# Physical projectors for multi-leg helicity amplitudes

## TL;DR

This paper introduces a new method for constructing simplified physical projector operators for multi-leg helicity amplitudes, improving efficiency and clarity in calculations, especially for five-gluon scattering.

## Contribution

The paper develops a novel approach to build physical projectors with fewer tensor structures, validated by reproducing known five-gluon amplitude results.

## Key findings

- Projectors depend on fewer tensor structures for more than four legs.
- Analytic formulas for five-gluon scattering projectors are provided.
- Validated by reproducing known one-loop five-gluon amplitude results.

## Abstract

We present a method for building physical projector operators for multi-leg helicity amplitudes. For any helicity configuration of the external particles, we define a physical projector which singles out the corresponding helicity amplitude. For processes with more than four external legs, these physical projectors depend on significantly fewer tensor structures and exhibit a remarkable simplicity compared with projector operators defined with traditional approaches. As an example, we present analytic formulas for a complete set of projectors for five-gluon scattering. These have been validated by reproducing known results for five-gluon amplitudes up to one-loop.