# Supersymmetric Regularization Two-Loop QCD Amplitudes and Coupling Shifts

## Abstract

We present a definition of the four-dimensional helicity (FDH) regularization scheme valid for two or more loops. This scheme was previously defined and utilized at one loop. It amounts to a variation on the standard 't Hooft-Veltman scheme and is designed to be compatible with the use of helicity states for ''observed'' particles. It is similar to dimensional reduction in that it maintains an equal number of bosonic and fermionic states, as required for preserving supersymmetry. Supersymmetry Ward identities relate different helicity amplitudes in supersymmetric theories. As a check that the FDH scheme preserves supersymmetry, at least through two loops, we explicitly verify a number of these identities for gluon-gluon scattering (gg {yields} gg) in supersymmetric QCD. These results also cross-check recent non-trivial two-loop calculations in ordinary QCD. Finally, we compute the two-loop shift between the FDH coupling and the standard {bar M}{bar S} coupling, {alpha}{sub s}. The FDH shift is identical to the one for dimensional reduction. The two-loop coupling shifts are then used to obtain the three-loop QCD {beta} function in the FDH and dimensional reduction schemes.

- Authors:

- Publication Date:

- Research Org.:
- Stanford Linear Accelerator Center, Menlo Park, CA (US)

- Sponsoring Org.:
- USDOE Office of Energy Research (ER) (US)

- OSTI Identifier:
- 799012

- Report Number(s):
- SLAC-PUB-9104

TRN: US0205155

- DOE Contract Number:
- AC03-76SF00515

- Resource Type:
- Technical Report

- Resource Relation:
- Other Information: PBD: 8 Mar 2002

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AMPLITUDES; HELICITY; QUANTUM CHROMODYNAMICS; SCATTERING; SUPERSYMMETRY

### Citation Formats

```
Dixon, Lance.
```*Supersymmetric Regularization Two-Loop QCD Amplitudes and Coupling Shifts*. United States: N. p., 2002.
Web. doi:10.2172/799012.

```
Dixon, Lance.
```*Supersymmetric Regularization Two-Loop QCD Amplitudes and Coupling Shifts*. United States. doi:10.2172/799012.

```
Dixon, Lance. Fri .
"Supersymmetric Regularization Two-Loop QCD Amplitudes and Coupling Shifts". United States. doi:10.2172/799012. https://www.osti.gov/servlets/purl/799012.
```

```
@article{osti_799012,
```

title = {Supersymmetric Regularization Two-Loop QCD Amplitudes and Coupling Shifts},

author = {Dixon, Lance},

abstractNote = {We present a definition of the four-dimensional helicity (FDH) regularization scheme valid for two or more loops. This scheme was previously defined and utilized at one loop. It amounts to a variation on the standard 't Hooft-Veltman scheme and is designed to be compatible with the use of helicity states for ''observed'' particles. It is similar to dimensional reduction in that it maintains an equal number of bosonic and fermionic states, as required for preserving supersymmetry. Supersymmetry Ward identities relate different helicity amplitudes in supersymmetric theories. As a check that the FDH scheme preserves supersymmetry, at least through two loops, we explicitly verify a number of these identities for gluon-gluon scattering (gg {yields} gg) in supersymmetric QCD. These results also cross-check recent non-trivial two-loop calculations in ordinary QCD. Finally, we compute the two-loop shift between the FDH coupling and the standard {bar M}{bar S} coupling, {alpha}{sub s}. The FDH shift is identical to the one for dimensional reduction. The two-loop coupling shifts are then used to obtain the three-loop QCD {beta} function in the FDH and dimensional reduction schemes.},

doi = {10.2172/799012},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2002},

month = {3}

}