Elusive electron-phonon coupling in quantitative analyses of the spectral function

We examine multiple techniques for extracting information from angle-resolved photoemission spectroscopy (ARPES) data, and test them against simulated spectral functions for electron-phonon coupling. We find that, in the low-coupling regime, it is possible to extract self-energy and bare-band parameters through a self-consistent Kramers-Kronig bare-band fitting routine. We also show that the effective coupling parameters deduced from the renormalization of quasiparticle mass, velocity, and spectral weight are momentum dependent and, in general, distinct from the true microscopic coupling; the latter is thus not readily accessible in the quasiparticle dispersion revealed by ARPES.