Erratum to: JHEP05(2015)069ArXiv ePrint: 1503.03502The two models containing two ALPs in section 2.3 of ref.[1] lead to too light non-SM charged leptons E of only a few GeV. (The single ALP model of section 2.2 does not suffer from this problem.)This problem can be amended without significant modifications by considering two heavy vector-like fermions E and E ′ instead of one. Instead of the last two terms of eq. (2.40), (2.41) and (2.47) of [1], we should consider the four termswhere we already fixed the r, r ′ powers without affecting any formula. One should use s = s ′ = 1 if needed. Now the heavy leptons E, E ′ have intermediate scale masses of order 10 9÷10 GeV. The charge of the discrete symmetries are only modified for E L,R and E ′ L,R in a predictable manner; see table below. Appropriate normalization of these charges leads to the PQ charges X, X ′ and the extended lepton numbers L, L ′ . Note that U(1) X [U(1) X ′ ] is vectorial for E ′ (E) and that the first two terms of the Lagrangian above implies E R and E ′ R have equal charges (X, X ′ , Z, Z ′ , L, L ′ ). The rest of the formulas and the phenomenological consequences remain unchanged.Additionally, the lowest order operator couplingL-S R for model II isLHS R σ 4 σ ′ instead ofLHS R σ 2 σ ′ * . This implies m DS is negligible in eq. (2.52).