A Phenomenological Approach to Multi-Higgs Production at High Energy

TL;DR

This paper presents a phenomenological approach to multi-Higgs production at high energies, suggesting that factorial amplitude growth is due to perturbation theory limitations rather than new physics, and introduces jet observables based on Higgs splitting functions.

Contribution

Develops a phenomenological framework using Higgs splitting functions and Sudakov factors to analyze multi-Higgs production, challenging the notion of new physics from factorial growth.

Findings

Pure Higgs splittings maintain good UV behavior.

Factorial growth likely due to perturbation theory breakdown.

High multiplicity does not necessarily imply unitarity violation.

Abstract

We tackle the issue of the factorial growth in the amplitudes of multi-Higgs production at high energy by developing a phenomenological approach based on the Higgs splitting functions and Sudakov factors. We utilize the method of generating functionals to define several jet observables for the Higgs sector. Our results suggest that pure Higgs splittings should retain a good UV behavior in contrast to the common picture represented by the breakdown of perturbation theory and violation of unitarity due to the high multiplicity of particles produced at or near threshold, which is found in scalar theories. We thus argue that the issue of the factorial growth in the amplitude of multi-Higgs production is probably associated with applying perturbation theory in a regime where it is no longer valid, as opposed to being a sign of new physics.