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Unstable Higgs Particle and the Equivalence Theorem

We consider the subtleties involved in the application of the Equivalence Theorem to the decay of an unstable Higgs particle. This is formally justified from consideration of unitarity and resonant elastic scattering of the stable decay products. By explicit perturbative calculation we find that the imaginary parts of the one-loop amplitudes for that decay are in agreement with the Equivlence Theorem only when one includes the imaginary parts generated by evaluatuing the tree-level amplitudes at the complex on-shell value of the four-momentum squared of the unstable particle.