We use the invariance of physical picture under a change of Lagrangian, the reparametrization invariance in the space of Lagrangians and its particular case -the rephrasing invariance, for analysis of the two-Higgs-doublet extension of the SM. We found that some parameters of theory like tan β are reparametrization dependent and therefore cannot be fundamental. We use the Z2-symmetry of the Lagrangian, which prevents a φ1 ↔ φ2 transitions, and the different levels of its violation, soft and hard, to describe the physical content of the model. In general, the broken Z2-symmetry allows for a CP violation in the physical Higgs sector. We argue that the 2HDM with a soft breaking of Z2-symmetry is a natural model in the description of EWSB. To simplify the analysis we choose among different forms of Lagrangian describing the same physical reality a specific one, in which the vacuum expectation values of both Higgs fields are real.A possible CP violation in the Higgs sector is described by using a two-step procedure with the first step identical to a diagonalization of the mass matrix for CP-even fields in the CP conserving case. We find very simple necessary and sufficient condition for a CP violation in the Higgs sector. We determine the range of parameters for which CP violation and Flavor Changing Neutral Current effects are naturally small -it corresponds to a small dimensionless mass parameter ν = Re m 2 12 /(2v1v2). We show that for small ν some Higgs bosons can be heavy, with mass up to about 0.6 TeV, without violating of the unitarity constraints. If ν is large, all Higgs bosons except one can be arbitrary heavy. We discuss in particular main features of this case, which corresponds for ν → ∞ to a decoupling of heavy Higgs bosons.In the Model II for Yukawa interactions we obtain the set of relations among the couplings to gauge bosons and to fermions which allows to analyse different physical situations (including CP violation) in terms of these very couplings, instead of the parameters of Lagrangian.

Physics at the Large Hadron Collider (LHC) and the International e + e − Linear Collider (ILC) will be complementary in many respects, as has been demonstrated at previous generations of hadron and lepton colliders. This report addresses the possible interplay between the LHC and ILC in testing the Standard Model and in discovering and determining the origin of new physics. Mutual benefits for the physics programme at both machines can occur both at the level of a combined interpretation of Hadron Collider and Linear Collider data and at the level of combined analyses of the data, where results obtained at one machine can directly influence the way analyses are carried out at the other machine. Topics under study comprise the physics of weak and strong electroweak symmetry breaking, supersymmetric models, new gauge theories, models with extra dimensions, and electroweak and QCD precision physics. The status of the work that has been carried out within the LHC / LC Study Group so far is summarised in this report. Possible topics for future studies are outlined.4

The Compact Linear Collider (CLIC) is an option for a future collider operating at centre-of-mass energies up to , providing sensitivity to a wide range of new physics phenomena and precision physics measurements at the energy frontier. This paper is the first comprehensive presentation of the Higgs physics reach of CLIC operating at three energy stages: , 1.4 and . The initial stage of operation allows the study of Higgs boson production in Higgsstrahlung () and -fusion (), resulting in precise measurements of the production cross sections, the Higgs total decay width , and model-independent determinations of the Higgs couplings. Operation at provides high-statistics samples of Higgs bosons produced through -fusion, enabling tight constraints on the Higgs boson couplings. Studies of the rarer processes and allow measurements of the top Yukawa coupling and the Higgs boson self-coupling. This paper presents detailed studies of the precision achievable with Higgs measurements at CLIC and describes the interpretation of these measurements in a global fit.

We describe the physics potential of e + e − linear colliders in this report. These machines are planned to operate in the first phase at a center-of-mass energy of 500 GeV, before being scaled up to about 1 TeV. In the second phase of the operation, a final energy of about 2 TeV is expected. The machines will allow us to perform precision tests of the heavy particles in the Standard Model, the top quark and the electroweak bosons. They are ideal facilities for exploring the properties of Higgs particles, in particular in the intermediate mass range. New vector bosons and novel matter particles in extended gauge theories can be searched for and studied thoroughly. The machines provide unique opportunities for the discovery of particles in supersymmetric extensions of the Standard Model, the spectrum of Higgs particles, the supersymmetric partners of the electroweak gauge and Higgs bosons, and of the matter particles. High precision analyses of their properties and interactions will allow for extrapolations to energy scales close to the Planck scale where gravity becomes significant. In alternative scenarios, like compositeness models, novel matter particles and interactions can be discovered and investigated in the energy range above the existing colliders up to the TeV scale. Whatever scenario is realized in Nature, the discovery potential of e + e − linear colliders and the high-precision with which the properties of particles and their interactions can be analysed, define an exciting physics programme complementary to hadron machines.

We discuss the parameter space of the Inert Doublet Model, a two Higgs doublet model with a dark matter candidate. An extensive set of theoretical and experimental constraints on this model is considered, where both collider as well as astroparticle data limits, the latter in the form of dark matter relic density as well as direct detection, are taken into account. We discuss the effects of these constraints on the parameter space of the model. In particular, we do not require the IDM to provide the full dark matter content of the universe, which opens up additional regions in the parameter space accessible at collider experiments. The combination of all constraints leads to a relatively strong mass degeneracy in the dark scalar sector for masses 200 GeV, and to a minimal scale ∼ 45 GeV for the dark scalar masses. We also observe a stringent mass hierarchy M ± H > M A . We propose benchmark points and benchmark planes for dark scalar pair-production for the current LHC run being in compliance with all theoretical as well as experimental bounds.