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Register a new userProgress in kaon physics on the lattice
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Andreas Juttner
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CKM-unitarity, direct and indirect CP-violation and the Delta I=1/2 rule in full lattice QCD are the focus of this talk. To this end I will discuss and compare recent lattice results for leptonic, semi-leptonic and non-leptonic decays of the kaon and neutral kaon mixing and I will motivate current best estimates f_K/f_pi=1.198(10), f_+^{Kpi}(0)=0.964(5) and hat{B}_K=0.720(39). Moreover new theoretical advances that will improve the quality of these computations in the future will be discussed.
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I critically review recent lattice QCD results relevant for kaon phenomenology, as well as the methods that are used to obtain them. The focus is on calculations with N_f=2 and N_f=2+1 flavors of sea quarks. Concerning methodology, the subjects covered include a discussion of how best to extrapolate and/or interpolate results to the physical quark-mass point, a scheme for assessing the extent to which a lattice QCD calculation includes the various effects required to compute a given quantity reliably and a procedure for averaging lattice results. The phenomenological topics that I review comprise leptonic and semileptonic kaon decays, as well as neutral kaon mixing and CP violation in K->pipi decays.
This talk reviews recent lattice QCD simulations of the K->pi semi-leptonic form factor.
Recent Lattice QCD results relevant for Kaon, Charm and B Physics are summarized. There is general agreement among calculations using a wide range of different lattice actions. This bolsters confidence in the lattice results and in their quoted errors. One notes considerable progress since CKM2008 in reducing lattice errors with some quantities now being calculated at the subpercent to a few percent level accuracy. Much work remains, however, and further improvements can be expected in the coming years.
We present the first lattice-QCD calculation of the kaon valence-quark distribution functions using the large-momentum effective theory (LaMET) approach. The calculation is performed with multiple pion masses with the lightest one around 220 MeV, 2 lattice spacings $a=0.06$ and 0.12 fm, $(M_pi)_text{min} L approx 5.5$, and high statistics ranging from 11,600 to 61,312 measurements. We also calculate the valence-quark distribution of pion and find it to be consistent with the FNAL E615 experimental results, and our ratio of the $u$ quark PDF in the kaon to that in the pion agrees with the CERN NA3 experiment. We also make predictions of the strange-quark distribution of the kaon.
We present a lattice calculation of the electromagnetic (EM) effects on the masses of light pseudoscalar mesons. The simulations employ 2+1 dynamical flavors of asqtad QCD quarks, and quenched photons. Lattice spacings vary from $approx 0.12$ fm to $approx 0.045$ fm. We compute the quantity $epsilon$, which parameterizes the corrections to Dashens theorem for the $K^+$-$K^0$ EM mass splitting, as well as $epsilon_{K^0}$, which parameterizes the EM contribution to the mass of the $K^0$ itself. An extension of the nonperturbative EM renormalization scheme introduced by the BMW group is used in separating EM effects from isospin-violating quark mass effects. We correct for leading finite-volume effects in our realization of lattice electrodynamics in chiral perturbation theory, and remaining finite-volume errors are relatively small. While electroquenched effects are under control for $epsilon$, they are estimated only qualitatively for $epsilon_{K^0}$, and constitute one of the largest sources of uncertainty for that quantity. We find $epsilon = 0.78(1)_{rm stat}({}^{+phantom{1}8}_{-11})_{rm syst}$ and $epsilon_{K^0}=0.035(3)_{rm stat}(20)_{rm syst}$. We then use these results on 2+1+1 flavor pure QCD HISQ ensembles and find $m_u/m_d = 0.4529(48)_{rm stat}( {}_{-phantom{1}67}^{+150})_{rm syst}$.
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