## This content will become publicly available on January 1, 2021

# Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes

## Abstract

Using a careful choice of infrared (IR) subtraction scheme, we demonstrate cancellation of all terms with transcendental weights 0, 1, 2 from the finite part of the full-color two-loop four-gluon N = 2 supersymmetric QCD amplitude, with Nf massless supersymmetric quarks. This generalizes the previously observed cancellation of weight-2 terms in the superconformal theory, where Nf = 2Nc for gauge group SU(Nc). The subtraction scheme follows naturally both from general IR factorization principles and from an integrand-level analysis of divergences in this amplitude. The divergences are written in terms of scalar triangle integrals whose expressions are known to all orders in the dimensional regulator ϵ = (4 − D)/2. We also present integrated expressions for the full-color two-loop four-point amplitudes with both matter and vectors on external legs in which lower-weight terms also cancel using an appropriate IR scheme. This provides us with values for the two-loop cusp, gluonic, and quark anomalous dimensions in N = 2 supersymmetric QCD, which are cross-checked between the three different amplitudes.

- Authors:

- Publication Date:

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

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1605201

- Report Number(s):
- SLAC-PUB-17488

Journal ID: ISSN 1029-8479

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

- Country of Publication:
- United States

- Language:
- English

### Citation Formats

```
Kälin, Gregor, Mogull, Gustav, Ochirov, Alexander, and Verbeek, Bram. Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes. United States: N. p., 2020.
Web. doi:10.1007/jhep01(2020)068.
```

```
Kälin, Gregor, Mogull, Gustav, Ochirov, Alexander, & Verbeek, Bram. Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes. United States. doi:10.1007/jhep01(2020)068.
```

```
Kälin, Gregor, Mogull, Gustav, Ochirov, Alexander, and Verbeek, Bram. Wed .
"Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes". United States. doi:10.1007/jhep01(2020)068.
```

```
@article{osti_1605201,
```

title = {Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes},

author = {Kälin, Gregor and Mogull, Gustav and Ochirov, Alexander and Verbeek, Bram},

abstractNote = {Using a careful choice of infrared (IR) subtraction scheme, we demonstrate cancellation of all terms with transcendental weights 0, 1, 2 from the finite part of the full-color two-loop four-gluon N = 2 supersymmetric QCD amplitude, with Nf massless supersymmetric quarks. This generalizes the previously observed cancellation of weight-2 terms in the superconformal theory, where Nf = 2Nc for gauge group SU(Nc). The subtraction scheme follows naturally both from general IR factorization principles and from an integrand-level analysis of divergences in this amplitude. The divergences are written in terms of scalar triangle integrals whose expressions are known to all orders in the dimensional regulator ϵ = (4 − D)/2. We also present integrated expressions for the full-color two-loop four-point amplitudes with both matter and vectors on external legs in which lower-weight terms also cancel using an appropriate IR scheme. This provides us with values for the two-loop cusp, gluonic, and quark anomalous dimensions in N = 2 supersymmetric QCD, which are cross-checked between the three different amplitudes.},

doi = {10.1007/jhep01(2020)068},

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

number = 1,

volume = 2020,

place = {United States},

year = {2020},

month = {1}

}

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