Affleck-Dine leptogenesis via multiple flat directions

Abstract

We investigate the Affleck-Dine mechanism when multiple flat directions simultaneously have large values. We consider in detail the case when both the LH u and the H u H d flat directions are operative with a nonrenormalizable superpotential. In the case where Hubble induced A terms are present for these two flat directions, their initial values are determined completely by the potential and there are no ambiguities in how they are mixed. Moreover, CP is violated even when the Hubble parameter is large due to the Hubble induced A term and a cross coupling of the F term, so that the lepton asymmetry is generated just after the end of inflation. As a result, compared with the case of a single flat direction, the resultant lepton-to-entropy ratio is enhanced by a factor of H osc /m 3/2 , where H osc is the Hubble parameter at the onset of oscillation of the flat direction and m 3/2 is the gravitino mass. However, when the Hubble induced A terms do not exist, there remains indefiniteness of initial phases and CP is violated spontaneously by the phase difference between the initial phases and the points of the minima of the hidden-sector induced A terms. Therefore, CP violation is not effective until the onset of the oscillation of the scalar fields around the origin and there is a suppression factor from thermal effects as in the case of a single flat direction. In this case, the amplitude of baryon isocurvature perturbations imposes constraints on the model parameters.