text: Due to the additional gauge symmetry U(1)B  L, the covariant derivative for each ﬁelds 
  − 
  
  is given by 
  
  Dµ = D(SM )  iqB  LgB 
  LZ ′µ, 
  (2) 
  µ 
  − 
  −  − 
  
  where D(SM )  is the covariant derivative in the SM, and qB  L is the charge of each ﬁelds  µ 
  − 
  
  under the U(1)B  L with its gauge coupling gB  L. 
  −  − 
  
  Yukawa interactions relevant for the neutrino masses are given by 
  
  3  2  3 
  
  1 
  2  yαi ¯Lα ˜ΦNi − 
  ¯NiΨPRNi + h.c.,  λRi 
  Lint = 
  (3) 
  
  Xα=1  Xi=1  Xi=1 
  
  where ˜Φ =  iτ2Φ∗ for Φ being the SM Higgs doublet, and without loss of generality we have 
  − 
  
  worked out in the basis where the second term in the right-hand-side is in ﬂavor diagonal 
  
  for RH neutrinos. Because of the Z2 parity, the DM candidate N3 has no Yukawa couplings 