Partial-Wave Unitarity Bounds on Higher-Dimensional Operators from 2-to-$N$ Scattering
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| Format: | Preprint |
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2025
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| _version_ | 1866917250379808768 |
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| author | Degrande, Céline Li, Hao-Lin Xu, Ling-Xiao |
| author_facet | Degrande, Céline Li, Hao-Lin Xu, Ling-Xiao |
| contents | We present a systematic method for deriving partial-wave unitarity bounds on Wilson coefficients of higher-dimensional operators in effective field theories involving more than four fields, which naturally appear in tree-level 2-to-$N$ scattering processes with $N \geq 3$. Unlike 2-to-2 scattering, 2-to-$N$ scattering with $N \geq 3$ features multiple amplitudes associated with the same total angular momentum. To resolve these degeneracies, we provide a way to construct an orthonormal amplitude basis by parameterizing the phase space manifold of massless particles using spinor-helicity variables, enabling analytical integration over the phase space with arbitrary particle numbers. We provide Mathematica code to analytically evaluate phase space integrals of interference between two local on-shell amplitudes up to four final-state particles, with straightforward generalization to $N$ final-state particles. As practical applications, we demonstrate the use of this tool by deriving unitarity bounds on some dimension-7 and dimension-8 operators in the Standard Model effective field theory involving five and six fields, respectively. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_15524 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Partial-Wave Unitarity Bounds on Higher-Dimensional Operators from 2-to-$N$ Scattering Degrande, Céline Li, Hao-Lin Xu, Ling-Xiao High Energy Physics - Phenomenology We present a systematic method for deriving partial-wave unitarity bounds on Wilson coefficients of higher-dimensional operators in effective field theories involving more than four fields, which naturally appear in tree-level 2-to-$N$ scattering processes with $N \geq 3$. Unlike 2-to-2 scattering, 2-to-$N$ scattering with $N \geq 3$ features multiple amplitudes associated with the same total angular momentum. To resolve these degeneracies, we provide a way to construct an orthonormal amplitude basis by parameterizing the phase space manifold of massless particles using spinor-helicity variables, enabling analytical integration over the phase space with arbitrary particle numbers. We provide Mathematica code to analytically evaluate phase space integrals of interference between two local on-shell amplitudes up to four final-state particles, with straightforward generalization to $N$ final-state particles. As practical applications, we demonstrate the use of this tool by deriving unitarity bounds on some dimension-7 and dimension-8 operators in the Standard Model effective field theory involving five and six fields, respectively. |
| title | Partial-Wave Unitarity Bounds on Higher-Dimensional Operators from 2-to-$N$ Scattering |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2511.15524 |