A prescription for projectors to compute helicity amplitudes in D dimensions

• Published in: The European physical journal. C, Particles and fields Vol. 81; no. 5; pp. 1 - 33
• Main Author: Chen, Long
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-05-2021; Springer; Springer Nature B.V; SpringerOpen
• Subjects: Amplitudes; Astronomy; Astrophysics and Cosmology; Commutation; Elementary Particles; Hadrons; Heavy Ions; Helicity; Mathematical analysis; Measurement Science and Instrumentation; Nuclear Energy; Nuclear Physics; Physics; Physics and Astronomy; Projectors; Quantum Field Theories; Quantum Field Theory; Regular Article - Theoretical Physics; Regularization; String Theory; Subtraction; Tensors
• ISSN: 1434-6044; 1434-6052
• DOI: 10.1140/epjc/s10052-021-09210-9

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.