Gegenbauer Goldstones
Gauthier Durieux, Matthew McCullough, Ennio Salvioni

TL;DR
This paper explores the stability of Gegenbauer polynomial potentials for pseudo-Nambu-Goldstone bosons, revealing a natural relation between the symmetry breaking scale and the polynomial order, impacting Higgs compositeness tests.
Contribution
It demonstrates that Gegenbauer polynomial potentials are radiatively stable and introduces a new relation between the symmetry breaking scale and polynomial order in pNGB models.
Findings
Gegenbauer potentials are radiatively stable eigenfunctions.
A natural relation v ∝ f/n emerges in Gegenbauer pNGB models.
Higgs coupling corrections are decoupled from v/f tuning in these models.
Abstract
We investigate radiatively stable classes of pseudo-Nambu-Goldstone boson (pNGB) potentials for approximate spontaneously broken . 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 , where is the order of the Gegenbauer polynomial. For a Gegenbauer Higgs boson, this breaks the usual correlation between Higgs coupling corrections and `' tuning. Based on this, we argue that to conclusively determine whether or not the Higgs is a composite pNGB in scenarios with up to fine-tuning will require going beyond both the Higgs coupling precision and heavy resonance mass reach of the…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
