Isospin conserving Dark Matter with isospin dependent interaction, and reconciliation of contrasting results from direct Dark Matter experiments

A simple model of Dark Matter (DM) which couples with the two nucleons with different coupling strengths without violating isospin conservation is explored as an example of the importance of keeping the experimental data analysis as model independent as possible. The apparent contrast between the recent CRESST event excess and current XENON100 spin-independent (SI) exclusions is shown to be removed by simply not assuming that the couplings of the DM with the two nucleons are equal.