## Elliptic polylogarithms and Feynman parameter integrals

## Abstract

In this paper we study the calculation of multiloop Feynman integrals that cannot be expressed in terms of multiple polylogarithms. We show in detail how certain types of two- and three-point functions at two loops, which appear in the calculation of higher order corrections in QED, QCD and in the electroweak theory (EW), can naturally be expressed in terms of a recently introduced elliptic generalisation of multiple polylogarithms by direct integration over their Feynman parameter representation. Moreover, we show that in all examples that we considered a basis of pure Feynman integrals can be found.

- Authors:

- Humboldt Univ. of Berlin (Germany)
- European Organization for Nuclear Research (CERN), Geneva (Switzerland); Université Catholique de Louvain, Louvain-la-Neuve (Belgium)
- SLAC National Accelerator Lab., Menlo Park, CA (United States)
- European Organization for Nuclear Research (CERN), Geneva (Switzerland)

- Publication Date:

- Research Org.:
- SLAC National Accelerator Lab., Menlo Park, CA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1532395

- Grant/Contract Number:
- AC02-76SF00515

- 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: 5; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING; NLO Computations; QCD Phenomenology

### Citation Formats

```
Broedel, Johannes, Duhr, Claude, Dulat, Falko, Penante, Brenda, and Tancredi, Lorenzo. Elliptic polylogarithms and Feynman parameter integrals. United States: N. p., 2019.
Web. doi:10.1007/jhep05(2019)120.
```

```
Broedel, Johannes, Duhr, Claude, Dulat, Falko, Penante, Brenda, & Tancredi, Lorenzo. Elliptic polylogarithms and Feynman parameter integrals. United States. doi:10.1007/jhep05(2019)120.
```

```
Broedel, Johannes, Duhr, Claude, Dulat, Falko, Penante, Brenda, and Tancredi, Lorenzo. Tue .
"Elliptic polylogarithms and Feynman parameter integrals". United States. doi:10.1007/jhep05(2019)120. https://www.osti.gov/servlets/purl/1532395.
```

```
@article{osti_1532395,
```

title = {Elliptic polylogarithms and Feynman parameter integrals},

author = {Broedel, Johannes and Duhr, Claude and Dulat, Falko and Penante, Brenda and Tancredi, Lorenzo},

abstractNote = {In this paper we study the calculation of multiloop Feynman integrals that cannot be expressed in terms of multiple polylogarithms. We show in detail how certain types of two- and three-point functions at two loops, which appear in the calculation of higher order corrections in QED, QCD and in the electroweak theory (EW), can naturally be expressed in terms of a recently introduced elliptic generalisation of multiple polylogarithms by direct integration over their Feynman parameter representation. Moreover, we show that in all examples that we considered a basis of pure Feynman integrals can be found.},

doi = {10.1007/jhep05(2019)120},

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

number = 5,

volume = 2019,

place = {United States},

year = {2019},

month = {5}

}

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