# Results and techniques for higher order calculations within the gradient-flow formalism

## 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 $$\overline{\mbox{MS}}$$ scheme are presented as applications. We also re-evaluate an earlier result for the three-loop gluon condensate, improving on its accuracy.

- Authors:

- RWTH Aachen Univ., Aachen (Germany)
- Illinois Inst. of Technology, Chicago, IL (United States); Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
- Albert-Ludwigs-Univ., Freiburg (Germany)

- Publication Date:

- Research Org.:
- Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

- OSTI Identifier:
- 1529333

- Report Number(s):
- [arXiv:1905.00882; FERMILAB-PUB-19-151-T; FR-PHENO-2019-003; IIT-CAPP-19-02; TTK-19-15]

[Journal ID: ISSN 1029-8479; 1732898]

- Grant/Contract Number:
- [AC02-07CH11359]

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of High Energy Physics (Online)

- Additional Journal Information:
- [Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2019; Journal Issue: 6]; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Lattice QCD; Perturbative QCD

### Citation Formats

```
Artz, Johannes, Harlander, Robert V., Lange, Fabian, Neumann, Tobias, and Prausa, Mario. Results and techniques for higher order calculations within the gradient-flow formalism. United States: N. p., 2019.
Web. doi:10.1007/JHEP06(2019)121.
```

```
Artz, Johannes, Harlander, Robert V., Lange, Fabian, Neumann, Tobias, & Prausa, Mario. Results and techniques for higher order calculations within the gradient-flow formalism. United States. doi:10.1007/JHEP06(2019)121.
```

```
Artz, Johannes, Harlander, Robert V., Lange, Fabian, Neumann, Tobias, and Prausa, Mario. Mon .
"Results and techniques for higher order calculations within the gradient-flow formalism". United States. doi:10.1007/JHEP06(2019)121. https://www.osti.gov/servlets/purl/1529333.
```

```
@article{osti_1529333,
```

title = {Results and techniques for higher order calculations within the gradient-flow formalism},

author = {Artz, Johannes and Harlander, Robert V. and Lange, Fabian and Neumann, Tobias and Prausa, Mario},

abstractNote = {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 $\overline{\mbox{MS}}$ scheme are presented as applications. We also re-evaluate an earlier result for the three-loop gluon condensate, improving on its accuracy.},

doi = {10.1007/JHEP06(2019)121},

journal = {Journal of High Energy Physics (Online)},

number = [6],

volume = [2019],

place = {United States},

year = {2019},

month = {6}

}

*Citation information provided by*

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