Leptogenesis, μ-τ Symmetry and θ₁₃

We show that in theories where neutrino masses arise from type I see-saw formula with three right-handed neutrinos and where large atmospheric mixing angle owes its origin to an approximate leptonic μ-τ interchange symmetry, the primordial lepton asymmetry of the Universe, εl can be expressed in a simple form in terms of low energy neutrino oscillation parameters as εl=(aΔm⊙2+bΔmA2θ132), where a and b are parameters characterizing high scale physics and are each of order ≤10-2 eV-2. We also find that for the case of two right-handed neutrinos, εl∝θ132 as a result of which, the observed value of baryon to photon ratio implies a lower limit on θ13. For specific choices of the CP phase δ we find θ13 is predicted to be between 0.10-0.15.