text: d2q 
  (2π)2 χ(q, ω)G(k + q, ω + Ω)  dω 
  2π 
  Σ(k, Ω) = 3g2  (6) 
  
  Z 
  
  where g is the spin-fermion coupling, and χ(q, ω) is the 
  spin susceptibility whose dynamics changes between NS 
  and SCS. 
  
  From our analysis we found that the introduction of 
  a ﬁnite fermionic bandwidth by means of a lattice has 
  generally a notable eﬀect on both W and ∆W . We 
  found that for all models except for BCSI model, only 
  70% − 80% of the optical spectral weight is obtained by 
  integrating up to the bandwidth. In these three models, 
  there also exists a wide range of ωc in which the behavior 
  of ∆W (ωc) is due to variation of ∆f (ωc) which is domi- 
  nant comparable to the ∆WK term. This dominance of 
  the cut oﬀ term is consistent with the analysis in Refs. 
  21,22,33. 