Unitarity in Multi-Higgs Production

TL;DR

This paper investigates multi-Higgs production amplitudes at high energies, resolving previous unitarity violations by calculating the transition rate through Schwinger-Dyson equations, showing amplitudes grow quadratically and unitarity holds.

Contribution

It introduces a self-consistent spectral approach to compute multi-Higgs amplitudes, demonstrating unitarity preservation contrary to earlier exponential growth predictions.

Findings

Amplitude grows quadratically with energy

Propagator decreases asymptotically

Unitarity is maintained in the Standard Model

Abstract

It has long been known that perturbative calculations in scalar multi-particle production could break down since fast growing amplitudes appear. A recent calculation in the regime $ \lambda n \gg 1$, where $ n $ is the multiplicity and $ \lambda $ is the self-coupling, gives an amplitude which grows exponentially with the energy, resulting in a divergent propagator and leading to the violation of perturbative unitarity. In this paper the transition rate is calculated from the solution of the self-consistent Schwinger-Dyson equation in spectral representation. We get an amplitude growing quadratically with the energy which leads to an asymptotically decreasing propagator contrary to previous results. Hence, unitarity is not violated, as expected in the Standard Model.