Leptogenesis in the $μτ$ basis

We formulate three-flavor type-I leptogenesis in the $μτ$ basis which is convenient because in the three-flavor regime, both $μ$ and $τ$ charged lepton Yukawa interactions are in thermal equilibrium and the thermal bath is symmetric under the exchange $μ\leftrightarrow τ$. We apply this formalism to models with $μτ$-reflection $\mathsf{CP}^{μτ}$ symmetry. We confirm the previous result that leptogenesis fails in the three-flavor regime with exact $\mathsf{CP}^{μτ}$ symmetry. Allowing $\mathsf{CP}^{μτ}$ symmetry to be broken to various degrees, we show that leptogenesis can be successful in the three-flavor regime only in certain tuned parameter space, which could further imply additional symmetry is at play. As a bonus, we derive analytical expressions which could be utilized whenever the branching ratios for the decays to $μ$ and $τ$ flavors are equal or approximately so.

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