All tree-level unitarity conditions in spin-≤1 theories are captured by four- and five-point amplitudes and can be diagnosed from particle content alone.
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S-matrix consistency forces the complete gluon amplitude structure and requires Yang-Mills Lie algebra plus Higgs mechanism for unitarised massive vector boson scattering.
A modular assembly method constructs D-dimensional higher-derivative four-point amplitudes involving fermions from gauge-invariant blocks, color factors, and permutation-invariant scalar polynomials.
SMEFT contact terms are decomposed into spurion structures whose coefficients come from higher-order Higgs singlet combinations, with W/Z masses, mixing, and fermion couplings fully saturated by dimension-eight operators.
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Explicit Conditions for Diagnosing Tree-Level Unitarity
All tree-level unitarity conditions in spin-≤1 theories are captured by four- and five-point amplitudes and can be diagnosed from particle content alone.
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The Spurion Massive EFT (SMEFT)
SMEFT contact terms are decomposed into spurion structures whose coefficients come from higher-order Higgs singlet combinations, with W/Z masses, mixing, and fermion couplings fully saturated by dimension-eight operators.