Vacuum amplitudes and time-like causal unitary in the loop-tree duality

TL;DR

This paper introduces a novel causal unitary approach based on loop-tree duality for decay processes, enabling well-defined calculations in four dimensions and providing insights into singularity cancellations and renormalization.

Contribution

It presents the first proof-of-concept application of LTD causal unitary to decay processes at higher orders, with explicit expressions and physical interpretation of singularity cancellations.

Findings

Successful demonstration of the method on selected decay processes

Explicit expressions for vacuum amplitudes and decay rates

Numerical results showing advantages of the approach

Abstract

We present the first proof-of-concept application to decay processes at higher perturbative orders of LTD causal unitary, a novel methodology that exploits the causal properties of vacuum amplitudes in the loop-tree duality (LTD) and is directly well-defined in the four physical dimensions of the space-time. The generation of loop- and tree-level contributions to the differential decay rates from a kernel multiloop vacuum amplitude is shown in detail, and explicit expressions are presented for selected processes that are suitable for a lightweight understanding of the method. Specifically, we provide a clear physical interpretation of the local cancellation of soft, collinear and threshold singularities, and of the local renormalisation of ultraviolet singularities. The presentation is illustrated with numerical results that showcase the advantages of the method.