Non-perturbative quark mass renormalization in two-flavor QCD

Abstract

The running of renormalized quark masses is computed in lattice QCD with two flavors of massless O(a) improved Wilson quarks. The regularization and flavor independent factor that relates running quark masses to the renormalization group invariant ones is evaluated in the Schroedinger Functional scheme. Using existing data for the scale r_0 and the pseudoscalar meson masses, we define a reference quark mass in QCD with two degenerate quark flavors. We then compute the renormalization group invariant reference quark mass at three different lattice spacings. Our estimate for the continuum value is converted to the strange quark mass with the help of chiral perturbation theory.

Figures (6)

• Figure 1: The Schrödinger Functional.
• Figure 2: Continuum extrapolations of $\Sigma_{\rm P}$. The $L/a=6$ data have been excluded from the fits. For the third smallest coupling, the two points at $L/a=6$ refer to 1--loop and 2--loop values for the boundary improvement coefficient $c_t$Luscher:1992anBode:1999sm.
• Figure 3: Comparison of the non--perturbative data for the step scaling function $\sigma_{\rm P}(u)$ with perturbation theory. 2/3--loop refers to the 2--loop $\tau$-function and 3--loop $\beta$--function, analogously 1/2--loop.
• Figure 4: The non--perturbative running of $\overline{m}$. 2/3--loop refers to the 2--loop $\tau$-function and 3--loop $\beta$--function, analogously 1/2--loop.
• Figure 5: Summary of the strange quark mass data from lattice simulations. In the legend the discretizations used are indicated in the form gauge action/fermion action. The dictionary reads: W: Wilson gauge action; I: Iwasaki gauge action; LW: 1--loop tadpole improved Lüscher--Weisz gauge action; CW: Wilson--clover fermion action; KS: Asqtad staggered fermion action. The dotted lines represent the quenched result Garden:1999fg.