Gegenbauer's Twin

TL;DR

Gegenbauer's Twin is a symmetry-based model that reduces fine-tuning in Higgs physics, predicts measurable deviations in Higgs couplings, and could be tested at the High-Luminosity LHC through di-Higgs measurements.

Contribution

It introduces Gegenbauer's Twin, combining Gegenbauer Goldstone models with Twin Higgs to achieve naturalness without fine-tuning and consistent collider results.

Findings

Single-Higgs coupling deviations of a few percent

Trilinear self-coupling deviations of order one

Potential first evidence through di-Higgs measurements at HL-LHC

Abstract

In Twin Higgs models the dominant source of fine-tuning is the cancellation of order $v^2/f^2$ required to obtain a Standard Model-like Higgs, where $v$ and $f$ are the electroweak and new physics scales, respectively. Recently proposed Gegenbauer Goldstone models naturally realise $v^2/f^2 \ll 1$ and hence remove this source of fine-tuning. By combining the two into `Gegenbauer's Twin', we obtain a symmetry-based model for Higgs sector naturalness consistent with current collider measurements without fine-tuning of parameters. Single-Higgs coupling deviations of a few percent and trilinear self-coupling deviations of order one are irreducible in the natural parameter space. Thus, notably, the fingerprints of Gegenbauer's Twin could emerge first through di-Higgs measurements at the High-Luminosity LHC.