Predictions on the neutrinoless double beta decay from the leptogenesis via the LHu flat direction

If the baryon asymmetry in the present universe is generated by decays of the $L H_u$ flat direction, the observed baryon asymmetry requires the mass of the lightest neutrino to be much smaller than the mass scale indicated from the atmospheric and solar neutrino oscillations. Such a small mass of the lightest neutrino leads to a high predictability on the rate of the neutrinoless double beta ($0\nu\beta\beta$) decay. In this letter we show general predictions on the $0\nu\beta\beta$ decay in the leptogenesis via the $LH_u$ flat direction.