Effective field theory search for high-energy nuclear recoils using the XENON100 dark matter detector

We report on weakly interacting massive particles (WIMPs) search results in the XENON100 detector using a nonrelativistic effective field theory approach. The data from science run II ($34\mathrm{kg}\times 224.6$ live days) were reanalyzed, with an increased recoil energy interval compared to previous analyses, ranging from $(6.6–240){\mathrm{keV}}_{\mathrm{nr}}$. The data are found to be compatible with the background-only hypothesis. We present 90% confidence level exclusion limits on the coupling constants of WIMP-nucleon effective operators using a binned profile likelihood method. We also consider the case of inelastic WIMP scattering, where incident WIMPs may up-scatter to a higher mass state, and set exclusion limits on this model as well.

Figure 1

Example EFT recoil spectra for elastic scattering of spin-$1/2$ WIMPs on xenon nuclei (weighted according to the isotope abundances in the XENON100 experiment). Left (right) shows the predicted spectra for EFT operator ${\mathcal{O}}_1$ (${\mathcal{O}}_6$). The normalization is controlled by the coupling coefficient of each EFT operator and the experimental exposure. The solid vertical line at $43{\mathrm{keV}}_{\mathrm{nr}}$ shows the approximate division between the two signal regions used in this analysis. As shown, the standard SI (${\mathcal{O}}_1$) spectrum is concentrated mainly in the already explored energy region. However, some EFT operators, for certain WIMP masses, predict a significant fraction of recoil events above the upper energy cut used in the standard spin-independent analysis, motivating an extension of this cut. The highest recoil energy shown in the plots, $240{\mathrm{keV}}_{\mathrm{nr}}$, roughly corresponds to the highest energy accounted for this analysis.

Figure 2

Summary of regions of interest, backgrounds, and observed data. ER calibration data, namely ${}^{60}\mathrm{Co}$ and ${}^{232}\mathrm{Th}$ data, are shown as light cyan dots. NR calibration data (${}^{241}\mathrm{AmBe}$) are shown as light red dots. Dark matter search data are shown as black dots. The red line is the threshold between the low- and high-energy channels. The lines in blue are the bands. For the low-energy channel, the bands are constructed to achieve constant expected signal density and are operator and mass dependent, shown here for a $50\mathrm{GeV}/c^2$ WIMP using the ${\mathcal{O}}_1$ operator. For the high-energy region, the nine analysis bins are presented also in blue lines.

Figure 3

The total acceptance of all cuts used. Data from calibration are shown in black, with a third-order polynomial fit in red.

Figure 4

The expected signal in the high-energy region for a $300\mathrm{GeV}/c^2$ WIMP mass, normalized to five events. Left (right) is the spectra for $O_1$ ($O_6$). Notice that for $O_1$ most of the events are not expected to deposit energy higher than 30 PE, whereas for $O_6$, a large fraction of the events appear in this region.

Figure 5

The expected signal in the low-energy region for a $300\mathrm{GeV}/c^2$ WIMP mass, normalized to five events. Left (right) is the spectra for ${\mathcal{O}}_1$ (${\mathcal{O}}_6$). Notice that for ${\mathcal{O}}_1$ most of the events are expected to deposit energy lower than 30 PE, whereas for ${\mathcal{O}}_6$, a large fraction of the events do not appear in this region at all. The black lines indicate the bands constructed on these specific mass and operator models and are dividing the signal into eight equally distributed signal subregions. This parameter space can be mapped with a one-to-one mapping to the $(y-\mathrm{cS}1)$ space.

Figure 6

The XENON100 limits ($90\%\mathrm{C}.\mathrm{L}{.}_s$) on isoscalar dimensionless coupling for all elastic scattering EFT operators. The limits are indicated in solid black. The expected sensitivity is shown in green and yellow ($1\sigma$ and $2\sigma$, respectively). Limits from CDMS-II Si, CDMS-II Ge, and SuperCDMS [33] are presented as blue asterisks, green triangles, and orange rectangles, respectively. For operators 3 and 8, a full limit was published, for all other operators only $m_{\chi }=10$ and $m_{\chi }=300$ are available.

Figure 7

$90\%\mathrm{C}.\mathrm{L}{.}_s$ limits, for the inelastic model, on the magnitude of the coupling constant for ${\mathcal{O}}_1$, reported as a function of the WIMP mass and mass splitting $\delta$.

Figure 8

The XENON100 $90\%\mathrm{C}.\mathrm{L}{.}_s$ limits on a $1\mathrm{TeV}/c^2$ WIMP isoscalar dimensionless coupling constant as a function of the WIMP mass splitting ${\delta }_m$ for all inelastic scattering EFT operators. Limits are indicated in solid black. The expected sensitivity is shown in green and yellow ($1\sigma$ and $2\sigma$, respectively). For ${\mathcal{O}}_1$, (SI) results from XENON100 (red triangle), CDMS-II (blue rectangle), and ZEPLIN-III (black star) are overlaid.

Figure 9

The full XENON100 dark matter science run data up to 1000 PE in cS1 (shown in black). In blue, we show data from ER calibration (${}^{60}\mathrm{Co}$ and ${}^{232}\mathrm{Th}$), and in red, we show data from NR calibration (${}^{241}\mathrm{AmBe}$). See the text for details on these populations. While the black vertical line represents the highest energy considered for quantitative interpretation in this analysis, there is no indication of elastic NRs even above that energy.

Figure 10

A visualization of the detector response table for $-1\sigma$ (i.e., conservative) ${\mathcal{L}}_{\text{eff}}$, as provided in the supplemental material [21]. The y axis indicates the bins used for the high-energy signal region of this analysis (explained in Table 1). The $x$ axis shows recoil energies, and the colors give the probability density for a recoil of a given recoil energy to produce an event in each analysis bin. To produce a signal model for this analysis, one simply multiplies the table values by $\mathrm{d}R/\mathrm{d}E$ and integrates over $E$. The result is the predicted signal rate for each analysis bin.