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We have studied the d-wave pairing-instability in the two-dimensionalHolstein-Hubbard model at the level of a full fluctuation exchangeapproximation which treats both Coulomb and electron-phonon (EP) interactiondiagrammatically on an equal footing. A generalized numerical renormalizationgroup technique has been developed to solve the resulting self-consistent fieldequations. The $d$-wave superconducting phase diagram shows an optimal T_c atelectron concentration <n> ~ 0.9 for the purely electronic Hubbard system. TheEP interaction suppresses the d-wave T_c which drops to zero when thephonon-mediated on-site attraction $U_p$ becomes comparable to the on-siteCoulomb repulsion $U$. The isotope exponent $\alpha$ is negative in this modeland small compared to the classical BCS value $\alpha_{BCS} = 1/2$ or comparedto typical observed values in non-optimally doped cuprate superconductors.Comment: 4 pages RevTeX + 3 PS figures include

Superconducting instability in the Holstein-Hubbard model: A numerical renormalization-group study