Precision flavor physics from the lattice

Abstract

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 $M_{\pi }$, $M_K$ and $M_{\Omega }$ as the only input quantities. Using perturbative 4-loop respectively 2-loop running and dispersive input from $\eta \to 3\pi$, we obtain $m_u^{\overline{\mathrm{MS}}}(2\mathrm{GeV})=2.17(4)(10)\mathrm{MeV}$, $m_d^{\overline{\mathrm{MS}}}(2\mathrm{GeV})=4.79(7)(12)\mathrm{MeV}$, $m_s^{\overline{\mathrm{MS}}}(2\mathrm{GeV})=95.5(1.1)(1.5)\mathrm{MeV}$ and ${\hat{B}}_K=0.773(8)(8)$ where the first error is statistical and the second systematic.

Comments: 6 pages, 6 figures. Contribution to the proceedings of the 47th recontres de Moriond, EW session