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Three-loop counterterms for the Standard Model (SM) revealed that the matrix of anomalous dimensions ($gamma$) of quarks is divergent in the $d to 4$ limit unless a carefully chosen non-Hermitian square-root of $Z$ matrix is used in the textbook formula for $gamma$. Here, an alternative prescription is given, which expresses $gamma$ and $beta$ functions directly in terms of counterterms (instead of $sqrt{Z}$ and conventional `bare couplings) and produces finite results. In the SM, this prescription $automatically$ reproduces results obtained previously by adjusting $sqrt{Z}$.
We present the full analytic result for the three-loop angle-dependent cusp anomalous dimension in QCD. With this result, infrared divergences of planar scattering processes with massive particles can be predicted to that order. Moreover, we define a
We present the details of the analytic calculation of the three-loop angle-dependent cusp anomalous dimension in QCD and its supersymmetric extensions, including the maximally supersymmetric $mathcal{N}=4$ super Yang-Mills theory. The three-loop resu
In a previous paper, one of us pointed out that the anomalous dimension matrices for all physical processes that have been calculated to date are complex symmetric, if stated in an orthonormal basis. In this paper we prove this fact and show that it
We present numerical results for the nonplanar lightlike cusp and collinear anomalous dimension at four loops in ${mathcal N} = 4$ SYM theory, which we infer from a calculation of the Sudakov form factor. The latter is expressed as a rational linear
We compute the nonplanar contribution to the universal anomalous dimension of the SU(4)-singlet twist-two operators in N=4 supersymmetric Yang-Mills theory at four loops through Lorentz spin 18. From this, we numerically evaluate the nonplanar contri