Three-loop off-forward evolution kernel for axial-vector operators in Larin’s scheme

Evolution equations for leading-twist operators in high orders of perturbation theory can be restored from the spectrum of anomalous dimensions and the calculation of the special conformal anomaly at one order less using conformal symmetry of QCD at the Wilson-Fisher critical point at noninteger d =...

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Bibliographic Details
Published in:Physical review. D 2021-05, Vol.103 (9), p.1, Article 094018
Main Authors: Braun, Vladimir M., Manashov, Alexander N., Moch, Sven-O., Strohmaier, Matthias
Format: Article
Language:English
Subjects:
Critical point
Elastic scattering
Evolution
Form factors
Kernels
Mathematical analysis
Operators
Perturbation theory
Subtraction
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Summary:Evolution equations for leading-twist operators in high orders of perturbation theory can be restored from the spectrum of anomalous dimensions and the calculation of the special conformal anomaly at one order less using conformal symmetry of QCD at the Wilson-Fisher critical point at noninteger d = 4 − 2ϵ space-time dimensions. In this work, we generalize this technique to axial-vector operators. We calculate the corresponding three-loop evolution kernels in Larin's scheme and derive explicit expressions for the finite renormalization kernel that describes the difference to the vector case to restore the conventional modified minimal subtraction scheme. The results are directly applicable to deeply virtual Compton scattering and the transition form factor γ ∗ γ → π.
ISSN:2470-0010
2470-0029
DOI:10.1103/PhysRevD.103.094018