Form Factor Effects in the Direct Detection of Isospin-Violating Dark Matter

Isospin-violating dark matter (IVDM) provides a possible mechanism to ameliorate the tension among recent direct detection experiments. For IVDM, we demonstrate that the results of direct detection experiments based on neutron-rich target nuclei may depend strongly on the density dependence of the symmetry energy which is presently largely unknown and controls the neutron skin thickness that reflects the relative difference of neutron and proton form factors in the neutron-rich nuclei. In particular, using the neutron and proton form factors obtained from Skyrme-Hartree-Fock calculations by varying the symmetry energy within the uncertainty region set by the latest model-independent measurement of the neutron skin thickness of $^{208}$Pb from PREX experiment at JLab, we find that, for IVDM with neutron-to-proton coupling ratio fixed to $f_n/f_p=-0.7$, the form factor effect may enhance the sensitivity of Xe-based detectors (e.g., XENON100 and LUX) to the DM-proton cross section by a factor of $3$ in the DM mass region constrained by CMDS-II(Si) and even by more than an order of magnitude for heavy DM with mass larger than $80$ GeV, compared with the results using the empirical Helm form factor. Our results further indicate that the form factor effect can significantly modify the recoil spectrum of Xe-based detectors for heavy IVDM with $f_n/f_p=-0.7$.