As a consequence of the process of domestication, wild and domestic individuals are adapted to very different environmental conditions. Although the phenotypic consequences of domestication are observable, the genetic causes are not evident in many cases. Artificial selection could be modifying the selection coefficients of new and standing variation in the population under domestication. Here, we aim to detect a genome-wide signal of domestication under a model of polygenic adaptation. We use forward simulations to investigate the 1D and 2D site frequency spectra (SFS) of mutations in two populations (Wild and Domestic) with divergent histories (demographic and selective) following a domestication split. We simulate ten different scenarios, varying the strength of selection upon beneficial mutations and the proportion of mutations whose selection coefficients change after domestication. First, we describe that in domesticated populations selection at linked sites needs to be invoked to explain the SFS of neutral mutations and that the mode of linked selection affecting the neutral SFS depends on the duration of the domestication bottleneck. Second, we find that some aspects of the full distribution of fitness effects (DFE), such as the shape and strength of the deleterious DFE, are accurately estimated in both populations when using only the 1D-SFS. However, the detection of significant differences in the beneficial DFE between populations remains challenging in most, but not all simulated scenarios when only the 1D-SFS is used. Third, when considering the 2D-SFS and a new joint DFE model, we are able to detect more subtle differences in the full DFE that are hidden in the 1D-SFS analysis. In conclusion, our work highlights the strengths and limitations of detecting a polygenic signal of domestication under a variety of domestication scenarios and genetic architectures.