# TTP06-27 Four-loop $\beta$ function and anomalous mass dimension in Dimensional Reduction

TTP06-27 Four-loop $\beta$ function and anomalous mass dimension in Dimensional Reduction

TTP06-27 Four-loop $\beta$ function and anomalous mass dimension in Dimensional Reduction

Within the framework of QCD we compute renormalization constants for the strong coupling and the quark masses to four-loop order. We apply the DR-bar scheme and put special emphasis on the additional couplings which have to be taken into account. This concerns the epsilon-scalar–quark Yukawa coupling as well as the vertex containing four epsilon-scalars. For a supersymmetric Yang Mills theory, we find, in contrast to a previous claim, that the evanescent Yukawa coupling equals the strong coupling constant through three loops as required by supersymmetry.

 R. Harlander, D.R.T. Jones, P. Kant, L. Mihaila, M. Steinhauser JHEP 0612 024 2006 PDF PostScript arXiv
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