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 $m_{ud}=(m_u+m_d)/2$, $m_s$ and $B_K$ in the RI scheme with $M_π$, $M_K$ and $M_Ω$ as the only input quantities. Using perturbative 4-loop respectively 2-loop running and dispersive input from $η\rightarrow 3π$, we obtain $m_u^\mathrm{\bar{MS}}(2 \mathrm{GeV})=2.17(4)(10) \mathrm{MeV}$, $m_d^\mathrm{\bar{MS}}(2 \mathrm{GeV})=4.79(7)(12) \mathrm{MeV}$, $m_s^\mathrm{\bar{MS}}(2 \mathrm{GeV})=95.5(1.1)(1.5) \mathrm{MeV}$ and $\hat{B}_K=0.773(8)(8)$ where the first error is statistical and the second systematic.

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