Weak scale supersymmetry (SUSY) remains a prime explanation for the radiative stability of the Higgs field. A natural account of the Higgs boson mass, however, strongly favors extensions of the Minimal Supersymmetric Standard Model (MSSM). A plausibl
e option is to introduce a new supersymmetric sector coupled to the MSSM Higgs fields, whose associated states resolve the little hierarchy problem between the third generation squark masses and the weak scale. SUSY also accomodates a weakly interacting cold dark matter (DM) candidate in the form of a stable neutralino. In minimal realizations, the thus-far null results of direct DM searches, along with the DM relic abundance constraint, introduce a level of fine-tuning as severe as the one due to the SUSY little hierarchy problem. We analyse the generic implications of new SUSY sectors parametrically heavier than the minimal SUSY spectrum, devised to increase the Higgs boson mass, on this little neutralino DM problem. We focus on the SUSY operator of smallest scaling dimension in an effective field theory description, which modifies the Higgs and DM sectors in a correlated manner. Within this framework, we show that recent null results from the LUX experiment imply a tree-level fine-tuning for gaugino DM which is parametrically at least a few times larger than that of the MSSM. Higgsino DM whose relic abundance is generated through a thermal freeze-out mechanism remains also severely fine-tuned, unless the DM lies below the weak boson pair-production threshold. As in the MSSM, well-tempered gaugino-Higgsino DM is strongly disfavored by present direct detection results.
We study the implications of a large degree of compositeness for the light generation quarks in composite pseudo-Nambu-Goldstone-boson Higgs models. We focus in particular on viable scenarios where the right-handed up-type quarks have a sizable mixin
g with the strong dynamics. For concreteness we assume the latter to be characterized by an SO(5)/SO(4) symmetry with fermionic resonances in the SO(4) singlet and fourplet representations. Singlet partners dominantly decay to a Higgs boson and jets. As no dedicated searches are currently looking for these final states, singlet partners can still be rather light. Conversely, some fourplet partners dominantly decay to an electroweak gauge boson and a jet, a signature which has been analyzed at the LHC. To constrain the parameter space of this scenario we have reinterpreted various LHC analyses. In the limit of first two generation degeneracy, as in minimal flavor violation or U(2)-symmetric flavor models, fourplet partners need to be relatively heavy, with masses above 1.8 TeV, or the level of compositeness needs to be rather small. The situation is rather different in models that deviate from the first two generation degeneracy paradigm, as the charm parton distribution functions are suppressed relative to the up quark ones. The right-handed charm quark can be composite and its partners being as light as 600 GeV, while the right-handed up quark needs either to be mostly elementary or to have its partners as heavy as 2 TeV. Models with fully composite singlet fermions are also analyzed, leading to similar conclusions. Finally, we consider the case where both the fourplet and the singlet states are present. In this case the bounds could be significantly weaken due to a combination of smaller production rates and the opening of new channels including cascade processes.
