## Master integrals for the NNLO virtual corrections to μe scattering in QED: the planar graphs

## Abstract

Here, we evaluate the master integrals for the two-loop, planar box-diagrams contributing to the elastic scattering of muons and electrons at next-to-next-to leading-order in QED. We adopt the method of differential equations and the Magnus exponential series to determine a canonical set of integrals, finally expressed as a Taylor series around four space-time dimensions, with coefficients written as combination of generalized poly-logarithms. The electron is treated as massless, while we retain full dependence on the muon mass. The considered integrals are also relevant for crossing-related processes, such as di-muon production at e ^{+}e ^{–}-colliders, as well as for the QCD corrections to *top*-pair production at hadron colliders.

- Authors:

- Univ. di Padova, Padova (Italy); INFN - Sezione di Padova, Padova (Italy)
- INFN - Sezione di Padova, Padova (Italy)
- Argonne National Lab. (ANL), Argonne, IL (United States)

- Publication Date:

- Research Org.:
- Argonne National Lab. (ANL), Argonne, IL (United States)

- Sponsoring Org.:
- National Science Foundation (NSF); Perimeter Institute for Theoretical Physics; USDOE

- OSTI Identifier:
- 1494708

- Grant/Contract Number:
- AC02-06CH11357

- 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: 2017; Journal Issue: 11; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; NLO Computations

### Citation Formats

```
Mastrolia, Pierpaolo, Passera, Massimo, Primo, Amedeo, and Schubert, Ulrich. Master integrals for the NNLO virtual corrections to μe scattering in QED: the planar graphs. United States: N. p., 2017.
Web. doi:10.1007/JHEP11(2017)198.
```

```
Mastrolia, Pierpaolo, Passera, Massimo, Primo, Amedeo, & Schubert, Ulrich. Master integrals for the NNLO virtual corrections to μe scattering in QED: the planar graphs. United States. doi:10.1007/JHEP11(2017)198.
```

```
Mastrolia, Pierpaolo, Passera, Massimo, Primo, Amedeo, and Schubert, Ulrich. Wed .
"Master integrals for the NNLO virtual corrections to μe scattering in QED: the planar graphs". United States. doi:10.1007/JHEP11(2017)198. https://www.osti.gov/servlets/purl/1494708.
```

```
@article{osti_1494708,
```

title = {Master integrals for the NNLO virtual corrections to μe scattering in QED: the planar graphs},

author = {Mastrolia, Pierpaolo and Passera, Massimo and Primo, Amedeo and Schubert, Ulrich},

abstractNote = {Here, we evaluate the master integrals for the two-loop, planar box-diagrams contributing to the elastic scattering of muons and electrons at next-to-next-to leading-order in QED. We adopt the method of differential equations and the Magnus exponential series to determine a canonical set of integrals, finally expressed as a Taylor series around four space-time dimensions, with coefficients written as combination of generalized poly-logarithms. The electron is treated as massless, while we retain full dependence on the muon mass. The considered integrals are also relevant for crossing-related processes, such as di-muon production at e+e–-colliders, as well as for the QCD corrections to top-pair production at hadron colliders.},

doi = {10.1007/JHEP11(2017)198},

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

number = 11,

volume = 2017,

place = {United States},

year = {2017},

month = {11}

}

*Citation information provided by*

Web of Science

Web of Science