Recent three loop calculations in perturbative QCD

Abstract

Recent three loop calculations of various quantities in QCD are reported. First, the QCD lagrangian is renormalized at three loops in the modified regularization invariant, (RI′), scheme which is primarily used in lattice regularization. Several composite operators are renormalized at three loops in RI′ including the tensor current, Ψσ uv Ψ , and the non-singlet operators ΨΥ μ D ν Ψ and Ψσ μν D ρ Ψ . The anomalous dimension of the latter operator is also given in the MS scheme and represents the first three loop information for a moment of the transversity operator. The dimension two BRST invariant composite operator 1/2 A a u A a u + αc -a c a is also renormalized at three loops in 166-6. It is shown that its anomalous dimension is related to the gluon and ghost anomalous dimensions in the Landau gauge indicating the existence of a new Slavnov-Taylor identity.