Two-loop renormalization of fermion bilinear operators on the lattice

Abstract

We compute the renormalization functions on the lattice, in the RI' scheme, of local bilinear quark operators $\bar{\psi }\Gamma \psi$, where $\Gamma =1,{\gamma }_5,{\gamma }_{\mu },{\gamma }_5{\gamma }_{\mu },{\gamma }_5{\sigma }_{\mu \nu }$. This calculation is carried out to two loops for the first time. We consider both the flavor non-singlet and singlet operators. As a prerequisite for the above, we compute the quark field renormalization, $Z_{\psi }$, up to two loops. We also compute the 1-loop renormalization functions for the gluon field, $Z_A$, ghost field, $Z_c$, gauge parameter, $Z_{\alpha }$, and coupling constant $Z_g$. We use the clover action for fermions and the Wilson action for gluons. Our results are given as an explicit function of the coupling constant, the clover coefficient $c_{SW}$, and the number of fermion colors ($N_c$) and flavors ($N_f$), in the renormalized Feynman gauge. All 1-loop quantities are evaluated in an arbitrary gauge. Finally, we present our results in the MS-bar scheme, for easier comparison with calculations in the continuum. We have generalized to fermionic fields in an arbitrary representation. Some special features of superficially divergent integrals, obtained from the evaluation of two-loop Feynman diagrams, are presented in detail in Ref. 1.

arXiv comment7 pages, 5 figures. Presented at the "XXVII International Symposium on Lattice Field Theory", July 26-31 2009, Peking University, Beijing, China

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• Renormalisation and off-shell improvement in lattice perturbation theory
• High-precision determination of the light-quark masses from realistic lattice QCD
• Proton decay matrix elements with domain-wall fermions
• Two-loop renormalization of vector, axial-vector and tensor fermion bilinears on the lattice
• Non-perturbative renormalization of the static axial current in two-flavour QCD
• Two-loop renormalization of scalar and pseudoscalar fermion bilinears on the lattice
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Cited by in corpus (1)

• Non-perturbative renormalization in lattice QCD