A Relation between the Resonance Neutron Peak and ARPES Data in Cuprates

We argue that the resonant peak observed in neutron scattering experiments on superconducting cuprates and the peak/dip/hump features observed in ARPES measurements are by-products of the same physical phenomenon. Both are due to feedback effects on the damping of spin fluctuations in a $d$-wave superconductor. We solve a set of coupled integral equations for fermionic and bosonic propagators, and show that the dynamical spin susceptibility below $T_c$ possesses the resonance peak at ${\Omega }_{\mathrm{res}}\propto {\xi }^{-1\mathrm{}}$. The scattering of these magnetic excitations by electrons gives rise to a peak/dip/hump behavior of the electronic spectral function, the peak-dip separation is exactly ${\Omega }_{\mathrm{res}}$.