Effects of residue background events in direct dark matter detection experiments on the determination of the WIMP mass

In the earlier work on the development of a model- independent data analysis method for determining the mass 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 determination of the WIMP mass, the maximal acceptable fraction of residue background events in the analyzed data sets of O(50) total events is similar to 20%, for background windows of the entire experimental possible energy ranges, or in low energy ranges; while, for background windows in relatively higher energy ranges, this maximal acceptable fraction of residue background events can not be larger than similar to 10%. For a WIMP mass of 100 GeV with 20% background events in the windows of the entire experimental possible energy ranges, the reconstructed WIMP mass and the 1 sigma statistical uncertainty are similar to 97 GeV +61%-35% (similar to 94 GeV +55%-33% for background- free data sets).