Speaker
Description
We investigate radiatively stable classes of pseudo-Nambu-Goldstone boson (pNGB) potentials for approximate spontaneously broken $\text{SO}(N+1)\to\text{SO}(N)$. Using both the one-loop effective action and symmetry, it is shown that a Gegenbauer polynomial potential is radiatively stable, being effectively an eigenfunction' from a radiative perspective. In Gegenbauer pNGB models, one naturally and automatically obtains $ v \propto f/n $, where $ n \in 2 \mathbb{Z} $ is the order of the Gegenbauer polynomial. For a Gegenbauer Higgs boson, this breaks the usual correlation between Higgs coupling corrections and$v/f$' tuning. Based on this, we argue that to conclusively determine whether or not the Higgs is a composite pNGB in scenarios with up to $\mathcal{O}(10\%)$ fine-tuning will require going beyond both the Higgs coupling precision and heavy resonance mass reach of the High-Luminosity LHC.
