# Prescriptive unitarity

## Abstract

We introduce a prescriptive approach to generalized unitarity, resulting in a strictly-diagonal basis of loop integrands with coefficients given by specifically-tailored residues in field theory. We illustrate the power of this strategy in the case of planar, maximally supersymmetric Yang-Mills theory (SYM), where we construct closed-form representations of all (n-point N k MHV) scattering amplitudes through three loops. The prescriptive approach contrasts with the ordinary description of unitarity-based methods by avoiding any need for linear algebra to determine integrand coefficients. We describe this approach in general terms as it should have applications to many quantum field theories, including those without planarity, supersymmetry, or massless spectra defined in any number of dimensions.

- Authors:

- Univ. of California, Santa Barbara, CA (United States). Kavli Inst. for Theoretical Physics; Univ. of Copenhagen (Denmark). The Niels Bohr Inst.
- California Inst. of Technology (CalTech), Pasadena, CA (United States); Univ. of California, Santa Barbara, CA (United States). Kavli Inst. for Theoretical Physics
- Univ. of California, Santa Barbara, CA (United States). Kavli Inst. for Theoretical Physics; Univ. of California, Davis, CA (United States)

- Publication Date:

- Research Org.:
- California Inst. of Technology (CalTech), Pasadena, CA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1426866

- Grant/Contract Number:
- SC0011632

- Resource Type:
- Journal Article: 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: 6; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

### Citation Formats

```
Bourjaily, Jacob L., Herrmann, Enrico, and Trnka, Jaroslav.
```*Prescriptive unitarity*. United States: N. p., 2017.
Web. doi:10.1007/JHEP06(2017)059.

```
Bourjaily, Jacob L., Herrmann, Enrico, & Trnka, Jaroslav.
```*Prescriptive unitarity*. United States. doi:10.1007/JHEP06(2017)059.

```
Bourjaily, Jacob L., Herrmann, Enrico, and Trnka, Jaroslav. Mon .
"Prescriptive unitarity". United States.
doi:10.1007/JHEP06(2017)059. https://www.osti.gov/servlets/purl/1426866.
```

```
@article{osti_1426866,
```

title = {Prescriptive unitarity},

author = {Bourjaily, Jacob L. and Herrmann, Enrico and Trnka, Jaroslav},

abstractNote = {We introduce a prescriptive approach to generalized unitarity, resulting in a strictly-diagonal basis of loop integrands with coefficients given by specifically-tailored residues in field theory. We illustrate the power of this strategy in the case of planar, maximally supersymmetric Yang-Mills theory (SYM), where we construct closed-form representations of all (n-point N k MHV) scattering amplitudes through three loops. The prescriptive approach contrasts with the ordinary description of unitarity-based methods by avoiding any need for linear algebra to determine integrand coefficients. We describe this approach in general terms as it should have applications to many quantum field theories, including those without planarity, supersymmetry, or massless spectra defined in any number of dimensions.},

doi = {10.1007/JHEP06(2017)059},

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

number = 6,

volume = 2017,

place = {United States},

year = {Mon Jun 12 00:00:00 EDT 2017},

month = {Mon Jun 12 00:00:00 EDT 2017}

}

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