Precision flavor physics from the lattice

We present results for the light quark masses and the neutral kaon mixing parameter $B_K$ from lattice QCD. Our data set includes lighter than physical light quark masses and 5 lattice spacings so that chiral extrapolation is not necessary and cutoff effects are fully under control. We obtain fully nonperturbative predictions for $m_{ud}=(m_u+m_d)\mathrm{/}2$, $m_s$ and $B_K$ in the RI scheme with $M_{\pi }$, $M_K$ and $M_{\mathrm{\Omega }}$ as the only input quantities. Using perturbative 4-loop respectively 2-loop running and dispersive input from $\eta \to 3\pi$, we obtain $m_u^$\overline{\mathrm{M}\mathrm{S}}$(2 $\mathrm{G}\mathrm{e}\mathrm{V}$)=2.17(4)(10) $\mathrm{M}\mathrm{e}\mathrm{V}$$,$m_d^$\overline{\mathrm{M}\mathrm{S}}$(2 $\mathrm{G}\mathrm{e}\mathrm{V}$)=4.79(7)(12) $\mathrm{M}\mathrm{e}\mathrm{V}$$,$m_s^$\overline{\mathrm{M}\mathrm{S}}$(2 $\mathrm{G}\mathrm{e}\mathrm{V}$)=95.5(1.1)(1.5) $\mathrm{M}\mathrm{e}\mathrm{V}$$and$\hat{B}_K=0.773(8)(8)$ where the first error is statistical and the second systematic.