# EFTs meet Higgs Nonlinearity, Compositeness and (Neutral) Naturalness

## TL;DR

This paper develops a low-energy effective framework for composite Higgs models that captures Higgs nonlinearity and compositeness effects through form factors, enabling global fits and revealing potential deviations in Higgs-top couplings.

## Contribution

It introduces a systematic construction of form factors encoding Higgs nonlinearity and compositeness, and analyzes their impact on Higgs couplings and naturalness conditions.

## Key findings

- Higgs top coupling can be larger than the Standard Model value.
- Higgs nonlinearity effects are amplified by large mass splittings.
- Distinct correlation patterns between $t\bar{t}h$ and $t\bar{t}hh$ couplings for linear vs nonlinear Higgs models.

## Abstract

Composite Higgs and neutral-naturalness models are popular scenarios in which the Higgs boson is a pseudo Nambu-Goldstone boson, and naturalness problem is addressed by composite top partners. Since the standard model effective field theory (SMEFT) with dimension-six operators cannot fully retain the information of Higgs nonlinearity due to its PNGB nature, we systematically construct low energy Lagrangian in which the information of compositeness and Higgs nonlinearity are encoded in the form factors, the two-point functions in the top sector. We classify naturalness conditions in various scenarios, and first present these form factors in composite neutral naturalness models. After extracting out Higgs effective couplings from these form factors and performing the global fit, we find the value of Higgs top coupling could still be larger than the standard model one if the top quark is embedded in the higher dimensional representations. Also we find the impact of Higgs nonlinearity is enhanced by the large mass splitting between composite states. In this case, pattern of the correlation between the $t\bar{t}h$ and $t\bar{t}hh$ couplings is quite different for the linear and nonlinear Higgs descriptions.