# The Higgs Trilinear Coupling and the Scale of New Physics

## TL;DR

This paper estimates the energy scale at which new physics must appear to modify the Higgs trilinear coupling, using unitarity violation as a model-independent criterion, with implications for future collider experiments.

## Contribution

It provides a model-independent upper bound of approximately 13 TeV on the scale of new physics from Higgs coupling modifications, highlighting the potential of future colliders to explore this scale.

## Key findings

- Bound of ~13 TeV for Higgs trilinear modification
- Unitarity violation indicates the scale of new physics
- Future Higgs coupling measurements can reveal new physics scale

## Abstract

We consider modifications of the Higgs potential due to new physics at high energy scales. These upset delicate cancellations predicted by the Standard Model for processes involving Higgs bosons and longitudinal gauge bosons, and lead to a breakdown of the theory at high energies. We focus on modifications of the Higgs trilinear coupling and use the violation of tree-level unitarity as an estimate of the scale where the theory breaks down. We obtain a completely model-independent bound of ~ 13 TeV for an order-1 modification of the trilinear. We argue that this bound can be saturated only in fine-tuned models, and the scale of new physics is likely to be much lower. The most stringent bounds are obtained from amplitudes involving multiparticle states that are not conventional scattering states. Our results show that a future determination of the Higgs cubic coupling can point to a well-defined scale of new physics that can be targeted and explored at future colliders.