# TVID 2: evaluation of planar-type three-loop self-energy integrals with arbitrary masses

## Abstract

We present TVID 2, a program to numerically evaluate an important class of planar three-loop self-energy master integrals with arbitrary masses. As with the predecessor version (TVID 1) the integrals are separated into a known piece, containing the UV divergencies, and a finite piece that is integrated numerically, implemented in C. The set of master integrals under consideration was found with self-energy diagrams containing two closed fermion loops in mind. Two techniques are employed in deriving the expressions for the finite pieces that are then numerically integrated: (a) Sub-loop dispersion relations in the case of topologies containing sub-bubbles, and (b) a modification of the procedure suggested by Ghinculov for integrals with only sub-loop triangles.

- Authors:

- Munich School of Philosophy, Munich (Germany)
- Univ. of Pittsburgh, PA (United States). Pittsburgh Particle-physics Astro-physics & Cosmology Center (PITT-PACC)
- Argonne National Lab. (ANL), Argonne, IL (United States); Northwestern Univ., Evanston, IL (United States)

- Publication Date:

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

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

- OSTI Identifier:
- 1597274

- Grant/Contract Number:
- AC02-06CH11357; PHY-1820760; FG02-91ER40684

- 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: 2020; Journal Issue: 1; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Higgs Physics; Quark Masses and SM Parameters

### Citation Formats

```
Bauberger, Stefan, Freitas, Ayres, and Wiegand, Daniel. TVID 2: evaluation of planar-type three-loop self-energy integrals with arbitrary masses. United States: N. p., 2020.
Web. doi:10.1007/JHEP01(2020)024.
```

```
Bauberger, Stefan, Freitas, Ayres, & Wiegand, Daniel. TVID 2: evaluation of planar-type three-loop self-energy integrals with arbitrary masses. United States. doi:10.1007/JHEP01(2020)024.
```

```
Bauberger, Stefan, Freitas, Ayres, and Wiegand, Daniel. Tue .
"TVID 2: evaluation of planar-type three-loop self-energy integrals with arbitrary masses". United States. doi:10.1007/JHEP01(2020)024. https://www.osti.gov/servlets/purl/1597274.
```

```
@article{osti_1597274,
```

title = {TVID 2: evaluation of planar-type three-loop self-energy integrals with arbitrary masses},

author = {Bauberger, Stefan and Freitas, Ayres and Wiegand, Daniel},

abstractNote = {We present TVID 2, a program to numerically evaluate an important class of planar three-loop self-energy master integrals with arbitrary masses. As with the predecessor version (TVID 1) the integrals are separated into a known piece, containing the UV divergencies, and a finite piece that is integrated numerically, implemented in C. The set of master integrals under consideration was found with self-energy diagrams containing two closed fermion loops in mind. Two techniques are employed in deriving the expressions for the finite pieces that are then numerically integrated: (a) Sub-loop dispersion relations in the case of topologies containing sub-bubbles, and (b) a modification of the procedure suggested by Ghinculov for integrals with only sub-loop triangles.},

doi = {10.1007/JHEP01(2020)024},

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

number = 1,

volume = 2020,

place = {United States},

year = {2020},

month = {1}

}

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