Non-susy AdS Instability Conjecture Limits 2HDM Higgs Mass to 125 GeV

The search for physics beyond the Standard Model frequently explores extensions to the Higgs sector, and a compelling approach involves considering extra spatial dimensions. M. A. Rbah, S. Saoud, R. Sammani, and colleagues, including R. Ahl Laamara from Mohammed V University, investigate how compactifying a Two-Higgs-Doublet Model affects its properties, specifically by considering the influence of these extra dimensions on the Higgs potential. Their work reveals a crucial link between the stability of these extra dimensions and the mass of additional Higgs-like particles, establishing a model-independent bound of greater than 350 GeV for these heavier scalars. This finding demonstrates how theoretical consistency requirements, inspired by the broader ‘Swampland’ programme, can deliver concrete, testable predictions for experiments searching for extended Higgs sectors and potentially unveil new physics beyond our current understanding.

Key to this research are ‘swampland’ conjectures, which suggest that not all mathematically consistent quantum field theories are actually realized in nature, with the swampland referring to theories incompatible with a full theory of quantum gravity. Researchers are also investigating models where gravity propagates in extra dimensions, focusing on the radion, a scalar field associated with the size of these extra dimensions, and how stabilizing the radion affects the Higgs potential and the parameters of two-Higgs-doublet models. This process generated a three-dimensional effective action incorporating tree-level interactions, one-loop corrections from Kaluza-Klein modes, and a contribution from the radion field, a consequence of the Goldberger-Wise mechanism. The team derived this complete effective action, demonstrating that for a Higgs mass of 125 GeV, the radion potential admits a stable minimum with near-zero vacuum energy. To achieve this, researchers expanded the Higgs doublets into a sum of Kaluza-Klein modes, accounting for the infinite series of fields arising from the extra dimension.

Integrating over this compact dimension then yielded the three-dimensional effective action, rescaling the original four-dimensional cosmological constant and Planck mass. The resulting action incorporates contributions from both gravity and the Higgs fields, each modified by a factor related to the radius of the compactified circle. The study further refined this action by incorporating one-loop quantum corrections, crucial for determining vacuum stability. The team demonstrated that the large momentum modes in the Kaluza-Klein spectrum are exponentially suppressed, allowing for a decoupling of heavy modes from the low-energy dynamics. The resulting effective potential incorporates tree-level interactions, one-loop corrections from Kaluza-Klein towers, and a radion contribution inspired by the Goldberger-Wise mechanism. The study illustrates how Swampland-inspired constraints can yield sharp, phenomenologically testable predictions for extended Higgs sectors. By deriving a three-dimensional effective potential that includes tree-level interactions, Kaluza-Klein contributions, and radion effects, the researchers mapped how compactification reshapes the theory’s vacuum structure and demonstrated that the compactification radius is dynamically determined by the coupling between the radion potential and Higgs-dependent corrections to the vacuum energy. A key finding is a critical threshold around 680 GeV for heavier Higgs masses; below this value, the effective potential develops a negative minimum, indicating an unstable vacuum, while masses above this threshold restore a stable, positive-energy configuration. This demonstrates how compactification and quantum gravity principles can combine to place predictive limits on extended Higgs spectra without requiring fine-tuning.