This is exact to O ( λ ω$_{c}$ $_{E$_{f}$}$), where λ ’s are the dimensionless coupling constants exhibited b elow. In the con tinuum approximation for fermions near the fermi-energy, γ ( k , k $^{′}$) ∝ i ( k × k $^{′}$). The pairing vertex is then Since Re χ ( k − k $^{′}$) , ω ) < 0 for − ω$_{c}$ < ω < ω$_{c}$ , independent of momentum, the p airing symmetry is given simply by expressing ( k × k $^{′}$) 2 in separable form : Pairing interaction in the s -wave channel is repulsive, that in the two d -wave channels is equally attractive, and in the odd-parity channels is zero. The factor i in γ ( k , k $^{′}$), present be- cause the coupling is to fluctuations of time-reversal odd operators, is crucial in determining the sign of the interactions of the pairing vertex. To estimate T$_{c}$ , we use what has been discussed in Sec.(II) about the effect of inelastic ( k × k $^{′}$) 2 = 1 / 2 $^{[}$( k 2 x + k 2 $_{y}$)( k $^{′}$2 x + k $^{′}$2 y ) − ( k 2 x − k 2 $_{y}$)( k $^{′}$2 x − k $^{′}$2 y ) − 4( k$_{x}$k$_{y}$ )( k ′ $_{x}$k ′ $_{y}$) $^{]}$. (43) Λ ( k , k , ) ∝ − ( k × k $^{′}$) $^{2}$Re χ ( k − k $^{′}$, ω ) . (42) FIG. 14: Universality of Raman scattering in Cuprates near and Ba$_{x}$K$_{1}$$_{−}$$_{x}$BiO$_{3}$ for comp ositions of doping with the highest T$_{c}$ . The figure is taken from (88). 48