Resonant CP violation in rare τ ^± decays

In this work, we study the lepton number violating tau decays via intermediate on-shell Majorana neutrinos N_j into two scalar mesons and a lepton τ^± → M₁ ^±N_j → M₁ ^±M₂ ^±ℓ^∓. We calculate the Branching ratios Br(τ^±) and the CP asymmetry (Γ(τ⁺) − Γ(τ⁻))/(Γ(τ⁺) + Γ(τ⁻)) for such decays, in a scenario that contains at least two heavy Majorana neutrinos. The results show that the CP asymmetry is small, but becomes comparable with the branching ratio Br(τ^±) when their mass difference is similar with their decay width ΔM_N ∼ Γ_N. We also present regions of the heavy-light neutrino mixing elements, in which the CP asymmetry could be explored in future tau factories.