"An effective two dimensionality" cases bring a new hope to the Kaluza-Klein[like] theories

One step towards realistic Kaluza-Klein[like] theories and a loop hole through the Witten's "no-go theorem" is presented for cases which we call an effective two dimensionality cases: In $d=2$ the equations of motion following from the action with the linear curvature leave spin connections and zweibeins undetermined. We present the case of a spinor in $d=(1+5)$ compactified on a formally infinite disc with the zweibein which makes a disc curved on an almost $S^2$ and with the spin connection field which allows on such a sphere only one massless normalizable spinor state of a particular charge, which couples the spinor chirally to the corresponding Kaluza-Klein gauge field. We assume no external gauge fields. The masslessness of a spinor is achieved by the choice of a spin connection field (which breaks parity), the zweibein and the normalizability condition for spinor states, which guarantee a discrete spectrum forming the complete basis. We discuss the meaning of the hole, which manifests the noncompactness of the space.Comment: 26 pages, 1 figure, an addition which helps to clarify the assumptions and their consequences (the discreteness of spectrum, the massless solution of one handedness,..

Puzzles of Dark Matter - More Light on Dark Atoms?

Positive results of dark matter searches in experiments DAMA/NaI and DAMA/LIBRA confronted with results of other groups can imply nontrivial particle physics solutions for cosmological dark matter. Stable particles with charge -2, bound with primordial helium in O-helium "atoms" (OHe), represent a specific nuclear-interacting form of dark matter. Slowed down in the terrestrial matter, OHe is elusive for direct methods of underground Dark matter detection using its nuclear recoil. However, low energy binding of OHe with sodium nuclei can lead to annual variations of energy release from OHe radiative capture in the interval of energy 2-4 keV in DAMA/NaI and DAMA/LIBRA experiments. 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. Moreover there is no bound systems of OHe with light and heavy nuclei, so that there is no radiative capture of OHe in detectors with xenon or helium content. Due to dipole Coulomb barrier, transitions to more energetic levels of Na+OHe system with much higher energy release are suppressed in the correspondence with the results of DAMA experiments. The proposed explanation inevitably leads to prediction of abundance of anomalous Na, corresponding to the signal, observed by DAMA.Comment: Contribution to Proceedings of XIII Bled Workshop "What Comes beyond the Standard Model?