Effects of Residue Background Events in Direct Dark Matter Detection Experiments on the Estimation of the Spin-Independent WIMP-Nucleon Coupling

In our work on the development of a model-independent data analysis method for estimating the spin-independent (SI) scalar coupling of Weakly Interacting Massive Particles (WIMPs) on nucleons 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 estimation of the SI WIMP-nucleon coupling, the maximal acceptable fraction of residue background events in the analyzed data set of O(50) total events is ~ 10% - 20%. For a WIMP mass of 100 GeV and 20% residue background events, the systematic deviation of the reconstructed SI WIMP coupling (with a reconstructed WIMP mass) would in principle be ~ +13% with a statistical uncertainty of ~ ^{+21%}_{-14%} (~ -3.3%^{+18%}_{-13%} for background-free data sets).