Sphalerons in composite and non-standard Higgs models

Abstract

After the discovery of the Higgs boson and the rather precise measurement of all electroweak boson's masses the local structure of the electroweak symmetry breaking potential is already quite well established. However, despite being a key ingredient to a fundamental understanding of the underlying mechanism of electroweak symmetry breaking, the global structure of the electroweak potential remains entirely unknown. The existence of sphalerons, unstable solutions of the classical action of motion that are interpolating between topologically distinct vacua, is a direct consequence of the Standard Model's $\mathrm{SU}(2{)}_L$ gauge group. Nevertheless, the sphaleron energy depends on the shape of the Higgs potential away from the minimum and can therefore be a litmus test for its global structure. Focusing on two scenarios, the minimal composite Higgs model $\mathrm{SO}(5)/\mathrm{SO}(4)$ or an elementary Higgs with a deformed electroweak potential, we calculate the change of the sphaleron energy compared to the Standard Model prediction. We find that the sphaleron energy would have to be measured to $\mathcal{O}(10)\%$ accuracy to exclude sizeable global deviations from the Standard Model Higgs potential. We further find that because of the periodicity of the scalar potential in composite Higgs models a second sphaleron branch with larger energy arises.

23 pages, 8 figures. v2: Published version. Typos corrected, comments and references added. v3: Added clarifications on notation, removed inconsistencies in the naming of one of the Higgs profile functions

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• Mapping the shape of the scalar potential with gravitational waves
• On the phenomenology of sphaleron-induced processes at the LHC and beyond
• On the Validity of the Effective Potential and the Precision of Higgs Self Couplings
• Walls, bubbles and doom -- the cosmology of HEFT
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• The Emergence of Electroweak Skyrmions through Higgs Bosons
• Baryogenesis and gravitational waves in the Zee-Babu Model
• Bubble Trouble: a Review on Electroweak Baryogenesis
• Dual electroweak phase transition in the two-Higgs-doublet model with the $S_3$ discrete symmetry
• Sphaleron bound in some nonstandard cosmology scenarios
• Constraining strongly coupled new physics from cosmic rays with machine learning techniques
• The Higgs boson decay into ZZ decaying to identical fermion pairs
• Matter and dark matter asymmetry from a composite Higgs model
• Sphaleron in the Higgs Triplet Model
• BaryoGEN, a Monte Carlo Generator for Sphaleron-Like Transitions in Proton-Proton Collisions
• A generalized Higgs potential with two degenerate minima for a dark QCD matter scenario
• Do we understand the internal spaces of second quantized fermion and boson fields, with gravity included? Relation with strings theories
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• Proceedings to the 27th Workshop "What Comes Beyond the Standard Models" Bled, July 8-17, 2024