# Testing Naturalness

## TL;DR

This paper proposes a method to test naturalness in particle physics by measuring Higgs couplings to top quarks and partners at future colliders, aiming to verify the cancellation of quadratic divergences.

## Contribution

It introduces a simplified model for naturalness and demonstrates a technique to test Higgs coupling deviations at a 100 TeV collider.

## Key findings

- Naturalness can be tested with 10% precision at a 100 TeV collider.
- The method is effective for top partner masses up to 2.5 TeV.
- Boosted decision trees improve particle tagging accuracy.

## Abstract

Solutions to the electroweak hierarchy problem typically introduce a new symmetry to stabilize the quadratic ultraviolet sensitivity in the self-energy of the Higgs boson. The new symmetry is either broken softly or collectively, as for example in supersymmetric and little Higgs theories. At low energies such theories contain naturalness partners of the Standard Model fields which are responsible for canceling the quadratic divergence in the squared Higgs mass. Post the discovery of any partner-like particles, we propose to test the aforementioned cancellation by measuring relevant Higgs couplings. Using the fermionic top partners in little Higgs theories as an illustration, we construct a simplified model for naturalness and initiate a study on testing naturalness. After electroweak symmetry breaking, naturalness in the top sector requires $a_T = - \lambda_t^2$ at leading order, where $\lambda_t$ and $a_T$ are the Higgs couplings to a pair of top quarks and top partners, respectively. Using a multivariate method of Boosted Decision Tree to tag boosted particles in the Standard Model, we show that, with a luminosity of 30 $ab^{-1}$ at a 100 TeV $pp$-collider, naturalness could be tested with a precision of 10 % for a top partner mass up to 2.5 TeV.