Non-perturbative quark mass renormalization in quenched lattice QCD

Abstract

The renormalization factor relating the bare to the renormalization group invariant quark masses is accurately calculated in quenched lattice QCD using a recursive finite-size technique. The result is presented in the form of a product of a universal factor times another factor, which depends on the details of the lattice theory but is easy to compute, since it does not involve any large scale differences. As a byproduct the Lambda-parameter of the theory is obtained with a total error of 8%.

Figures (8)

• Figure 1: Running coupling $\alpha_{{\rm \overline{MS}}}=\bar{g}^2_{{\rm \overline{MS}}}/4\pi$ in quenched QCD. From the dotted to the full curve, the perturbative accuracy increases from two to four loops.
• Figure 2: Running quark mass in quenched QCD. The flavour index has been omitted, since the entire graph is independent of which quark flavour is considered.
• Figure 3: Polynomial fit of the data for the step scaling function $\sigma(u)$. The errors on the data are about equal to the symbol size.
• Figure 4: Comparison of the numerically computed values of the running coupling in the SF scheme with perturbation theory. The dotted and dashed curves are obtained from eq. (\ref{['f_Lambda_def']}) using the $2$- and $3$-loop expressions for the $\beta$-function. The errors on the data are smaller than the symbol size.
• Figure 5: Polynomial fit of the data for the step scaling function $\sigma_{\rm P}(u)$.