Journal of High Energy Physics (Jun 2019)
Results and techniques for higher order calculations within the gradient-flow formalism
Abstract
Abstract We describe in detail the implementation of a systematic perturbative approach to observables in the QCD gradient-flow formalism. This includes a collection of all relevant Feynman rules of the five-dimensional field theory and the composite operators considered in this paper. Tools from standard perturbative calculations are used to obtain Green’s functions at finite flow time t at higher orders in perturbation theory. The three-loop results for the quark condensate at finite t and the conversion factor for the “ringed” quark fields to the M S ¯ $$ \overline{\mathrm{MS}} $$ scheme are presented as applications. We also re-evaluate an earlier result for the three-loop gluon condensate, improving on its accuracy.
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