The perturbative gradient flow at higher orders

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The gradient flow formalism as defined by M. Lüscher in 2010 has been considered mostly within the framework of lattice gauge theory up to now. In this project, it shall be treated with perturbative methods. To some extent, the potential resulting from the comparison and the combination of both approaches has already been pointed out in the literature. For example, it offers a new possibility to derive a value for the strong coupling constant in the perturbative regime from non-perturbative lattice data.First results in this direction have already been obtained by the applicant. However, they were based on a rather pragmatic, computer intensive approach. One of the goals of this proposal is the development of a systematic method for perturbative calculations in the gradient-flow formalism. Using this setup, phenomenologically relevant quantities shall be calculated to higher orders in perturbation theory (mostly NNLO).