Pseudo-Nambu-Goldstone boson Higgs models: Naturalness at a tipping point

In scenarios where the Higgs is viewed as a pseudo-Nambu-Goldstone boson, the question of naturalness finds itself, from a phenomenological perspective, at a tipping point between direct searches and precision. If, by the end of the High-Luminosity LHC operation, all experimental results were to remain consistent with the Standard Model, precision Higgs coupling measurements would begin to drive the naturalness tension. To illustrate this from a fresh perspective, we construct a maximally natural “kitchen sink” model, throwing into the mix three approaches to symmetry-based naturalness: supersymmetry, twin Higgs, and pseudo-Nambu-Goldstone boson Higgs models with a Gegenbauer potential. In other words, we build a “supersymmetric Gegenbauer’s twin” model. This model not only maximizes naturalness, at least from a technical perspective, but can also interpolate between all three ingredients smoothly, revealing the interplay between direct exploration and precision. Implications for FCC-ee and FCC-hh are discussed.