text: Our RH neutrino DM can elastically scatter oﬀ with nucleon, unlike another RH neutrino 
  
  DM model has been proposed by Krauss et. al. [21] and studied [22, 23]. The main process 
  
  is Higgs exchange and the resultant cross section for a proton is given by 
  
  2 
  
  mpmN 
  mp + mN (cid:19)  4 
  π (cid:18) 
  σ(p) 
  SI =  f 2 
  p , 
  (17) 
  
  with the hadronic matrix element 
  
  fp 
  mp  αq 
  mq  αq 
  mq  2 
  27 
  f (p) 
  T q  f (p) 
  T G 
  ,  =  +  (18) 
  
  Xq=u,d,s  Xc,b,t 
  
  and the eﬀective vertex (see Appendix for notations) 
  
  ∂Φ 
  ∂h  ∂Ψ 
  ∂h  ∂Φ 
  ∂H  ∂Ψ 
  ∂H (cid:19) 
  1 
  M 2 
  h  1 
  M 2 
  H 
  αq = 
  λN yq (cid:18) 
  − 
  ,  +  (19) 