From loops to trees by-passing Feynman's theorem

TL;DR

This paper introduces a duality relation connecting one-loop integrals with phase-space integrals via a modified Feynman prescription, simplifying calculations in quantum field theory.

Contribution

It presents a novel duality relation that replaces the traditional +i0 prescription, enabling more efficient calculations of one-loop amplitudes in relativistic quantum field theories.

Findings

Derivation of a Lorentz covariant duality relation

Regularization of propagators with a new prescription

Applicability to analytical and numerical calculations in quantum field theory

Abstract

We derive a duality relation between one-loop integrals and phase-space integrals emerging from them through single cuts. The duality relation is realized by a modification of the customary +i0 prescription of the Feynman propagators. The new prescription regularizing the propagators, which we write in a Lorentz covariant form, compensates for the absence of multiple-cut contributions that appear in the Feynman Tree Theorem. The duality relation can be applied to generic one-loop quantities in any relativistic, local and unitary field theories. %It is suitable for applications to the analytical calculation of %one-loop scattering amplitudes, and to the numerical evaluation of %cross-sections at next-to-leading order. We discuss in detail the duality that relates one-loop and tree-level Green's functions. We comment on applications to the analytical calculation of one-loop scattering amplitudes, and to the numerical evaluation of cross-sections at next-to-leading order.