Properties of Multi-Higgs Models

• Applicant: Professor Dr. Otto Nachtmann
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
• Term: from 2007 to 2011
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 56255912

The investigation of multi-Higgs models is exciting for at least two reasons: Firstly, the Higgs mechanism, responsible for the generation of masses of quarks, leptons and gauge bosons, is even in the Standard Model (SM) not yet verified experimentally. In the SM the Higgs mechanism requires one physical Higgs particle which may be discovered at the Large Hadron Collider (LHC) at CERN, which starts taking data soon. It is quite possible that more than one Higgs particle will be found. Secondly, the Higgs sector may play a major role in understanding the observed absence of antibaryons in our Universe. In particular, extensions of the Standard Model with additional Higgs doublets and singlets have the capability to explain the dynamical generation of baryon asymmetry just from experimentally accessible electroweakscale physics. For instance, in the next-to-minimal extension of the Standard Model the Higgs potential is known to have the right properties for a strong first order phase transition accompanied by CP violation as required to account for the baryogenesis leading to the observed baryon-antibaryon asymmetry in the universe. In previous works we have investigated certain aspects of multi-Higgs models. We have, in particular, demonstrated that the introduction of gauge invariant functions for the Higgs fields occurring in the potential is a powerful tool to study the properties of multi-Higgs models. With the help of these invariant functions we have investigated the general two-Higgs doublet model and the next to minimal supersymmetric standard model. We have found strong constraints on the parameters of the models in a very concise way from the requirement that the potential is stable and leads to the correct electroweak symmetry breaking observed in Nature. These studies were done at the tree level. In the present proposal we will extend our investigations of general Higgs models in a number of ways. The stability and electroweak symmetry breaking properties of Higgs potentials shall be studied for models with Higgs doublets, singlets, and triplets at tree and one loop level using efficient techniques. Part of our work shall be to develop further these methods. The question of CP invariance and the effects of finite temperature in such multi-Higgs models shall be studied. We shall study the models according to their fulfilling of Sakhorov s criteria for a dynamical generation of the baryon-antibaryon asymmetry observed in Nature. Higgs models lead in general to indirect effects which may be measurable at the LHC or at the future international linear collider for electrons and positrons, ILC. Such effects will be worked out in detail.

• DFG Programme: Research Grants