Abstract
In a spontaneously broken gauge theory we consider (sub)-processes in which one virtual intermediate state (it can be a Higgs or a gauge field) produces many on-shell Higgses and massive vector bosons. In the kinematic regime where all final states are produced on their mass threshold, we show how to compute iteratively all tree-level amplitudes \( {\mathcal{A}}_{1\to n+ m} \) involving an arbitrary number n of Higgs bosons and m of longitudinal vector bosons in the final state, and list the amplitudes coefficients for up to n=32 and m=32. Wefindthattheseamplitudesexhibitfactorialgrowthnotonlyinthenumberof scalar fields, but also in the number of longitudinal gauge fields, \( {\mathcal{A}}_{1\to n+ m} \) ~ n! m!. This growth is not expected to disappear at loop-level in the fixed-order perturbation theory. We conclude that at energies accessible at the next generation of hadron colliders, such as the 50-100 TeV FCC, where \( \sqrt{\widehat{s}} \) is sufficient to produce ≫1/α W of W, Z and H, perturbation theory breaks down when applied to the multiparticle electroweak production, at least near the kinematic multiparticle mass threshold where the electroweak gauge-Higgs sector becomes strongly coupled.
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Khoze, V.V. Multiparticle Higgs and vector boson amplitudes at threshold. J. High Energ. Phys. 2014, 8 (2014). https://doi.org/10.1007/JHEP07(2014)008
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DOI: https://doi.org/10.1007/JHEP07(2014)008