Two-loop renormalization of fermion bilinears on the lattice
Date
2009Source
Proceedings of ScienceEuropean Physical Society Europhysics Conference on High Energy Physics, EPS-HEP 2009
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We compute the renormalization functions on the lattice, in the RI′ scheme, of local bilinear quark operators ψ̄ Γψ, where Γ = Î, γ5, γμ, γ5, γμ, γ5 σμν. 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 L,RI′ ψ, up to two loops. We also compute the 1-loop renormalization functions for the gluon field, Z L,RI′ A, ghost field, ZL,RI′ C, gauge parameter, ZL,RI′ α, and coupling constant ZL,RI′ C 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 a0 = g2 o/16π2, the clover coefficient cSW, and the number of fermion colors (Nc) and flavors (Nf), in the renormalized Feynman gauge. All 1-loop quantities are evaluated in an arbitrary gauge. Finally, we present our results in the MS scheme, for easier comparison with calculations in the continuum [1, 2]. 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 (a partial set of such integrals can be found in Ref. [3]), are presented in detail in Ref. [4]. © Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence.