Flavoured CP-asymmetry at the effective neutrino mass floor

Both neutrinoless double beta decay and leptogenesis require neutrinos to be Majorana fermions. A relation between these two phenomena can be derived once the mechanism of neutrino mass generation is specified. We first derive the constraints on the Majorana phases by minimising the effective neutrino mass in neutrinoless double beta decay with respect to the smallest mass among the light neutrinos. Given these phases, we derive a lower bound on $M_{1}$ (the mass of the lightest of the heavy neutrinos) in the framework of Type-I seesaw mechanism, subject to the constraint that the CP asymmetry required for adequate leptogenesis is larger than $10^{-8}$. We find that $M_{1} \geq 10^{10}\,(10^{9})$ GeV for the case of Normal (Inverted) hierarchy. We extend our analysis to the case when one of the heavy neutrinos decouples (two right handed neutrino models). In this case we find $M_{1} \geq 10^{10}\,(10^{11})$ GeV for the case of Normal (Inverted) hierarchy.