Boson linewidth in high-temperature superconductors

We have considered boson exchange models of high-temperature superconductors which use Eliashberg theory and in which the bare bosons have sharp spectral features. In particular, we have calculated the boson linewidth due to the interaction with the charge carriers. We find for a recent model of Arnold, Mueller, and Swihart that the width of the 10-meV peak in their ${\mathrm{\alpha }}^2$F is consistent with a broadened boson peak. However, for a weak-coupling model with the boson peak in the eV range, the interaction causes a broadening in the boson peak that is comparable to or larger than the energy of the peak.