Determination of light quark masses from the electromagnetic splitting of pseudoscalar meson masses computed with two flavors of domain wall fermions

Abstract

We determine the light quark masses from lattice QCD simulations incorporating the electromagnetic interaction of valence quarks. The meson masses are calculated on lattice QCD configurations generated by the RBC Collaboration for two flavors of dynamical domain wall fermions, which are combined with QED configurations generated via quenched non-compact lattice QED. The electromagnetic part of the pion mass splitting is found to be $m_{π^+}-m_{π^0}=4.12(21)$ MeV, where only the statistical error is quoted, and similarly for the kaon, 1.443(55) MeV. Our results for the light quark masses are $m_u^{\rm\bar{MS}}$(2 GeV)=$3.02(27)(19)$ MeV, $m_d^{\rm\bar{MS}}$(2 GeV)=$5.49(20)(34)$ MeV, and $m_s^{\rm\bar{MS}}$(2 GeV)=$119.5(56)(74)$ MeV, where the first error is statistical and the second systematic. By averaging over $\pm e$ to cancel ${\cal O}(e)$ noise exactly on each combined gauge field configuration, we are able to work at physical $α=1/137$ and obtain very small statistical errors. In our calculation, several sources of systematic error remain, including finite volume, non-zero lattice spacing, chiral extrapolation, quenched QED, and quenched strange quark, which may be more significant than the errors quoted above.

Figures (7)

• Figure 1: One of the pseudoscalar mass-squared splittings computed for $e=1$ (circles) and also averaged over $e=\pm1$ (triangles). The latter has dramatically reduced statistical error (and is shifted for clarity).
• Figure 2: The quark mass dependence of charged vector meson mass and its chiral extrapolation using the $m_{sea}=m_{val}$ data and Eq. (\ref{['eq:vec1']}).
• Figure 3: The quark mass dependence of the $\rho^{+}$-$\rho^0$ mass splitting. The dashed line is a fit to Eq. (\ref{['eq:vec2']}).
• Figure 4: Same as Fig. \ref{['fig:vec_massdiff']} except the minimum distance in the mass fits is $t=5$ for all cases.
• Figure 5: The $\alpha_{\rm em}$ dependence of the splittings. The results from $\langle P\,P\rangle$ are shown.