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Register a new userKaon physics: a lattice perspective
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Laurent Lellouch
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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.
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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.
We study the KN interactions in the I(J^{pi})=0(1/2^-) and 1(1/2^-) channels and associated exotic state Theta^+ from 2+1 flavor full lattice QCD simulation for relatively heavy quark mass corresponding to m_{pi}=871 MeV. The s-wave KN potentials are obtained from the Bethe-Salpeter wave function by using the method recently developed by HAL QCD (Hadrons to Atomic nuclei from Lattice QCD) Collaboration. Potentials in both channels reveal short range repulsions: Strength of the repulsion is stronger in the I=1 potential, which is consistent with the prediction of the Tomozawa-Weinberg term. The I=0 potential is found to have attractive well at mid range. From these potentials, the $KN$ scattering phase shifts are calculated and compared with the experimental data.
This talk reviews recent lattice QCD simulations of the K->pi semi-leptonic form factor.
We present results for the interaction of two kaons at maximal isospin. The calculation is based on 2+1+1 flavour gauge configurations generated by the ETM Collaboration (ETMC) featuring pion masses ranging from about 230 MeV to 450 MeV at three values of the lattice spacing. The elastic scattering length $a_0^{I=1}$ is calculated at several values of the bare strange quark and light quark masses. We find $M_K a_0 =-0.397(11)(_{-8}^{+0})$ as the result of a chiral and continuum extrapolation to the physical point. This number is compared to other lattice results.
The rare kaon decays $Ktopiell^+ell^-$ and $Ktopi ubar{ u}$ are flavor changing neutral current (FCNC) processes and hence promising channels with which to probe the limits of the standard model and to look for signs of new physics. In this paper we demonstrate the feasibility of lattice calculations of $Ktopiell^+ell^-$ decay amplitudes for which long-distance contributions are very significant. We show that the dominant finite-volume corrections (those decreasing as powers of the volume) are negligibly small and that, in the four-flavor theory, no new ultraviolet divergences appear as the electromagnetic current $J$ and the effective weak Hamiltonian $H_W$ approach each other. In addition, we demonstrate that one can remove the unphysical terms which grow exponentially with the range of the integration over the time separation between $J$ and $H_W$. We will now proceed to exploratory numerical studies with the aim of motivating further experimental measurements of these decays. Our work extends the earlier study by Isidori, Turchetti and Martinelli which focussed largely on the renormalization of ultraviolet divergences. In a companion paper we discuss the evaluation of the long-distance contributions to $Ktopi ubar{ u}$ decays; these contributions are expected to be at the level of a few percent for $K^+$ decays.
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