Lattice QCD with the Overlap-Dirac Operator: Its $Λ$ Parameter, and One-Loop Renormalization of Fermionic Currents

Abstract

We compute the ratio between the scale $Λ_L$ associated with a lattice formulation of QCD using the overlap-Dirac operator, and $Λ_{MS-bar}$. To this end, the one-loop relation between the lattice coupling $g_0$ and the coupling renormalized in the MS-bar scheme is calculated, using the lattice background field technique. We also compute the one-loop renormalization $Z_Γ$ of the two-quark operators $\barψ Γψ$, where $Γ$ denotes a generic Dirac matrix. Furthermore, we study the renormalization of quark bilinears which are more extended and have better chiral properties. Finally, we present improved estimates of $Z_Γ$, coming from cactus resummation and from mean field perturbation theory.