Higher loop renormalization of fermion bilinear operators

Details Higher loop renormalization of fermion bilinear operators Higher loop renormalization of fermion bilinear operators

2007-08-30

arxiv.org/abs/0708.4087v1

PoSLAT2007:254,2007

Physics

High Energy Physics

High Energy Physics - Lattice

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

Scientific paper

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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