Higher loop renormalization of fermion bilinear operators

Abstract

We compute the two-loop renormalization functions, in the RI' scheme, of local bilinear quark operators $\bar{\psi }\Gamma \psi$, where $\Gamma$ denotes the Scalar and Pseudoscalar Dirac matrices, in the lattice formulation of QCD. We consider both the flavor non-singlet and singlet operators; the latter, in the scalar case, leads directly to the two-loop fermion mass renormalization, $Z_m$. As a prerequisite for the above, we also compute the quark field renormalization, $Z_{\psi }$, up to two loops. We use the clover action for fermions and the Wilson action for gluons. Our results are given as a polynomial in $c_{SW}$, in terms of both the renormalized and bare coupling constant, in the renormalized Feynman gauge. We also confirm the 1-loop renormalization functions, for generic gauge. A longer write-up of the present work, including the conversion of our results to the MSbar scheme and a generalization to arbitrary fermion representations, can be found in arXiv:0707.2906 .

arXiv comment7 pages, 4 figures, presented at the XXV International Symposium on Lattice Field Theory, July 30 - August 4, 2007, Regensburg, Germany

References in corpus (7)

• Renormalization and Running of Quark Mass and Field in the Regularization Invariant and MS-bar Schemes at Three and Four Loops
• Renormalisation and off-shell improvement in lattice perturbation theory
• High-precision determination of the light-quark masses from realistic lattice QCD
• Quark Mass Renormalization in the $\MSbar$ and RI schemes up to the NNLO order
• The three-loop beta-fuction of QCD with the clover action
• Two-loop renormalization of scalar and pseudoscalar fermion bilinears on the lattice
• Free Energy and Plaquette expectation value for gluons on the lattice, in three dimensions