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The CKM matrix element $|V_{us}|$ can be extracted from the experimental measurement of semileptonic $Ktopi$ decays. The determination depends on theory input for the corresponding vector form factor in QCD. We present a preliminary update on our efforts to compute it in $N_f=2+1$ lattice QCD using domain wall fermions for several lattice spacings and with a lightest pion mass of about $170,mathrm{MeV}$. By using partially twisted boundary conditions we avoid systematic errors associated with an interpolation of the form factor in momentum-transfer, while simulated pion masses near the physical point reduce the systematic error due to the chiral extrapolation.
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We present a new calculation of the K->pi semileptonic form factor at zero momentum transfer in domain wall lattice QCD with Nf=2+1 dynamical quark flavours. By using partially twisted boundary conditions we simulate directly at the phenomenologically relevant point of zero momentum transfer. We perform a joint analysis for all available ensembles which include three different lattice spacings (a=0.09-0.14fm), large physical volumes (m_pi*L>3.9) and pion masses as low as 171 MeV. The comprehensive set of simulation points allows for a detailed study of systematic effects leading to the prediction f+(0)=0.9670(20)(+18/-46), where the first error is statistical and the second error systematic. The result allows us to extract the CKM-matrix element |Vus|=0.2237(+13/-8) and confirm first-row CKM-unitarity in the Standard Model at the sub per mille level.
We discuss the reduction of errors in the calculation of the form factor $f_+^{K pi}(0)$ with HISQ fermions on the $N_f=2+1+1$ MILC configurations from increased statistics on some key ensembles, new data on ensembles with lattice spacings down to 0.042 fm and the study of finite-volume effects within staggered ChPT. We also study the implications for the unitarity of the CKM matrix in the first row and for current tensions with leptonic determinations of $vert V_{us}vert$.
We present new preliminary results for bag parameters and ratios of the BSM kaon mixing operators measured at the physical point. The results are obtained from simulations of domain wall fermion QCD with 2+1 flavours with an Iwasaki gauge, and now include pion and kaon masses very close to the physical point. We compare these results to our collaborations previous results obtained from heavier simulated quarks.
We present a lattice QCD calculation of the axial $gamma W$-box diagrams relevant for the kaon semileptonic decays. We utilize a recently proposed method, which connects the electroweak radiative corrections in Sirlins representation to that in chiral perturbation theory. It allows us to use the axial $gamma W$-box correction in the SU(3) limit to obtain the low energy constants for chiral perturbation theory. From first principles our results confirm the previously used low energy constants provided by the minimal resonance model with a significant reduction in uncertainties.
The nucleon($N$)-Omega($Omega$) system in the S-wave and spin-2 channel ($^5$S$_2$) is studied from the (2+1)-flavor lattice QCD with nearly physical quark masses ($m_pi simeq 146$~MeV and $m_K simeq 525$~MeV). The time-dependent HAL QCD method is employed to convert the lattice QCD data of the two-baryon correlation function to the baryon-baryon potential and eventually to the scattering observables. The $NOmega$($^5$S$_2$) potential, obtained under the assumption that its couplings to the D-wave octet-baryon pairs are small, is found to be attractive in all distances and to produce a quasi-bound state near unitarity: In this channel, the scattering length, the effective range and the binding energy from QCD alone read $a_0= 5.30(0.44)(^{+0.16}_{-0.01})$~fm, $r_{rm eff} = 1.26(0.01)(^{+0.02}_{-0.01})$~fm, $B = 1.54(0.30)(^{+0.04}_{-0.10})$~MeV, respectively. Including the extra Coulomb attraction, the binding energy of $pOmega^-$($^5$S$_2$) becomes $B_{pOmega^-} = 2.46(0.34)(^{+0.04}_{-0.11})$~MeV. Such a spin-2 $pOmega^-$ state could be searched through two-particle correlations in $p$-$p$, $p$-nucleus and nucleus-nucleus collisions.
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