text: Fig. 1 shows the relic density ΩN h2 as a function of the DM mass mN for a set of 
  
  parameters: (v′, Mh, MH, MZ ′, sin θ) = (4000 GeV, 120 GeV, 200 GeV, 1000 GeV, 0.7), for 
  
  example. Willkinson Microwave Anisotropy Probe measured the value of DM abundance as 
  
  ΩDM h2 
  only near Higgs resonances, mN ≈ 
  
  0.1 [15]. The ﬁgure shows that a desired DM relic abundance can be obtained for 
  ≃ 
  
  Mh/2 or MH /2. 
  
  Fig. 2 shows the relic density ΩN h2 as a function of the DM mass mN for a smaller Higgs 
  
  mixing sin θ = 0.3 (others are the same as in Fig. 1). Compared with Fig. 1, for mN . MW 
  where the DM particles dominantly annihilate into f ¯f , the relic density further increases 
  
  because of the small mixing angle. When the DM is heavier, the annihilation mode into 
  
  Higgs boson pairs is opened and the relic density slightly deceases, but the reduction is not 
  
  enough to reach ΩN h2 
  ≃ 
  
   1000 