2020/02/27 by Michael Dine, Dine, Michael, Hiren H. Patel +3 · 1 citation
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Particle physics theoretical and experimental studies #Quantum and Classical Electrodynamics #Scientific Research and Discoveries
paper · pdf · doi:10.48550/arxiv.2002.12449
openalex publication_date 2020/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It has been suggested that scattering cross sections at very high energies for producing large numbers of Higgs particles may exhibit factorial growth, and that curing this growth might be relevant to other questions in the Standard Model. We point out, first, that the question is inherently non-perturbative; low orders in the formal perturbative expansion do not give a good approximation to the scattering amplitude for sufficiently large N for any fixed, small value of the coupling. Focusing on λϕ4 theory, we argue that there may be a systematic approximation scheme for processes where N particles near threshold scatter to produce N particles, and discuss the leading contributions to the scattering amplitude and cross sections in this limit. Scattering amplitudes do not grow as rapidly as in perturbation theory. Additionally, partial and total cross sections do not show factorial growth. In the case of cross sections for 2 → N particles, there is no systematic large N approximation available. That said, we provide evidence that non-perturbatively, there is no factorial growth in partial or total cross sections.