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

Abstract

We compute the ratio between the scale ${\Lambda }_L$ associated with a lattice formulation of QCD using the overlap-Dirac operator, and ${\Lambda }_{MS-bar}$. 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 $Z_{\Gamma }$ of the two-quark operators $\bar{\psi }\Gamma \psi$, where $\Gamma$ 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 $Z_{\Gamma }$, 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

References in corpus (2)

• Finite-size scaling of the quark condensate in quenched lattice QCD
• Operator improvement for Ginsparg-Wilson fermions

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• Light Hadron Weak Matrix Elements
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• Scalar condensate and light quark masses from overlap fermions
• Analysis of the DeltaI=1/2 Rule and e'/e with Overlap Fermions
• Perturbative renormalization of moments of quark momentum, helicity and transversity distributions with overlap and Wilson fermions
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• Exact Chiral Symmetry on the Lattice: QCD Applications
• Quenched Results for Light Quark Physics with Overlap Fermions
• Progress using generalized lattice Dirac operators to parametrize the Fixed-Point QCD action
• Nonperturbative renormalization of composite operators with overlap fermions
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• Perturbative renormalization of the first two moments of non-singlet quark distributions with overlap fermions
• Nonperturbative renormalisation of composite operators with overlap quarks
• Perturbative renormalization of the first moment of structure functions for domain-wall QCD
• Improved Perturbation Theory for Improved Lattice Actions
• Light quark masses in quenched QCD with exact chiral symmetry
• QCD with overlap fermions: Running coupling and the 3-loop beta-function
• The Lattice Free Energy with Overlap Fermions: A Two-Loop Result
• Perturbative renormalization in parton distribution functions using Overlap fermions and Symanzik improved gluons
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• Quenched Chiral Behavior of Hadrons with Overlap Fermions
• Beauty mesons in $N_f=2+1+1+1$ lattice QCD with exact chiral symmetry
• Higher Loop Results for the Plaquette, Using the Clover and Overlap Actions
• Lattice renormalisation of O(a) improved heavy-light operators
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• Random Matrix Theory and the Spectra of Overlap Fermions