Model-independent limits from spin-dependent WIMP dark matter experiments

Spin-dependent weakly interacting massive particle (WIMP) searches have traditionally presented results within an odd group approximation and by suppressing one of the spin-dependent interaction cross sections. We here elaborate on a model-independent analysis in which spin-dependent interactions with both protons and neutrons are simultaneously considered. Within this approach, equivalent current limits on the WIMP-nucleon interaction at WIMP mass of $50\mathrm{GeV}/c^2$ are either ${\sigma }_p\le 0.7\mathrm{pb}$, ${\sigma }_n\le 0.2\mathrm{pb}$ or $|a_p|\le 0.4$, $|a_n|\le 0.7$ depending on the choice of cross section or coupling strength representation. These limits become less restrictive for either larger or smaller masses; they are less restrictive than those from the traditional odd group approximation regardless of WIMP mass. Combinations of experimental results are seen to produce significantly more restrictive limits than those obtained from any single experiment. Experiments traditionally considered spin-independent are moreover found to severely limit the spin-dependent phase space. The extension of this analysis to the case of positive signal experiments is explored.

Figure 1

${\sigma }_p^{\lim (A)}$ (left) and ${\sigma }_n^{\lim (A)}$ (right) vs $M_W$ for various elements, from the experiments of Table  using Eq. (3). All curves are calculated at 90% C.L., except for DAMA/NaI which is a $3\sigma$ result.

Figure 2

3D exclusion plots in the cross section representation, for DAMA/Xe-2 with $a_n⟨S_n⟩/a_p⟨S_p⟩>0$ (left) and $a_n⟨S_n⟩/a_p⟨S_p⟩<0$ (right). The shape in the $M_W$ direction is inherited from Fig. 1 via Eq. (5).

Figure 3

Exclusion plots in the ${\sigma }_p-{\sigma }_n$ plane at $50\mathrm{GeV}/c^2$ WIMP mass, for CRESST-I and $a_n⟨S_n⟩/a_p⟨S_p⟩>0$ (left) and $a_n⟨S_n⟩/a_p⟨S_p⟩<0$ (right). Since $⟨S_n⟩/⟨S_p⟩>0$, the left figure is for $a_n/a_p>0$, the right for $a_n/a_p<0$. The allowed areas are shaded.

Figure 4

Typical allowed regions (shaded) in the ${\sigma }_p-{\sigma }_n$ plane at $50\mathrm{GeV}/c^2$ WIMP mass, for NAIAD with $a_n⟨S_n⟩/a_p⟨S_p⟩>0$ (left) and $a_n⟨S_n⟩/a_p⟨S_p⟩<0$ (right).

Figure 5

3D exclusion plots in the coupling strength representation for (left) DAMA/Xe-2 and (right) NAIAD. The shape in the $M_W$ direction is inherited from Fig. 1 via Eq. (8).

Figure 6

2D exclusion plots in the coupling strength representation for (left) CDMS-II and (right) ZEPLIN-I. The dashed and dotted lines result from attributing the entire rate to a single isotope (see text).

Figure 7

Allowed regions (shaded) in the ${\sigma }_p-{\sigma }_n$ plane for $M_W=20$, 50 and $100\mathrm{GeV}/c^2$ with $a_p/a_n<0$ (left) and $a_p/a_n>0$ (right).

Figure 8

Exclusion plots for $M_W=20$, 50 and $100\mathrm{GeV}/c^2$ in the coupling strength representation. The overall allowed region, given by the intersection of all experiments, is shaded.

Figure 9

Exclusion plots for positive signal experiments at $M_W=50\mathrm{GeV}/c^2$ in the cross section representation. The thick border region is the intersection of DAMA/NaI’s $3\sigma$ exclusion plot with the current ZEPLIN-I 90% C.L. result. The hatched areas are obtained by attributing an arbitrary positive signal to ZEPLIN-I, while the F-based experiment is a similar projection from SIMPLE. The overall allowed region, given by the intersection of all experiments, is solid, and in this example only exists for negative $a_p/a_n$.

Figure 10

Exclusion plots for positive signal experiments at $M_W=50\mathrm{GeV}/c^2$ in the coupling strength representation. The thick border regions are the intersection of DAMA/NaI’s $3\sigma$ exclusion plot with the current ZEPLIN-I 90% C.L. result. The hatched areas are obtained by attributing an arbitrary positive signal to ZEPLIN-I, while the F-based experiment is a similar projection from SIMPLE. The overall allowed region, given by the intersection of all experiments, is solid.

Figure 11

“Relative sensitivity” $D$ for various nuclides. In the coupling strength representation, $D$ is the modulus of the stiffness of the region permitted by an experiment using only that isotope. Isotopes below the dashed line yield a quasihorizontal or quasivertical permitted region.

Figure 12

Eccentricities for several experiments of Table .