# Determining the Shape of Higgs Potential at Future Colliders

## TL;DR

This paper explores how future collider experiments can distinguish between different theoretical models of the Higgs potential by analyzing double- and triple-Higgs production processes.

## Contribution

It systematically categorizes various new physics scenarios for the Higgs potential and identifies collider processes needed to determine its shape.

## Key findings

- Double-Higgs production at 27 TeV LHC can differentiate Higgs potential scenarios.
- Triple-Higgs production at 100 TeV collider is essential for full potential shape determination.
- Different Higgs models predict distinct signatures in multi-Higgs production rates.

## Abstract

Although the Higgs boson has been discovered, its self-couplings are poorly constrained. This leaves the nature of the Higgs boson undetermined. Motivated by different Higgs potential scenarios other than the Landau-Ginzburg type in the standard model, we systematically organize various new physics scenarios -- elementary Higgs, Nambu-Goldstone Higgs, Coleman-Weinberg Higgs, and Tadpole-induced Higgs, etc. We find that double-Higgs production at the 27 TeV high energy LHC can be used to discriminate different Higgs potential scenarios, while it is necessary to use triple-Higgs production at a future 100 TeV proton-proton collider to fully determine the shape of the Higgs potential.