Gegenbauer's Twin

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$^{2}$ « 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.