Effects of Residue Background Events in Direct Dark Matter Detection Experiments on the Determinations of Ratios of WIMP-Nucleon Cross Sections

In our work on the development of model-independent data analysis methods for determining ratios between different couplings/cross sections 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, assuming that the spin-dependent (SD) WIMP-nucleus interaction dominates over the spin-independent (SI) one, the maximal acceptable fraction of residue background events in the analyzed data sets for determining the ratio of the SD WIMP coupling on neutrons to that on protons is ~ 20% - 40%; whereas considering a general combination of the SI and SD WIMP interactions, the maximal acceptable background ratio for determining the ratio between two SD WIMP couplings as well as the ratios of the SD cross section on protons (neutrons) to the SI one is ~ 10% - 20%. Moreover, by considering different forms of background spectrum, we find that only background events in the lowest energy ranges could affect the reconstructions (significantly); those in high energy ranges would almost not change the reconstructed ratios or only very slightly.