An improved analysis of the diphoton decay rate of the Higgs boson in the Inert Doublet Model is presented together with a critical discussion of the results existing in the literature. For a Higgs boson mass M h of 125 GeV and taking into account various constraints -vacuum stability, existence of the Inert vacuum, perturbative unitarity, electroweak precision tests and the LEP bounds -we find regions in the parameter space where the diphoton rate is enhanced. The resulting regions are confronted with the allowed values of the Dark Matter mass. We find that a significant enhancement in the two-photon decay of the Higgs boson is only possible for constrained values of the scalar couplings λ3 ∼ hH + H − , λ345 ∼ hHH and the masses of the charged scalar and the Dark Matter particle. The enhancement above 1.3 demands that the masses of H ± and H be less than 135 GeV (and above 62.5 GeV) and −1.46 < λ3, λ345 < −0.24. In addition, we analyze the correlation of the diphoton and Zγ rates.

We present a new method for renormalisation group improvement of the effective potential of a quantum field theory with an arbitrary number of scalar fields. The method amounts to solving the renormalisation group equation for the effective potential with the boundary conditions chosen on the hypersurface where quantum corrections vanish. This hypersurface is defined through a suitable choice of a field-dependent value for the renormalisation scale. The method can be applied to any order in perturbation theory and it is a generalisation of the standard procedure valid for the one-field case. In our method, however, the choice of the renormalisation scale does not eliminate individual logarithmic terms but rather the entire loop corrections to the effective potential. It allows us to evaluate the improved effective potential for arbitrary values of the scalar fields using the tree-level potential with running coupling constants as long as they remain perturbative. This opens the possibility of studying various applications which require an analysis of multi-field effective potentials across different energy scales. In particular, the issue of stability of the scalar potential can be easily studied beyond tree level.

We discuss the constraints on Dark Matter coming from the LHC Higgs data and WMAP relic density measurements for the Inert Doublet Model, which is one of the simplest extensions of the Standard Model providing a Dark Matter candidate. We found that combining the diphoton rate R γγ and the Ω DM h 2 data one can set strong limits on the parameter space of the Inert Doublet Model, stronger or comparable to the constraints provided by the XENON100 experiment for low and medium Dark Matter mass.

We derive a general quantum field theoretic formula for the force acting on expanding bubbles of a first order phase transition in the early Universe setting. In the thermodynamic limit the force is proportional to the entropy increase across the bubble of active species that exert a force on the bubble interface. When local thermal equilibrium is attained, we find a strong friction force which grows as the Lorentz factor squared, such that the bubbles quickly reach stationary state and cannot run away. We also study an opposite case when scatterings are negligible across the wall (ballistic limit), finding that the force saturates for moderate Lorentz factors thus allowing for a runaway behavior. We apply our formalism to a massive real scalar field, the standard model and its simple portal extension. For completeness, we also present a derivation of the renormalized, one-loop, thermal energy-momentum tensor for the standard model and demonstrate its gauge independence.