Multiscalar production amplitudes beyond threshold

Abstract

We present exact tree-order amplitudes for $H^{\ast }\to nH$, 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 ${\varphi }^4$ 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 ${\varphi }^4$ theory.

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

References in corpus (4)

• Summing tree graphs at threshold
• Summing One-Loop Graphs at Multi-Particle Threshold
• Summing one-loop graphs in a theory with broken symmetry
• Zeros of Tree-Level Amplitudes at Multi-Boson Thresholds

Cited by in corpus (13)

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• Multiscalar amplitudes to all orders in perturbation theory
• Multi-Higgs production in gluon fusion at 100 TeV
• 2 \to n threshold production at tree level
• Recursive equations for arbitrary scattering processes
• On the nullification of threshold amplitudes
• Suppression exponent for multiparticle production in $\lambda {\varphi }^4$ theory
• Partial wave amplitudes and multiparticle production
• "Isochronic" dynamical systems and nullification of amplitudes
• Nullification in scalar theories with derivative couplings
• On threshold amplitudes II: Amplitudes nullification via classical symmetries
• Multiboson threshold production by fermion-antifermion pair and hidden symmetry
• Amplitude Zeroes in Collinear Processes or What Is Left from a Factorizable 2d Model in Higher Dimensions