Multi-Particle Invariant Mass -- Standard Expressions and Corrections to Order $(m/E)^4$

M. P. Fewell

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arXiv · 2602.11556

Multi-Particle Invariant Mass -- Standard Expressions and Corrections to Order $(m/E)^4$

M. P. Fewell

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Abstract

In collider-based particle physics, $invariant\ mass$ refers to the magnitude of the total-momentum 4-vector of a system of particles. An expression for the invariant mass of a 2-particle system is well known; it assumes that both the total energy $E$ and the transverse momentum $p_\mathrm{T}$ of each particle in the system greatly exceed its mass $m$. This note explores these assumptions by computing correction terms in powers of $m/E$ up to order $(m/E)^4$. The assumptions are found to be robust: not only is the leading correction quadratic in $m/E$, but also cancellations reduce its coefficient and that of the next-to-leading correction, which is of order $(m/E)^4$. Three- and four-particle systems are also treated and the generalisation to larger numbers of particles indicated. The zeroth-order expressions for these multi-particle systems are remarkably simple; they deserve to be better known.

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M. P. Fewell. 2026-02-12. Multi-Particle Invariant Mass -- Standard Expressions and Corrections to Order $(m/E)^4$. https://arxiv.org/abs/2602.11556

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