text: 11 
  
  high-energy fermions and is an input for the low-energy 
  theory. Below we follow Refs. 31,33 and assume that 
  the momentum dependence of a collective boson is ﬂat 
  near (π, π). The self energy within such model has been 
  worked out consistently in Ref. 31,33. 
  In the normal 
  state 
  
  a SCS a gapless continuum described by Eq. (20) trans- 
  forms into a gaped continuum, with a gap about 2∆ and 
  a resonance at ω = ω0 < 2∆, where for a d−wave gap we 
  deﬁne ∆ as a maximum of a d−wave gap. 
  The spin susceptibility near (π, π) in a superconductor 
  can generally be written up as 
  
  χQ 
  1 − i Π(Ω) 
  ωsf 
  ω2 
  ω2  1 
  2 
  χ(q ∼ Q, Ω) =  (21) 
  Σ′′(ω) = −  λnωsf log  1 + 
  sf ! 
  
  ω 
  ωsf 
  Σ′(ω) = −λnωsf arctan 