Two-body lepton-flavour-violating decays in a 2HDM with soft family-lepton-number breaking

We evaluate the decays ℓ_1^± → ℓ_2^±γ , Z → ℓ_1^+ℓ_2^- , and h → ℓ_1^+ℓ_2^- , where ℓ 1 and ℓ 2 are charged leptons with different flavours and h is the scalar particle with mass 125.25 GeV, in a two-Higgs-doublet model where all the Yukawa-coupling matrices conserve the lepton flavours but the Majorana mass terms of the right-handed neutrinos break the flavour lepton numbers. We find that (1) the decays ℓ_1^± → ℓ_2^±γ require large Yukawa couplings and very light right-handed neutrinos in order to be visible, (2) the decays Z → ℓ_1^+ℓ_2^- will be invisible in all the planned experiments, except in a very restricted range of circumstances, but (3) the decays h → ℓ_1^+ℓ_2^- may be detected in future experiments for rather relaxed sets of input parameters.