Three loop anomalous dimension of non-singlet quark currents in the \(RI^\prime\) scheme. (English) Zbl 1037.81597
Summary: We renormalize QCD at three loops in the modified regularization invariant, \(RI^\prime\), scheme in arbitrary covariant gauge and deduce that the four loop \(\beta\)-function is equivalent to the \(\overline{MS}\) result. The anomalous dimensions of the scalar, vector and tensor currents are then determined in the \(RI^\prime\) scheme at three loops by considering the insertion of the operator in a quark two-point function. The expression for the scalar current agrees with the quark mass anomalous dimension and we deduce an expression for the four loop \(RI^\prime\) mass anomalous dimension in arbitrary covariant gauge and for any Lie group.
MSC:
| 81V05 | Strong interaction, including quantum chromodynamics |
| 81T15 | Perturbative methods of renormalization applied to problems in quantum field theory |
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 81T17 | Renormalization group methods applied to problems in quantum field theory |
| 22E70 | Applications of Lie groups to the sciences; explicit representations |
| 11S80 | Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.) |
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