text: II. THE MINIMAL GAUGED U (1)B  L MODEL WITH Z2 PARITY 
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  The model is based on the gauge group SU(3)C ×  SU(2)L ×  U(1)Y × 
  U(1)B  L. Additional 
  
  − 
  L, a SM singlet 
  ﬁelds besides the standard model ﬁelds are a gauge ﬁeld Z ′µ of the U(1)B 
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  B  L Higgs boson Ψ with two U(1)B  L charge, and three RH neutrinos Ni which are 
  − 
  − 
  
  necessary for the gauge and gravitational anomaly cancellations.  In describing the RH 
  
  neutrinos, we use the four component representation of RH neutrino constructed from the 
  
  Weyl spinor νRi, 
  
  νRi 
  
  Ni ≡ 
  ,  (1) 
     
  
  ǫ ν∗Ri 
     
  For the two RH neutrinos, N1 and N2, we assign Z2 parity even, while odd for N3, so that 
  
  the RH neutrino N3 is stable and, hence, the DM candidate. 