The boson mediators of high-Tc superconductivity: phonons versus composite bosons from the superconducting phenomenology

We address the question of whether boson mediators of high-$T_c$ superconductivity are composite (electronic) or independent phonons. For s-wave superconductivity we show from the available experiments that the hypothesis of composite bosons is rather unlikely. Our analysis points naturally towards phonon mediators. In addition we point out that the eventual presence of a peak in the temperature dependence of the microwave conductivity while the Hebel-Slichter peak is absent in the temperature dependence of the NMR relaxation rate, can be understood within a phonon mechanism if one takes into account the modulation of the electron-phonon coupling (predominance of forward scattering) induced by Coulomb correlation of the carriers.