text: For their analysis of the optical integral, Norman and 
  P´epin30 introduced a phenomenological model for the self 
  energy which ﬁts normal state scattering rate measure- 
  ments by ARPES41. 
  (ω) out 
  of two contributions - impurity scattering and electron- 
  electron scattering which they approximated phenomeno- 
  logically by the marginal Fermi liquid form of αω at small 
  frequencies6 (MFLI model). The total Σ 
  
  120 
  0  ′′ 
  It constructs the NS Σ 
  
  FIG. 10: Top –the conductivities in the NS and SCS in the 
  original MFLI model of Ref.30. We set Γ = 70 meV , α = 0.75, 
  ∆ = 32 meV , ω1 = 71 meV . Note that σ 
  (ω) in the SCS 
  begins at Ω = ∆ + ω1. Bottom – the behavior of WK with Γ. 
  is 
  
  ω 
  ωsat (cid:19) 
  where ωsat is about ∼ 1 
  2 of the bandwidth, and f (x) ≈ 1 
  for x < 1 and decreases for x > 1. In Ref 30 f (x) was 
  assumed to scale as 1/x at large x such that Σ′′ is ﬂat at 
  large ω. The real part of Σ(ω) is obtained from Kramers- 
  Kr¨onig relations. For the superconducting state, they 
  obtained Σ 
  by cutting oﬀ the NS expression on the lower 
  end at some frequency ω1 (the analog of ω0 + ∆ that we 
  had for EB model): 