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.
Isospin symmetry is explicitly broken in the Standard Model by the non-zero differences of mass and electric charge between the up and down quarks. Both of these corrections are expected to have a comparable size of the order of one percent relativel
y to hadronic energies. Although these contributions are small, they play a crucial role in hadronic and nuclear physics. In this review we explain how to properly define QCD and QED on a finite and discrete space-time so that isospin corrections to hadronic observables can be computed ab-initio. We then consider the different approaches to compute lattice correlation functions of QCD and QED observables. Finally we summarise the actual lattice results concerning the isospin corrections to the light hadron spectrum.
While electromagnetic and up-down quark mass difference effects on octet baryon masses are very small, they have important consequences. The stability of the hydrogen atom against beta decay is a prominent example. Here we include these effects by ad
ding them to valence quarks in a lattice QCD calculation based on $N_f=2+1$ simulations with 5 lattice spacings down to 0.054 fm, lattice sizes up to 6 fm and average up-down quark masses all the way down to their physical value. This allows us to gain control over all systematic errors, except for the one associated with neglecting electromagnetism in the sea. We compute the octet baryon isomultiplet mass splittings, as well as the individual contributions from electromagnetism and the up-down quark mass difference. Our results for the total splittings are in good agreement with experiment.
At the precision reached in current lattice QCD calculations, electromagnetic effects are becoming numerically relevant. Here, electromagnetic effects are included by superimposing $mathrm{U}(1)$ degrees of freedom on $N_f = 2+1$ QCD configurations f
rom the Budapest-Marseille-Wuppertal Collaboration. We present preliminary results for the electromagnetic corrections to light pseudoscalars mesons masses and discuss some of the associated systematic errors.
At the precision reached in current lattice QCD calculations, electromagnetic effects are becoming numerically relevant. We will present preliminary results for electromagnetic corrections to light hadron masses, based on simulations in which a $math
rm{U}(1)$ degree of freedom is superimposed on $N_f=2+1$ QCD configurations from the BMW collaboration.
