Determination of Light and Strange Quark Masses from Full Lattice QCD

Abstract

We compute the light and strange quark masses m_l = (m_u+m_d)/2 and m_s, respectively, in full lattice QCD with N_f=2 flavors of light dynamical quarks. The renormalization constants, which convert bare quark masses into renormalized quark masses, are computed nonperturbatively, including the effect of quark-line disconnected diagrams. We obtain m_l=4.7(2)(3) MeV and m_s=119(5)(8) MeV in the MSbar scheme at the scale 2 GeV.

Figures (5)

• Figure 1: Quark diagrams contributing to the renormalization of the mass operator ($\mathbf{\times}$). The left figure shows the connected (nonsinglet) contribution, the right figure the disconnected (singlet minus nonsinglet) contribution. Gluon lines have been omitted.
• Figure 2: Parameters of our dynamical gauge field configurations, together with lines of constant $r_0/a$ (solid lines) and lines of constant $m_{PS} r_0$ (dashed lines). The simulations are done on $24^3\, 48$ ($\times$) and $16^3\, 32$ ($\Circle$) lattices, respectively.
• Figure 4: The ratio $Z_m^S/Z_m^{NS}$ at $\beta=5.20$, 5.25, 5.29 and 5.40 (from top to bottom), together with a linear extrapolation to the chiral limit.
• Figure 6: The partially quenched pseudoscalar mass $m_{PS}$ as a function of $m_{\rm val}^R$ at $\beta=5.40$ for our three sea quark masses. The solid line shows the result of the fit for $m_{\rm sea}^R=0$.
• Figure 8: The light and strange quark masses, together with the extrapolation to the continuum limit. The errors shown are statistical only.