Gegenbauer Goldstones

Abstract

We investigate radiatively stable classes of pseudo-Nambu-Goldstone boson (pNGB) potentials for approximate spontaneously broken $\mathrm{SO}(N+1)\to \mathrm{SO}(N)$. 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.

arXiv comment20 pages, 5 figures, v2: minor changes, matches the published version

References in corpus (13)

• The Minimal Composite Higgs Model
• The Twin Higgs: Natural Electroweak Breaking from Mirror Symmetry
• Light custodians in natural composite Higgs models
• The Composite Nambu-Goldstone Higgs
• Composite Higgses
• Light Top Partners for a Light Composite Higgs
• A Geometric Formulation of Higgs Effective Field Theory: Measuring the Curvature of Scalar Field Space
• Solving the Hierarchy Problem Discretely
• Adler's Zero and Effective Lagrangians for Nonlinearly Realized Symmetry
• The Maximally Symmetric Composite Higgs
• A UV complete partially composite-pNGB Higgs
• Tadpole-Induced Electroweak Symmetry Breaking and pNGB Higgs Models
• Coset Cosmology

Cited by in corpus (2)

• Charting the Higgs self-coupling boundaries
• Dilaton at the LHC: Complementary Probe of Composite Higgs