Leptogenesis in the $\mu \tau$ basis

Abstract

We formulate three-flavor type-I leptogenesis in the $\mu \tau$ basis which is convenient because in the three-flavor regime, both $\mu$ and $\tau$ charged lepton Yukawa interactions are in thermal equilibrium and the thermal bath is symmetric under the exchange $\mu \leftrightarrow \tau$. We apply this formalism to models with $\mu \tau$-reflection ${\mathsf{CP}}^{\mu \tau }$ symmetry. We confirm the previous result that leptogenesis fails in the three-flavor regime with exact ${\mathsf{CP}}^{\mu \tau }$ symmetry. Allowing ${\mathsf{CP}}^{\mu \tau }$ 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 $\mu$ and $\tau$ flavors are equal or approximately so.

Comments: 22 pages, 7 figures, 4 appendices