text: Our model is quite analogous to the so-called gauge singlet scalar dark matter [16–18]. 
  
  Some recent studies can be found in Refs. [19, 20]. In the gauge singlet scalar DM model, the 
  
  thermal abundance is mainly controlled by the interactions between the SM Higgs boson and 
  
  the DM particle. In our model, B  L Higgs VEV v′ can play the same role for mN < MW , 
  − 
  
  namely a larger v′ corresponds to weaker coupling between DM and Higgs for a ﬁxed DM 
  
  mass. On the other hand, for mN > MW the diﬀerence appears. Even if the annihilation 
  
  6 