Electromagnetic effects are increasingly being accounted for in lattice quantum chromodynamics computations. Because of their long-range nature, they lead to large finite-size effects over which it is important to gain analytical control. Nonrelativi
stic effective field theories provide an efficient tool to describe these effects. Here we argue that some care has to be taken when applying these methods to quantum electrodynamics in a finite volume.
Indirect CP violation in K rightarrow {pi}{pi} decays plays a central role in constraining the flavor structure of the Standard Model (SM) and in the search for new physics. For many years the leading uncertainty in the SM prediction of this phenomen
on was the one associated with the nonperturbative strong interaction dynamics in this process. Here we present a fully controlled lattice QCD calculation of these effects, which are described by the neutral kaon mixing parameter B_K . We use a two step HEX smeared clover-improved Wilson action, with four lattice spacings from aapprox0.054 fm to aapprox0.093 fm and pion masses at and even below the physical value. Nonperturbative renormalization is performed in the RI-MOM scheme, where we find that operator mixing induced by chiral symmetry breaking is very small. Using fully nonperturbative continuum running, we obtain our main result B_K^{RI}(3.5GeV)=0.531(6)_{stat}(2)_{sys}. A perturbative 2-loop conversion yields B_K^{MSbar-NDR}(2GeV)=0.564(6)_{stat}(3)_{sys}(6)_{PT}, which is in good agreement with current results from fits to experimental data.
Some algorithmic details of our $N_f=2+1$ QCD mixed action simulations with overlap valence and improved Wilson sea quarks are presented.
