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The well-known Pavarini et al. [Phys. Rev. Lett. 87, 047003 (2001)]correlation between the critical temperature $T_c$, max and the shape of theFermi contour of the optimally hole-doped cuprates are explained within theframework of the BCS theory with Kondo exchange interaction incorporated as apairing mechanism. The strong influence of the relative position of the Cu4$s$level with respect to the Cu3$d_{x^2-y^2}$ level on the critical temperature$T_c$ reveals why the $s$-$d$ hybridization of the conduction band is soimportant. This hybridization is proportional to the $s$-$d$ exchangescattering amplitude between the conduction electrons -- the mechanism ofd-wave pairing in the CuO$_2$ plane. In other words the Kondo interactionconsidered as a pairing mechanism in the CuO$_2$ plane gives a naturalexplanation of the correlation between the critical temperature and the shapeof the Fermi contour. The lack of an alternative explanation for thedescription of the critical temperature of optimally doped cuprates for severaldecades gives a hint that the long sought pairing mechanism has already beenfound.

Kondo $s$-$d$ exchange interaction in the CuO$_2$ plane as the long sought mechanism of high temperature superconductivity in cuprates