Invariant relativistic kinematics: Phase space triangulation

TL;DR

This paper introduces a frame-independent approach to relativistic phase space using invariants, simplifying calculations of particle decay widths and scattering cross sections through geometric and diagrammatic methods.

Contribution

It develops a novel invariant phase space formulation with simple integration limits and a pictorial diagrammatic approach for arbitrary dimensions.

Findings

Frame-independent invariants relate to observable momenta and angles.

Derived expressions for n-dimensional phase spaces with straightforward integration.

Introduced phase space diagrams for identifying optimal integration variables.

Abstract

The calculation of particle decay widths and scattering cross sections naturally decomposes into a quantum mechanical amplitude and a relativistic phase space (PS). This PS can be formulated in terms of parallelotopes providing frame independent invariants. We demonstrate how these invariants are related to frame dependent observables such as momenta, energies, and angles between particles. Furthermore, we derive expressions for n-dimensional PSs featuring simple integration limits that are particularly well suited for an analytical treatment. To that end we develop a pictorial description using PS diagrams that allow to straightforwardly identify the optimal set of integration variables for arbitrary n.