What the resonance peak does

High-resolution angle-resolved photoemission with variable excitation energies is used to disentangle bilayer splitting effects and intrinsic (self-energy) effects in the electronic spectral function near the ($\pi$,0)-point of differently doped (Pb,Bi)$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$. In contrast to overdoped samples, where intrinsic effects at the ($\pi$,0)point are virtually absent, we find in underdoped samples \textit{intrinsic} effects in the superconducting-state ($\pi$,0) spectra of the antibonding band. This intrinsic effect is present only below the critical temperature and weakens considerably with doping. Our results give strong support for models which involve a strong coupling of electronic excitations with the resonance mode seen in inelastic neutron scattering experiments.