Two-loop renormalization of scalar and pseudoscalar fermion bilinears on the lattice
Date
2007ISSN
1550-7998Source
Physical Review D - Particles, Fields, Gravitation and CosmologyVolume
76Issue
9Google Scholar check
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We compute the two-loop renormalization functions, in the RI′ scheme, of local bilinear quark operators ψ̄Γψ, where Γ denotes the scalar and pseudoscalar Dirac matrices, in the lattice formulation of QCD. We consider both the flavor nonsinglet and singlet operators the latter, in the scalar case, leads directly to the two-loop fermion mass renormalization, Zm. As a prerequisite for the above, we also compute the quark field renormalization, Zψ, 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 cSW, in terms of both the renormalized and bare coupling constants, in the renormalized Feynman gauge. We also confirm the one-loop renormalization functions, for generic gauge. Finally, we present our results in the MS̄ scheme, for easier comparison with calculations in the continuum. The corresponding results, for fermions in an arbitrary representation, are included in the Appendix. © 2007 The American Physical Society.