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 \( \overline{\mathrm{MS}} \) 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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04 October 2019
The left-hand side of eq. (4.5)
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ArXiv ePrint: 1905.00882
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Artz, J., Harlander, R.V., Lange, F. et al. Results and techniques for higher order calculations within the gradient-flow formalism. J. High Energ. Phys. 2019, 121 (2019). https://doi.org/10.1007/JHEP06(2019)121
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DOI: https://doi.org/10.1007/JHEP06(2019)121