Linewidths in excitonic absorption spectra of cuprous oxide

We present a theoretical calculation of the absorption spectrum of cuprous oxide $\left(\mathrm{Cu_{2}O}\right)$ based on the general theory developed by Y. Toyozawa. An inclusion not only of acoustic phonons but also of optical phonons and of specific properties of the excitons in $\mathrm{Cu_{2}O}$ like the central-cell corrections for the $1S$-exciton allows us to calculate the experimentally observed line widths in experiments by T. Kazimierczuk et al [Nature 514, 343, (2014)] within the same order of magnitude, which demonstrates a clear improvement in comparison to earlier work on this topic. We also discuss a variety of further effects, which explain the still observable discrepancy between theory and experiment but can hardly be included in theoretical calculations.