Nuclear uncertainties in the spin-dependent structure functions for direct dark matter detection

We study the effect that uncertainties in the nuclear spin-dependent structure functions have in the determination of the dark matter (DM) parameters in a direct detection experiment.We show that different nuclear models that describe the spin-dependent structure function of specific target nuclei can lead to variations in the reconstructed values of the DM mass and scattering cross section. We propose a parametrization of the spin structure functions that allows us to treat these uncertainties as variations of three parameters, with a central value and deviation that depend on the specific nucleus. The method is illustrated for germanium and xenon detectors with an exposure of 300 kg yr, assuming a hypothetical detection of DM and studying a series of benchmark points for the DM properties. We find that the effect of these uncertainties can be similar in amplitude to that of astrophysical uncertainties, especially in those cases where the spin-dependent contribution to the elastic scattering cross section is sizableD. G. C. is supported by the Ramo´n y Cajal program of the Spanish MICINN. M. F. is supported by a Leverhulme Trust grant. J.-H. H. is supported by a MultiDark Fellowship. M. P. is supported by a MultiDark Scholarship. This work was supported by the Consolider-Ingenio 2010 Programme under MultiDark Grant No. CSD2009-00064. We also thank the support of the Spanish MICINN under Grants No. FPA2009-08958 and FPA2012-34694, the Spanish MINECO ‘‘Centro de excelencia Severo Ochoa Program’’ under Grant No. SEV-2012-0249, the Community of Madrid under Grant No. HEPHACOS S2009/ESP-1473, and the European Union under the Marie Curie-ITN Program No. PITN-GA-2009-23792