A comprehensive review of physics at an linear collider in the energy range of  GeV–3 TeV is presented in view of recent and expected LHC results, experiments from low-energy as well as astroparticle physics. The report focusses in particular on Higgs-boson, top-quark and electroweak precision physics, but also discusses several models of beyond the standard model physics such as supersymmetry, little Higgs models and extra gauge bosons. The connection to cosmology has been analysed as well.

Non-decoupling D-term extensions of the MS-SM enhance the tree-level Higgs mass compared to the MSSM; therefore, they relax fine-tuning and may allow lighter stops with rather low masses even without maximal mixing. We present the anatomy of various non-decoupling D-term extensions of the MSSM and explore the potential of the LHC and of the International Linear Collider (ILC) to determine their deviations in the Higgs couplings with respect to the Standard Model. Depending on the mass of the heavier Higgs m H , such deviations may be constrained at the LHC and determined at the ILC. We evaluate the Higgs couplings in different models and study the prospects for a model distinction at the different stages of the ILC at √ s = 250, 500 and 1000 GeV, including the full luminosity upgrade and compare it with the prospects at HL-LHC.

It is one of the most challenging tasks at the Large Hadron Collider and at a future Linear Collider not only to observe physics beyond the Standard Model, but to clearly identify the underlying new physics model. In this paper we concentrate on the distinction between two different supersymmetric models, the MSSM and the NMSSM, as they can lead to similar low energy spectra. The NMSSM adds a singlet superfield to the MSSM particle spectrum and simplifies embedding a SM-like Higgs candidate with the measured mass of about 125.5 GeV. In parts of the parameter space the Higgs sector itself does not provide sufficient indications for the underlying model. We show that exploring the gaugino/higgsino sectors could provide a meaningful way to distinguish the two models. Assuming that only the lightest chargino and neutralino masses and polarized cross sections $e^+e^-\to \tilde{\chi}^0_i\tilde{\chi}^0_j$, $\tilde{\chi}^+_i\tilde{\chi}^-_j$ are accessible at the linear collider, we reconstruct the fundamental MSSM parameters $M_1$, $M_2$, $\mu$, $\tan\beta$ and study whether a unique model distinction is possible based on this restricted information. Depending on the singlino admixture in the lightest neutralino states, as well as their higgsino or gaugino nature, we define several classes of scenarios and study the prospects of experimental differentiation.Comment: 20 pages, 11 figure

Future lepton colliders will be precision machines whose physics program includes close study of the Higgs sector and searches for new physics via polarised beams. The luminosity requirements of such machines entail very intense lepton bunches at the interaction point with associated strong electromagnetic fields. These strong fields not only lead to obvious phenomena such as beamstrahlung, but also potentially affect every particle physics process via virtual exchange with the bunch fields. For precision studies, strong field effects have to be understood to the sub-percent level. Strong external field effects can be taken into account exactly via the Furry Picture or, in certain limits, via the Quasi-classical Operator method . Significant theoretical development is in progress and here we outline the current state of play.

Future linear colliders designs, ILC and CLIC, are expected to be powerful machines for the discovery of Physics Beyond the Standard Model and subsequent precision studies. However, due to the intense beams (high luminosity, high energy), strong electromagnetic fields occur in the beam-beam interaction region. In the context of precision high energy physics, the presence of such strong fields may yield sensitive corrections to the observed electron-positron processes. The Furry picture of quantum states gives a conceptually simple tool to treat physics processes in an external field. A generalization of the quasi-classical operator method (QOM) as an approximation is considered too.