The Gegenbauer Higgs

Higgs precision measurements and resonance searches at the LHC have made sharper than ever the electroweak naturalness problem. Instead of abandoning symmetry-based explanations, we explore further the range of theoretical possibilities, to distinguish structural limitations from the consequences of minimality assumptions. In scenarios where the Higgs boson is the pion of a new strong sector, we consider radiatively stable potentials generated by symmetry-breaking spurions in non-minimal multi-index irreducible representations. They naturally lead to small Higgs vacuum expectation values and therefore relax the fine-tuning required to comply with Higgs coupling measurements. Twin-Higgs realisations also alleviate the tension arising from the separation between the Higgs and coloured top partner masses. Single-Higgs coupling deviations of a few percent and trilinear self-coupling deviations of order one are irreducible in the natural parameter space. More generally, a ratio between these coupling modifications spanning two orders of magnitude is structurally allowed and also realised in a simple custodial weak-quadruplet extension of the standard model.