The puzzles of dark matter searches

Positive results of dark matter searches in DAMA/NaI and DAMA/LIBRA experiments, being put together with negative results of other groups, imply nontrivial particle physics solutions for cosmological dark matter. Stable particles with charge -2 bind with primordial helium in O-helium "atoms" (OHe), representing a specific Warmer than Cold nuclear-interacting form of dark matter. Slowed down in the terrestrial matter, OHe is elusive for direct methods of underground Dark matter detection like those used in CDMS experiment, but its reactions with nuclei can lead to annual variations of energy release in the interval of energy 2-6 keV in DAMA/NaI and DAMA/LIBRA experiments. Schrodinger equation for system of nucleus and OHe is considered and reduced to an equation of relative motion in a spherically symmetrical potential well, formed by the Yukawa tail of nuclear scalar isoscalar attraction potential, acting on He beyond the nucleus, and dipole Coulomb repulsion between the nucleus and OHe at distances from the nuclear surface, smaller than the size of OHe. The values of coupling strength and mass of meson, mediating scalar isoscalar nuclear potential, are rather uncertain. Within these uncertainties we find a narrow window of these parameters, at which the sodium and/or iodine nuclei have a few keV binding energy with OHe. The concentration of OHe in the matter of underground detectors is adjusted to the incoming flux of cosmic O-helium at the timescale less than few minutes. Therefore the rate of radiative capture of Na and/or I by OHe should experience annual modulations. Transitions to more energetic levels of Na+OHe (I+OHe) system imply tunneling through dipole Coulomb barrier that leads to suppression of annual modulation of events with MeV-tens MeV energy release in the correspondence with the results of DAMA experiments. The proposed explanation inevitably leads to prediction of abundance of anomalous Na (and/or I) corresponding to the signal, observed by DAMA. At nuclear parameters, reproducing DAMA results, the energy release predicted for detectors with chemical content other than NaI differ in the most cases from the one in DAMA detector. In particular, it is shown that in the case of CDMS the energy of OHe-germanium bound state is beyond the range of 2-6 keV and its formation should not lead to ionization in the energy interval of DAMA signal.