Partial-Wave Unitarity Bounds on Higher-Dimensional Operators from 2-to-$N$ Scattering

TL;DR

The paper develops a comprehensive framework to impose unitarity constraints on Wilson coefficients of higher-dimensional SMEFT operators appearing in $2\to N$ scattering with $N\ge 3$. It combines a Casimir-operator–driven construction of an orthonormal $J$-basis for generalized partial waves with an analytic, spinor-helicity–based parameterization of massless $N$-body phase space, enabling closed-form normalization and interference calculations. The authors provide Mathematica code to automate phase-space integrals and $J$-basis metrics, and showcase concrete unitarity bounds for dimension-7 and dimension-8 SMEFT operators involving five and six fields, respectively. These results furnish explicit, theoretically grounded constraints and practical tools for interpreting SMEFT fits and ensuring consistency with fundamental principles at high energies.

Abstract

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.

Figures (1)

• Figure 1: An example output of the function GetJbasisMetric.