CP violation in the rare Higgs decays via exchange of on-shell almost degenerate Majorana neutrinos, H→ v_kN_j→ v_kℓ ⁻UD¯ and H→ v_kN_j→ v_kℓ ⁺U¯ D

We investigate rare decays of Higgs via exchange of two almost degenerate heavy on-shell Majorana neutrinos N_j (j = 1, 2): Γ_± = Γ(h → ν_kN_j→ ν_kℓ^±π^∓), and into the open quark channels Γ_± = Γ(h → ν_kN_j→ ν_kℓ^±UD), where UD are two jets of open quarks (U¯ D, or UD¯ , where U = u, c and D = d, s). The related CP violation asymmetry A_CP = (Γ₋− Γ₊)/(Γ₋ + Γ₊) is studied in detail. We take into account the N₁-N₂ overlap and oscillation effects. We can see that for certain, presently acceptable, range of input parameters, such decays with open quark channels, and their asymmetries, could be detected in the International Linear Collider (ILC).