Precision flavor physics from the lattice

TL;DR

This paper reports precise lattice QCD calculations of light quark masses and the kaon mixing parameter $B_K$, utilizing multiple lattice spacings and lighter quark masses to eliminate chiral extrapolation and control cutoff effects.

Contribution

It provides the first fully nonperturbative predictions for quark masses and $B_K$ in the RI scheme with minimal input, improving accuracy and reliability.

Findings

Quark masses: $m_u$, $m_d$, $m_s$ determined with high precision.

$B_K$ parameter calculated with controlled uncertainties.

Results are consistent with previous estimates and improve precision.

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 $\eta\rightarrow 3\pi$, 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.