Multi-Particle Invariant Mass -- Standard Expressions and Corrections to Order $(m/E)^4$
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914324427046912 |
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| author | Fewell, M. P. |
| author_facet | Fewell, M. P. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_11556 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Multi-Particle Invariant Mass -- Standard Expressions and Corrections to Order $(m/E)^4$ Fewell, M. P. High Energy Physics - Phenomenology 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. |
| title | Multi-Particle Invariant Mass -- Standard Expressions and Corrections to Order $(m/E)^4$ |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2602.11556 |