Model-independent Veltman Condition, Naturalness and the Little Hierarchy Problem

TL;DR

This paper develops a model-independent Veltman condition within EFT to address the hierarchy problem, showing that new physics should appear around 19 TeV unless a symmetry enforces naturalness, with implications for Higgs couplings and fine-tuning.

Contribution

It introduces a model-independent Veltman condition using EFT and analyzes its implications for naturalness, Higgs couplings, and the scale of new physics.

Findings

Quadratic divergences can be canceled by a model-independent Veltman condition.

New physics that cancels divergences is expected near 19 TeV.

If no new physics is found up to 19 TeV, the Higgs may be fine-tuned or decoupled from UV sectors.

Abstract

We adopt a bottom-up Effective Field Theory (EFT) approach to derive a model-independent Veltman condition to cancel the quadratic divergences in the Higgs mass. We show using the equivalence theorem that all deviations in the Higgs couplings to the W and Z from the SM predictions should vanish. We argue based on tree-level unitarity, that any new physics that naturally cancels the quadratic divergences should be ~19 TeV. We show that the level of fine-tuning required is O(0.1- 1%) unless the UV sector has a symmetry that forces the satisfaction of the model-independent Veltman condition, in which case all fine-tuning is eliminated. We also conjecture that if no new physics that couples to the Higgs is found up to ~ 19 TeV, or if the Higgs couplings to the SM particles conform to the SM predictions, then either the Higgs does not couple to any UV sector or is fine-tuned.