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.
Theoretical predictions for the cosmic antiproton spectrum currently fall short of the corresponding experimental level of accuracy. Among the main sources of uncertainty are the antiproton production cross sections in cosmic ray inelastic interactio
ns. We analyse existing data on antiproton production in $pp$ scattering, including for the first time the measurements performed by the NA49 Collaboration. We compute the antiproton spectrum finding that in the energy range where data are available (antiproton energies of about 4-550 GeV) different approaches lead to almost equivalent results, with an uncertainty of 10-20%. Extrapolations outside this region lead to different estimates, with the uncertainties reaching the 50% level around $1$ TeV, degrading the diagnostic power of the antiproton channel at those energies. We also comment on the uncertainties in the antiproton production source term coming from nuclei heavier than protons and from neutrons produced in $pp$ scatterings, and point out the need for dedicated experimental campaigns for all processes involving antiproton production in collisions of light nuclei.
