Article

# Higher loop renormalization of fermion bilinear operators

09/2007;
Source: arXiv

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 .

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### Keywords

arbitrary fermion representations

bare coupling constant

fermions

flavor non-singlet

generic gauge

lattice formulation

local bilinear quark operators $\bar\psi\Gamma\psi$

MSbar scheme

prerequisite

present work

Pseudoscalar Dirac matrices

renormalized

renormalized Feynman gauge

RI' scheme

Scalar

scalar case

singlet operators

two-loop fermion mass renormalization

two-loop renormalization functions

Wilson action