In complex materials various interactions play important roles in determining the material properties. Angle Resolved Photoelectron Spectroscopy (ARPES) has been used to study these processes by resolving the complex single particle self energy $Sigma(E)$ and quantifying how quantum interactions modify bare electronic states. However, ambiguities in the measurement of the real part of the self energy and an intrinsic inability to disentangle various contributions to the imaginary part of the self energy often leave the implications of such measurements open to debate. Here we employ a combined theoretical and experimental treatment of femtosecond time-resolved ARPES (tr-ARPES) and show how measuring the population dynamics using tr-ARPES can be used to separate electron-boson interactions from electron-electron interactions. We demonstrate the analysis of a well-defined electron-boson interaction in the unoccupied spectrum of the cuprate Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+x}$ characterized by an excited population decay time constant $tau_{QP}$ that maps directly to a discrete component of the equilibrium self energy not readily isolated by static ARPES experiments.
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