Acoustic plasmons and high-T_c superconductivity of cuprates with extended saddle point singularity in electron spectrum

It is shown that the strong anisotropy of the one-particle electron spectrum, due to the existence of extended saddle-point singularities close to the Fermi level in the hole-type cuprates, leads to the appearance of a low-frequency peak in the spectral function of the charge density fluctuations due to the presence of an acoustic plasmon branch in the collective electron spectrum. We argue that the retarded anisotropic electron-plasmon interaction suppresses the static screened Coulomb repulsion for small transferred momenta and provides the effective attraction between electrons in the d_x2-y2-wave channel of the Cooper pairing of current carriers.