The current experimental values of anomalous magnetic moments of muon and electron deviate from the Standard Model predictions by few standard deviations, which might be a hint of new physics. The sizes and signs of these deviations are different and opposite between the electron and muon, which makes it difficult to explain both of these anomalies in a consistent model without introducing large flavour-violating effects. It is shown that they can be simultaneously explained in the Minimal Supersymmetric Standard Model (MSSM) by arranging the sizes of bino-slepton and chargino-sneutrino contributions differently between the electron and muon sectors. The MSSM spectrum features very light selectrons and wino-like chargino, while they can evade LHC constraints due to degenerate spectra.

Spin-independent cross-section for neutralino dark matter scattering off nuclei is investigated in the NMSSM. Several classes of blind spots for direct detection of singlinoHiggsino dark matter are analytically identified, including such that have no analog in the MSSM. It is shown that mixing of the Higgs doublets with the scalar singlet has a big impact on the position of blind spots in the parameter space. In particular, this mixing allows for more freedom in the sign assignment for the parameters entering the neutralino mass matrix, required for a blind spot to occur, as compared to the MSSM or the NMSSM with decoupled singlet. Moreover, blind spots may occur for any composition of a singlino-Higgsino LSP. Particular attention is paid to cases with the singlet-dominated scalar lighter than the 125 GeV Higgs for which a vanishing tree-level spin-independent scattering cross-section may result from destructive interference between the Higgs and the singlet-dominated scalar exchange. Correlations of the spin-independent scattering cross-section with the Higgs observables are also discussed.

The relation between the Hubble constant and the scale of supersymmetry breaking is investigated in models of inflation dominated by a string modulus. Usually in this kind of models the gravitino mass is of the same order of magnitude as the Hubble constant which is not desirable from the phenomenological point of view. It is shown that slow-roll saddle point inflation may be compatible with a low scale of supersymmetry breaking only if some corrections to the lowest order Kähler potential are taken into account. However, choosing an appropriate Kähler potential is not enough. There are also conditions for the superpotential, and e.g. the popular racetrack superpotential turns out to be not suitable. A model is proposed in which slow-roll inflation and a light gravitino are compatible. It is based on a superpotential with a triple gaugino condensation and the Kähler potential with the leading string corrections. The problem of fine tuning and experimental constraints are discussed for that model.

It is pointed out that mixing effects in the CP-even scalar sector of the NMSSM can give 6-8 GeV correction to the SM-like Higgs mass in moderate or large tan β regions with a small value of the singlet-higgs-higgs superfields coupling λ ∼ O(0.1). This effect comes mainly from the mixing of the SM-like Higgs with lighter singlet. In the same parameter range, the mixing of the heavy doublet Higgs with the singlet may strongly modify the couplings of the singlet-like and the 125 GeV scalars. Firstly, the LEP bounds on a light singlet can be evaded for a large range of its masses. Secondly, the decay rates of both scalars can show a variety of interesting patterns, depending on the lightest scalar mass. In particular, a striking signature of this mechanism can be a light scalar with strongly suppressed (enhanced) branching ratios to bb (gg, cc, γγ) as compared to the SM Higgs with the same mass. The γγ decay channel is particularly promising for the search of such a scalar at the LHC. The 125 GeV scalar can, thus, be accommodated with substantially smaller than in the MSSM radiative corrections from the stop loops (and consequently, with lighter stops) also for moderate or large tan β, with the mixing effects replacing the standard NMSSM mechanism of increasing the tree level Higgs mass in the low tan β and large λ regime, and with clear experimental signatures of such a mechanism.

We propose a new type of supersymmetric Twin Higgs model where the SU(4) invariant quartic term is provided by a D-term potential of a new U(1) gauge symmetry. In the model the 125 GeV Higgs mass can be obtained for stop masses below 1 TeV, and a tuning required to obtain the correct electroweak scale can be as low as 20%. A stop mass of about 2 TeV is also possible with tuning of order O(10) %.