Combined limits on WIMPs from the CDMS and EDELWEISS experiments

The CDMS and EDELWEISS collaborations have combined the results of their direct searches for dark matter using cryogenic germanium detectors. The total data set represents $614\mathrm{kg}·\mathrm{days}$ equivalent exposure. A straightforward method of combination was chosen for its simplicity before data were exchanged between experiments. The results are interpreted in terms of limits on spin-independent weakly interacting, massive particle (WIMP)-nucleon cross section. For a WIMP mass of $90\mathrm{GeV}/{\mathrm{c}}^2$, where this analysis is most sensitive, a cross section of $3.3\times {10}^{-44}{\mathrm{cm}}^2$ is excluded at 90% C.L. At higher WIMP masses, the combination improves the individual limits, by a factor 1.6 above $700\mathrm{GeV}/{\mathrm{c}}^2$. Alternative methods of combining the data provide stronger constraints for some ranges of WIMP masses and weaker constraints for others.

Figure 1

Top: effective net exposure curves for CDMS (dotted red curve), EDELWEISS (dash-dotted blue curve), and for the combined experiments (dashed black curve). Middle: energies of the five observed candidate events in EDELWEISS (blue lines). Bottom: energies of the four observed candidate events in CDMS (red lines). All are below the EDELWEISS threshold. In the simple method of merging the two sets of data, experimental provenance of the individual events is not kept.

Figure 2

Top: 90% C.L. optimum interval upper limits on spin-independent WIMP couplings to nucleons as a function of WIMP mass, from the individual CDMS [7] (red dashes) and EDELWEISS [11] (EDW, blue crosses) experiments, and from their simple merger (continuous black line). Also represented are limits from the XENON 100 [14] (brown boxes), XENON 10 [26] (green crosses), CRESST II [15](brown dot-dashed line) and ZEPLIN-III [16] (pink dots) experiments (The limits for XENON 10, CRESST II and ZEPLIN-III use slightly larger halo escape velocities than this work ($600–650\mathrm{km}/\mathrm{s}$), and supersymmetric parameter-space predictions [27, 28] (filled gray regions). Bottom: gain obtained from the straightforward combination with respect to the strongest individual limit of CDMS and EDELWEISS (in effect that of CDMS). Below masses of $50\mathrm{GeV}/{\mathrm{c}}^2$, the combined limit is weaker than the best individual one; at higher masses, the gain is up to a factor 1.57.

Figure 3

Comparison of combined CDMS-EDELWEISS limits obtained by different statistical methods. The “minimum limit” method (orange crosses) is more constraining than the adopted, “simple merging” method (black curve) for low WIMP masses, but less constraining at high masses. The “probability product” method (purple circles) yields the strongest limits for masses above $30\mathrm{GeV}/{\mathrm{c}}^2$, but has the weakest limits for low masses, and is not defined for WIMPs with masses below $\sim 12\mathrm{GeV}/{\mathrm{c}}^2$ since such WIMPs cannot be observed in EDELWEISS due to its the higher threshold. The limit of the combined experiments under the simple method had no events been detected (red dashes) lies below these limits by a factor from $\sim 1.5$ to $\sim 9$. Bottom: gains of the alternative methods relative to the simple merger.