Rewording Theoretical Predictions at Colliders with Vacuum Amplitudes

TL;DR

This paper introduces a novel approach using multiloop vacuum amplitudes and loop-tree duality to improve theoretical predictions at high-energy colliders, ensuring gauge invariance, singularity cancellation, and a clear description of differential observables.

Contribution

It proposes the LTD causal unitary framework, providing a new representation of collider observables that is free of singularities and captures initial-state collinear singularities.

Findings

Locally free of ultraviolet and infrared singularities at all orders

Provides a new representation of differential cross sections and decay rates

Conjectures the local form of initial-state collinear singularities

Abstract

We propose multiloop vacuum amplitudes as the optimal building blocks for efficiently assembling theoretical predictions at high-energy colliders. This hypothesis is strongly supported by the manifestly causal properties of the loop-tree duality (LTD) representation of a vacuum amplitude. The vacuum amplitude, acting as a kernel, encodes all the final states contributing to a given scattering or decay process through residues in the on-shell energies of the internal propagators. It also naturally implements gauge invariance and the wave function renormalisation of the external legs. This methodological approach, dubbed LTD causal unitary, leads to a novel representation of differential cross sections and decay rates that is locally free of ultraviolet and infrared singularities at all orders in perturbation theory. Threshold singularities also match between different phase-space residues. Most notably, it allows us to conjecture for the first time the local functional form of initial-state collinear singularities. The fulfillment of all these properties provides a theoretical description of differential observables at colliders that is well defined in the four physical dimensions of the space-time.