Multiscalar production amplitudes beyond threshold

Abstract We present exact tree-order amplitudes for H ∗ → n H , for final states containing one or two particles with non-zero three-momentum, for various interaction potentials. We show that there are potentials leading to tree amplitudes that satisfy unitary, not only at threshold but also in the above kinematical configurations and probably beyond. As a by-product, we also calculated 2 → n tree amplitudes at threshold and show that for the unbroken ifφ4 theory they vanish for n ⩾ 4, for the standard Model Higgs they vanish for n ⪖ 3 and for a model potential, respecting tree-order unitarity, for n even and n ⩾ 4. Finally, we calculate the imaginary part of the one-loop 1 → n amplitude in both symmetric and spontaneously broken φ4 theory.