Dark matter in the Kim-Nilles mechanism

The Kim-Nilles mechanism relates the $\mu$ term with the axion scale $f_a$, leading to the axino-Higgsino-Higgs Yukawa coupling of order $\mu/f_a$. This can bring a dangerous thermal production of axinos. If the axino is stable, its mass has to be as small as ${\cal O}$(0.1keV), or the reheat temperature should be lower than ${\cal O}$(10GeV) taking the lower axion scale $10^{10}$ GeV in order not to overclose the Universe. If the axino decays to a neutralino, the overproduced neutralinos can re-annihilate appropriately to saturate the observed dark matter density if the annihilation rate is of order $10^{-8}{GeV}^{-2}$ for the axion scale larger than about $10^{11}$ GeV. Thus, a light Higgsino-like lightest supersymmetric particle with a sizable bino mixture becomes a good dark matter candidate whose nucleonic cross-section is of order $10^{-45}$cm$^2$.Comment: 10 pages, 1 figure; Corrected errors in Eq.(7) and in the direct detection cross-section of the Higgsino-like dark matter; Revised Fig.1; Added a discussion on the saxion; Added references; to appear in PR

Ultrametrics and infinite dimensional whitehead theorems in shape theory

We apply a Cantor completion process to construct a complete, non-Archimedean metric on the set of shape morphisms between pointed compacta. In the case of shape groups we obtain a canonical norm producing a complete, both left and right invariant ultrametric. On the other hand, we give a new characterization of movability and we use these spaces of shape morphisms and uniformly continuous maps between them, to prove an infinite-dimensional theorem from which we can show, in a short and elementary way, some known Whitehead type theorems in shape theory