Explicitly symmetrical treatment of three-body phase space

TL;DR

This paper derives symmetric expressions for three-body phase space, exploring geometric properties and employing the Jacobian zeta function for simplified representations in higher dimensions.

Contribution

It introduces explicit symmetry in three-body phase space calculations and utilizes elliptic integrals and the Jacobian zeta function for improved analytical expressions.

Findings

Symmetric formulas for three-body phase space derived.

Geometrical analysis of variables involved in elliptic integrals.

Use of Jacobian zeta function for four and six-dimensional cases.

Abstract

We derive expressions for three-body phase space that are explicitly symmetrical in the masses of the three particles. We study geometrical properties of the variables involved in elliptic integrals and demonstrate that it is convenient to use the Jacobian zeta function to express the results in four and six dimensions.