Lattice QCD with the Overlap-Dirac Operator: Its $\hat{I}›$ Parameter, and One-Loop Renormalization of Fermionic Currents

Abstract

We compute the ratio between the scale $\hat{I}{›}_L$ associated with a lattice formulation of QCD using the overlap-Dirac operator, and $\hat{I}{›}_{MS-bar}$. 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 $Z_{\hat{I}}“$ of the two-quark operators $\bar{\ddot{I}}ˆ\hat{I}“\ddot{I}ˆ$, where $\hat{I}“$ 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 $Z_{\hat{I}}“$, coming from cactus resummation and from mean field perturbation theory.

3 pages, LATeX with 2 PS figure files. Talk presented at Confinement IV, Vienna, July 2000. Longer write-ups in: hep-lat/9909158 (NPB 571 (2000) 257), hep-lat/0002010 (NPB 580 (2000) 394). One further reference added, no other changes