Multiscalar production amplitudes beyond threshold

Details Multiscalar production amplitudes beyond threshold Multiscalar production amplitudes beyond threshold

1992-11-11

arxiv.org/abs/hep-ph/9211237v2

Nucl.Phys. B395 (1993) 3-16

Physics

High Energy Physics

High Energy Physics - Phenomenology

11 pages, Latex, 3 figures (available on request)

Scientific paper

10.1016/0550-3213(93)90205-4

We present exact tree-order amplitudes for $H^* \to n~H$, 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 unitarity, not only at threshold but also in the above kinematical configurations and probably beyond. As a by-product, we also calculate $2\to n$ tree amplitudes at threshold and show that for the unbroken $\phi^4$ theory they vanish for $n>4~$, for the Standard Model Higgs they vanish for $n\ge 3~$ 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 $1\to n$ amplitude in both symmetric and spontaneously broken $\phi^4$ theory.

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