Exploring Extended Higgs Sectors from Colliders to the Early Universe

Abstract

The discovery of the Higgs boson completed the particle content of the Standard Model (SM), but it also reinforced the need to understand some of the caveats of the model, such as the baryon asymmetry of the universe and to look for possible solutions like Beyond Standard Model (BSM) models that modify the scalar sector of the SM. In particular, extended Higgs sectors can modify collider observables and the thermal history of the early Universe, thereby opening the possibility of a strong first-order electroweak phase transition and an associated stochastic gravitational-wave signal. This thesis investigates these connections by focusing on the scalar potential as the common origin of Higgs self-interactions, di-Higgs production, electroweak phase-transition dynamics, and gravitational-wave phenomenology.

The main phenomenological analysis is performed in the most general real singlet extension of the Standard Model without an imposed Z2 symmetry. Firstly, di-Higgs production is studied at the High-Luminosity Large Hadron Collider and at a future 1 TeV e+e− collider, with particular emphasis on the sensitivity to BSM trilinear scalar couplings and on the importance of using the full production cross section rather than simplified resonant approximations. A central part of the thesis is devoted to higher-order corrections to trilinear scalar couplings. A fully on-shell renormalisation scheme is constructed for the non Z2 symmetric real singlet model for the first time, allowing renormalisation-scale-independent predictions for the loop-corrected couplings relevant to di-Higgs production. The one-loop analysis shows that radiative corrections can be sizeable and can alter Higgs-pair production rates in a phenomenologically relevant way, demonstrating that higher-order effects are indispensable for a realistic interpretation of Higgs self-interactions in extended scalar sectors.

The cosmological implications of the model are then investigated through a dedicated implementation in BSMPT. By studying the one-loop finite-temperature effective potential, different thermal histories are studied, and scenarios featuring a strong first-order electroweak phase transition are identified. For those scenarios the corresponding stochastic gravitational-wave spectra are evaluated, with particular attention to their observability at LISA. Combining these results with the collider analysis shows that collider signatures and gravitational-wave signals provide genuinely complementary probes of extended Higgs sectors.

Finally, the thesis extends the study of Higgs self-interactions to two-loop order in the CP-conserving Two-Higgs-Doublet Model. In the alignment limit, a consistent on-shell treatment of the parameter controlling departures from exact alignment is developed, and the two-loop corrections to the trilinear couplings are computed using both diagrammatic and effective-potential methods. Overall, this thesis shows that a coherent understanding of extended Higgs sectors requires combining collider phenomenology, higher-order quantum corrections, phase-transition dynamics, and gravitational-wave signals, and that such an approach is essential for providing reliable answers to open questions in particle physics and cosmology.