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

## Abstract

In this study, we evaluate the master integrals for the two-loop non-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 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 polylogarithms. 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. In particular our results, together with the planar master integrals recently computed, represent the complete set of functions needed for the evaluation of the photonic two-loop virtual next-to-next-to-leading order QED corrections to μe → μe and e ^{+}e ^{–} → μ ^{+}μ ^{–}.

- Authors:

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

- Publication Date:

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

- Sponsoring Org.:
- USDOE Office of Science (SC); Swiss National Science Foundation (SNSF)

- OSTI Identifier:
- 1494707

- 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: 2018; Journal Issue: 9; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 97 MATHEMATICS AND COMPUTING; NLO Computations

### Citation Formats

```
Di Vita, Stefano, Laporta, Stefano, Mastrolia, Pierpaolo, Primo, Amedeo, and Schubert, Ulrich. Master integrals for the NNLO virtual corrections to μe scattering in QED: The non-planar graphs. United States: N. p., 2018.
Web. doi:10.1007/JHEP09(2018)016.
```

```
Di Vita, Stefano, Laporta, Stefano, Mastrolia, Pierpaolo, Primo, Amedeo, & Schubert, Ulrich. Master integrals for the NNLO virtual corrections to μe scattering in QED: The non-planar graphs. United States. doi:10.1007/JHEP09(2018)016.
```

```
Di Vita, Stefano, Laporta, Stefano, Mastrolia, Pierpaolo, Primo, Amedeo, and Schubert, Ulrich. Tue .
"Master integrals for the NNLO virtual corrections to μe scattering in QED: The non-planar graphs". United States. doi:10.1007/JHEP09(2018)016. https://www.osti.gov/servlets/purl/1494707.
```

```
@article{osti_1494707,
```

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

author = {Di Vita, Stefano and Laporta, Stefano and Mastrolia, Pierpaolo and Primo, Amedeo and Schubert, Ulrich},

abstractNote = {In this study, we evaluate the master integrals for the two-loop non-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 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 polylogarithms. 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. In particular our results, together with the planar master integrals recently computed, represent the complete set of functions needed for the evaluation of the photonic two-loop virtual next-to-next-to-leading order QED corrections to μe → μe and e+e– → μ+μ–.},

doi = {10.1007/JHEP09(2018)016},

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

number = 9,

volume = 2018,

place = {United States},

year = {2018},

month = {9}

}

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