Leptogenesis and Low energy CP violation, a link

How is CP violation of low energy related to CP violation required from baryon number asymmetry ? We give an example which shows a direct link between CP violation of neutrino oscillation and baryogenesis through leptogenesis.Comment: 3 pages and 2 figures, Talk presented at 4th Nufac02, July 1-6, 200

CP violation in neutrino oscillation and leptogenesis

We study the correlation between CP violation in neutrino oscillations and leptogenesis in the framework with two heavy Majorana neutrinos and three light neutrinos. Among three unremovable CP phases, a heavy Majorana phase contributes to leptogenesis. We show how the heavy Majorana phase contributes to Jarlskog determinant $J$ as well as neutrinoless double $\beta$ decay by identifying a low energy CP violating phase which signals the CP violating phase for leptogenesis. For some specific cases of the Dirac mass term of neutrinos, a direct relation between lepton number asymmetry and $J$ is obtained. For the most general case of the framework, we study the effect on $J$ coming from the phases which are not related to leptogenesis, and also show how the correlation can be lost in the presence of those phases.Comment: 4 pages and 3 figure

Spin dynamical properties and orbital states of the layered perovskite La_2-2x_Sr_1+2x_Mn_2_O_7 (0.3 <= x < 0.5)

Low-temperature spin dynamics of the double-layered perovskite La_2-2x_Sr_1+2x_Mn_2_O_7 (LSMO327) was systematically studied in a wide hole concentration range (0.3 <= x < 0.5). The spin-wave dispersion, which is almost perfectly 2D, has two branches due to a coupling between layers within a double-layer. Each branch exhibits a characteristic intensity oscillation along the out-of-plane direction. We found that the in-plane spin stiffness constant and the gap between the two branches strongly depend on x. By fitting to calculated dispersion relations and cross sections assuming Heisenberg models, we have obtained the in-plane (J_para), intra-bilayer (J_perp) and inter-bilayer (J') exchange interactions at each x. At x=0.30, J_para=-4meV and J_perp=-5meV, namely almost isotropic and ferromagnetic. Upon increasing x, J_perp rapidly approaches zero while |J_para| increases slightly, indicating an enhancement of the planar magnetic anisotropy. At x=0.48, J_para reaches -9meV, while J_perp turns to +1meV indicating an antiferromagnetic interaction. Such a drastic change of the exchange interactions can be ascribed to the change of the relative stability of the d_x^2-y^2 and d_3z^2-r^2 orbital states upon doping. However, a simple linear combination of the two states results in an orbital state with an orthorhombic symmetry, which is inconsistent with the tetragonal symmetry of the crystal structure. We thus propose that an ``orbital liquid'' state realizes in LSMO327, where the charge distribution symmetry is kept tetragonal around each Mn site.Comment: 10 pages including 7 figure