(Lₑ-Lμ-Lτ) discrete symmetry for heavy right-handed neutrinos and degenerate leptogenesis

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The degenerate leptogenesis is studied when the degeneracy in two of the heavy right-handed neutrinos [the third one is irrelevant if μ-τ symmetry is assumed] is due to L≡ (Lₑ-Lμ-Lτ) discrete symmetry. It is shown that a sizeable leptogenesis asymmetry (ε 10⁻⁶) is possible. The level of degeneracy required also predicts the Majorana phase needed for the asymmetry. Since it is the same phase, which appears in the double β% -decay and this prediction is testable. Implication of non-zero reactor angle θ₁₃ are discussed. It is shown that the contribution from % ²θ₁₃ to leptogenesis asymmetry parameter may even dominate.An accurate measument of ²θ₁₃ would have important implications for the mass degeneracy of heavy right-handed neutrinos.