Gegenbauer's Twin
Gauthier Durieux, Matthew McCullough, Ennio Salvioni

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 required to obtain a Standard Model-like Higgs, where and are the electroweak and new physics scales, respectively. Recently proposed Gegenbauer Goldstone models naturally realise 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.
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