We investigate the possibility that dark matter and the baryon asymmetry of the Universe are generated by the same mechanism, following an idea initially proposed by V.A. Kuzmin and recently discussed by R. Kitano and I. Low. In our model, based on a left-right extension of the Standard Model, the baryon asymmetry is generated through leptogenesis and dark matter is made of relic stable right-handed neutrinos with mass ∼ few GeV. Constraints on the model imply that this form of dark matter would unfortunately escape detection.

We provide simple examples of the generation of complex mass terms and hence CP violation through dimensional reduction. This CP violation originates in the ''Hosotani mechanism,'' relying on nontrivial Wilson lines, assumed to appear in the dimensional reduction.

Leptogenesis is considered in its natural context where Majorana neutrinos fit in a gauge unification scheme and therefore couple to some extra gauge bosons. The masses of some of these gauge bosons are expected to be similar to those of the heavy Majorana particles, and this can have important consequences for leptogenesis. In fact, the effect can go both ways. Stricter bounds are obtained on one hand due to the dilution of the CP-violating effect by new decay and scattering channels, while, in a re-heating scheme, the presence of gauge couplings facilitates the re-population of the Majorana states. The latter effect allows in particular for smaller Dirac couplings. * ncosme@ulb.ac.be 1 that is more precisely, the quantitym 1 = λ ν λ † ν 11 v 2 /M 1 for λ ν the left-handed neutrino Yukawa couplings matrix and M 1 the lightest Majorana mass.

We study flavor neutrinos confined to our four-dimensional world coupled to one "bulk" state, i.e., a Kaluza-Klein tower. We discuss the spatial development of the neutrino disappearance, the possibility of resurgence and the effective flavor transitions induced in this mechanism. We show that even a simple model can produce an energy independent suppression at large distances, and relate this to experimental data.

We present a mechanism to generate complex phases from real 4 + 1 dimensional couplings in a model of weak interactions through dimensional reduction of a gauge theory. The orbifolding of a 4 + 1 dimensional Sp(4) × U (1) group is the minimal setup which provides both CP violation and an SU (2) × U (1) structure. We show that grand unification requires at least SO(11).CP violation in the standard model, since gauge interactions are naturally CP symmetric, is provided by complex Yukawa couplings which eventually are combined in the CKM matrix in one observable CP violating phase. While this picture has been comforted through B-decay observations [1], the standard model does not tell us more on the origin of CP violation since it is explicitely introduced.On the other hand, a truly unified theory would relate Yukawa couplings to gauge interactions implying that this unified theory would be CP symmetric. In that context a CP breaking mechanism is needed and can be found, as addressed here, in dimensional reduction. One example of these possibilities has been studied in [2]. We present here a realistic realisation of these ideas in the standard model.In the context of five dimensional gauge theory, the reduction from 4 + 1 to 3 + 1 dimensions has to deal with the extra contribution to the energy coming from the extra component of the covariant derivative, that is: D y = ∂ y − ieA y , where the derivative leads to the well known Kaluza-Klein(KK) effective mass n R in 3 + 1 dimensions.For spinors, this contribution is associated to the usual 3 + 1 dimensional pseudoscalar:ψγ 5 ψ, since the Clifford algebra is extended to γ B = (γ µ , iγ 5 ) for 4 + 1 dimensions ( B = 0, 1, · · · , (4 = y)). Thus, whatever the reduction scheme is, the fermionic mass term may receive effective complex masses of the type:This effective complex mass will lead to CP violation( although in a pure minimal-coupling U (1) theory the complex phase can be rotated away by a redefinition of spinors).Several contributions can be considered for X, e.g. the KK mass n R combined with a non-minimal coupling to the photon has been studied by Thirring [3]. Otherwise, in order to distinguish CP violation from the use of exited states, some vacuum expectation value for the extra component of the gauge field, that is the gauge invariant line integral X = A y = dyA y , * ncosme@ulb.ac.be, frere@ulb.ac.be.together with an extention of the gauge group has been considered in [2]. This line integral keeps 3 + 1 dimensional Lorentz invariance and reduces to the usual Wilson loop in the case of a compact extra space.For instance, consider a 4 + 1D SU (2) gauge group with massive doublet Ψ = (ψ 1 , ψ 2 ), and take the expectation value W y = dy W y = w σ 3 to break the group to vectorlike effective interactions in 3 + 1 dimensions:with two massive W ± and one massless W 3 . Then, the Wilson loop contributes to a complex mass matrix:Both phases cannot be redefined and, while making the mass matrix real, a remaining phase appears in the charge current implying a W 3 ...