Influence of the pseudogap on the superconductivity-induced phonon renormalization in high-T_c superconductors

We investigate the influence of a d-density wave (DDW) gap on the superconductivity-induced renormalization of phonon frequency and linewidth. The results are discussed with respect to Raman and inelastic neutron scattering experiments. It turns out that the DDW gap can enhance the range of frequencies for $q=0$ phonon softening depending on the underlying band structure. Moreover we show that an anisotropic 'd-wave' pseudogap can also contribute to the q-dependent linewidth broadening of the 340cm$^{-1}$ phonon in YBa$_2$Cu$_3$O$_7$.