Effects of residue background events in direct dark matter detection experiments on the reconstruction of the velocity distribution function of halo WIMPs

In our earlier work on the development of a model-independent data analysis method for reconstructing the (moments of the) time-averaged one-dimensional velocity distribution function of Weakly Interacting Massive Particles (WIMPs) by using measured recoil energies from direct Dark Matter detection experiments directly, it was assumed that the analyzed data sets are background-free, i.e., all events are WIMP signals. In this article, as a more realistic study, we take into account a fraction of possible residue background events, which pass all discrimination criteria and then mix with other real WIMP-induced events in our data sets. Our simulations show that, for the reconstruction of the one-dimensional WIMP velocity distribution, the maximal acceptable fraction of residue background events in the analyzed data set(s) of O(500) total events is similar to 10%-20%. For a WIMP mass of 50 GeV with a negligible uncertainty and 20% residue background events, the deviation of the reconstructed velocity distribution would in principle be similar to 7.5% with a statistical uncertainty of similar to 18% (similar to 19% for a background-free data set).