Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
2007-07-19
Phys.Rev.D76:094514,2007; Erratum-ibid.D78:119901,2008
Physics
High Energy Physics
High Energy Physics - Lattice
30 pages, 15 figures. Correction of a minor mistake in the 2-loop result for $Z_S$ and $Z_P$. The mistake affects (very slight
Scientific paper
10.1103/PhysRevD.76.094514
We compute the two-loop renormalization functions, in the RI $^\prime$ 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. Finally, we present our results in the $\bar{MS}$ scheme, for easier comparison with calculations in the continuum. The corresponding results, for fermions in an arbitrary representation, are included in an Appendix.
Panagopoulos Haralambos
Skouroupathis Apostolos
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