# A prescription for projectors to compute helicity amplitudes in D dimensions

## TL;DR

This paper introduces a new method for computing helicity amplitudes in D dimensions using polarized projectors that simplifies calculations and maintains compatibility with existing regularization schemes.

## Contribution

It presents a novel prescription for polarized amplitude projectors in D dimensions that avoids tensor decomposition and dimensional splitting, enabling easier and more consistent calculations.

## Key findings

- The new projectors express helicity amplitudes solely in terms of external momenta.
- The prescription preserves Lorentz index contraction with loop integration.
- It is compatible with infrared subtraction frameworks and maintains unitarity.

## Abstract

This article discusses a prescription to compute polarized dimensionally regularized amplitudes, providing a recipe for constructing simple and general polarized amplitude projectors in D dimensions that avoids conventional Lorentz tensor decomposition and avoids also dimensional splitting. Because of the latter, commutation between Lorentz index contraction and loop integration is preserved within this prescription, which entails certain technical advantages. The usage of these D-dimensional polarized amplitude projectors results in helicity amplitudes that can be expressed solely in terms of external momenta, but different from those defined in the existing dimensional regularization schemes. Furthermore, we argue that despite being different from the conventional dimensional regularization scheme (CDR), owing to the amplitude-level factorization of ultraviolet and infrared singularities, our prescription can be used, within an infrared subtraction framework, in a hybrid way without re-calculating the (process-independent) integrated subtraction coefficients, many of which are available in CDR. This hybrid CDR-compatible prescription is shown to be unitary. We include two examples to demonstrate this explicitly and also to illustrate its usage in practice.