 2 Þ, and g à P ¼ 8.06ð44Þ, obtained using the pion-pole dominance ansatz to fit the Q 2 behavior of the induced pseudoscalar form factor G P ðQ 2 Þ. These results are consistent with current phenomenological values.

We present results for kaon mixing parameter BK calculated using HYP-smeared improved staggered fermions on the MILC asqtad lattices. We use three lattice spacings (a ≈ 0.12, 0.09 and 0.06 fm), ten different valence quark masses (m ≈ ms/10 − ms), and several light sea-quark masses in order to control the continuum and chiral extrapolations. We derive the next-to-leading order staggered chiral perturbation theory (SChPT) results necessary to fit our data, and use these results to do extrapolations based both on SU(2) and SU(3) SChPT. The SU(2) fitting is particularly straightforward because parameters related to taste-breaking and matching errors appear only at next-to-next-to-leading order. We match to the continuum renormalization scheme (NDR) using one-loop perturbation theory. Our final result is from the SU(2) analysis, with the SU(3) result providing a (less accurate) cross check. We find BK (NDR, µ = 2 GeV) = 0.529 ± 0.009 ± 0.032 and BK = BK (RGI) = 0.724 ± 0.012 ± 0.043, where the first error is statistical and the second systematic. The error is dominated by the truncation error in the matching factor. Our results are consistent with those obtained using valence domain-wall fermions on lattices generated with asqtad or domain-wall sea quarks.