Unified First-Principles Formula for Time-Resolved ARPES Spectra of Coherent and Incoherent Excitons

Despite major experimental progresses in time-resolved and angle-resolved photoemission spectroscopy, a quantitative, microscopic framework for interpreting exciton-induced modifications of electronic band structures – applicable even beyond the low-density limit – is still lacking. Here we close this gap by introducing a unified approach that links the dynamics of coherent and incoherent excitons to distinct and experimentally observable excitonic sidebands. Our central result is a general, first-principles formula for time-resolved photoemission spectra, applicable across a broad range of temperatures, excitation densities, and pump-probe delays. This advance provides a predictive tool for quantitatively tracking excitonic dynamics in complex materials.