First constraints on WIMP-nucleon effective field theory couplings in an extended energy region from LUX-ZEPLIN

Following the first science results of the LUX-ZEPLIN (LZ) experiment, a dual-phase xenon time projection chamber operating from the Sanford Underground Research Facility in Lead, South Dakota, USA, we report the initial limits on a model-independent nonrelativistic effective field theory describing the complete set of possible interactions of a weakly interacting massive particle (WIMP) with a nucleon. These results utilize the same 5.5 t fiducial mass and 60 live days of exposure collected for the LZ spin-independent and spin-dependent analyses while extending the upper limit of the energy region of interest by a factor of 7.5 to 270 keV. No significant excess in this high energy region is observed. Using a profile-likelihood ratio analysis, we report 90% confidence level exclusion limits on the coupling of each individual nonrelativistic WIMP-nucleon operator for both elastic and inelastic interactions in the isoscalar and isovector bases.

Figure 1

Differential recoil spectra for the fourteen non-relativistic NREFT WIMP-nucleon operators for a $1000\mathrm{GeV}/{\mathrm{c}}^2$ WIMP in both the isoscalar (solid line) and the isovector (dashed line) bases. The operators are categorized by their nuclear responses (as defined in Ref. [14]); $M$-only (top left), ${\mathrm{\Sigma }}^{\prime }$-only (top center), ${\mathrm{\Sigma }}^{\prime \prime }$-only (top right), $M$ and $\mathrm{\Delta }$ (bottom left), ${\mathrm{\Sigma }}^{\prime }$ and ${\mathrm{\Phi }}^{\prime \prime }$ (bottom center) and all other responses (bottom right). The spectra were generated with a coupling strength of unity, excluding the possibility of interference terms. The shaded gray regions indicate the energies at which the detection efficiency is below 50% after all data analysis cuts have been applied (see Fig. 4).

Figure 2

Calibration events in $\{{\log }_{10}(\mathrm{S}1c),{\log }_{10}(\mathrm{S}2c)\}$ space from tritium (light blue), D-D neutrons (orange), and ${}^{212}\mathrm{Pb}$ (green) in and above the ROI. The mean ER and NR responses from NEST for flat energy spectra are shown in dark blue and red, respectively; the dashed lines indicate the 10%–90% percentiles of the expected response. Additionally, the region highlighted in pink denotes the shift in the 10%–90% percentiles when considering the $\pm 1\sigma$ uncertainty in the NEST mean NR response beyond the D-D endpoint used for this study. Gray contours are lines of constant reconstructed energy, labeled for both ER and NR interactions. The gray dashed horizontal line denotes the upper ${\log }_{10}(\mathrm{S}2c)$ bound used in this analysis, however, the calibration events in this region were used to constrain the ER response model.

Figure 3

Data in reconstructed $r^2$ and $z$ after all analysis cuts. Black (gray) points show the data inside (outside) the fiducial volume after all cuts and vetoes have been applied. Red crosses and blue circles show events vetoed by a prompt Skin and OD signal, respectively. Solid green diamonds indicate the events removed by the $\gamma$-X BDT cut after all other cuts have been applied. Hollow diamonds indicate events outside the FV classified as $\gamma$-X. The solid line shows the fiducial volume definition, and the dashed line shows the extent of the active TPC.

Figure 4

Signal efficiency as a function of the NR energy from the trigger (blue), the threefold coincidence and 3 phd threshold on $\mathrm{S}1c$ (orange), the single-scatter (SS) reconstruction and analysis cuts (green), and the search ROI in $\mathrm{S}1c$ and $\mathrm{S}2c$ (black). The low energy behavior is shown in the inset, where the dotted line at $5.5{\mathrm{keV}}_{\mathrm{nr}}$ indicates the nuclear recoil energy at which the efficiencies equal 50%. The uncertainty on the detection efficiency (gray region) was assessed with ${}^3\mathrm{H}$, ${}^{220}\mathrm{Rn}$, and AmLi calibration data.

Figure 5

Example $\{{\log }_{10}(\mathrm{S}1c),{\log }_{10}(\mathrm{S}2c)\}$ distributions for a $1000\mathrm{GeV}/{\mathrm{c}}^2$ WIMP-nucleon isoscalar interaction for the momentum-independent operator ${\mathcal{O}}_1$ (top), and momentum-dependent operators ${\mathcal{O}}_6$ (middle) and ${\mathcal{O}}_{13}$ (bottom). Red and blue lines denote the flat ER and NR response regions as described in Fig. 2. Each pane shows the distribution for 100,000 WIMP nuclear recoils.

Figure 6

The final high-energy WIMP-search data after all cuts in $\{{\log }_{10}(\mathrm{S}1c),{\log }_{10}(\mathrm{S}2c)\}$ space. The contours that enclose $1\sigma$ (dark) and $2.5\sigma$ (light) regions represent the following models: the shaded red region indicates the detector neutrons, the shaded orange region indicate the detector ERs, the blue region is the combined representation of all other ER models (${}^{214}\mathrm{Pb}$, ${}^{212}\mathrm{Pb}$, ${}^{85}\mathrm{Kr}$, ${}^{37}\mathrm{Ar}$, ${}^{125}\mathrm{I}$, ${}^{124}\mathrm{Xe}$, ${}^{127}\mathrm{Xe}$, ${}^{136}\mathrm{Xe}$, and $\nu$ ER) and the black dashed lines show a $1000\mathrm{GeV}/{\mathrm{c}}^2$ ${\mathcal{O}}_6$ isoscalar signal model. The solid red line corresponds to the NR median, while the red dotted lines represent the 10–90% percentiles of the expected response. The model contours are produced with a linear scale for $\mathrm{S}{1}_c$ prior to being cast into log and take into account all the efficiencies used in the analysis. Contours of constant recoil energy have been included as thin gray lines. Grayed regions at the left and top of the plot indicate parameter space outside the energy ROI.

Figure 7

The 90% confidence limit (black lines) of the dimensionless isoscalar WIMP-nucleon couplings for each of the fourteen NREFT elastic interactions. The black dotted lines show the medians of the sensitivity projection, and the green and yellow bands correspond to the $1\sigma$ and $2\sigma$ sensitivity bands, respectively. Also shown are the NREFT results from the XENON100 experiment (magenta) and the PandaX-II experiment (blue). The latter upper limits are cast from their starting points of ${\mathcal{L}}_5$ (reduces to ${\mathcal{O}}_1$) and ${\mathcal{L}}_{15}$ (reduces to ${\mathcal{O}}_4$). The LUX limits (brown points), are from their $\delta =0\mathrm{keV}$ inelastic result. The LZ signal model uses nuclear density matrices that have been updated since the XENON100 and LUX analyses, leading to reduced rates for some operators such as ${\mathcal{O}}_{13}$, where the LUX result appears stronger than the LZ result.

Figure 8

The 90% confidence limit (black lines) of the dimensionless isovector WIMP-nucleon couplings for each of the 14 NREFT elastic interactions. The black dotted lines show the medians of the sensitivity projection, and the green and yellow bands correspond to the $1\sigma$ and $2\sigma$ sensitivity bands, respectively. Also shown are the SI and SD results of the PandaX-II experiment (blue). The latter upper limits are cast from their ${\mathcal{L}}_5$ (reduces to ${\mathcal{O}}_1$) and their ${\mathcal{L}}_{15}$ (reduces to ${\mathcal{O}}_4$).

Figure 9

The 90% confidence limit (solid lines) of the dimensionless isoscalar WIMP-nucleon couplings for each of the fourteen NREFT interactions. The dotted lines show the medians of the sensitivity projection and the shaded bands correspond to the $1\sigma$ sensitivity band. The upper limit is evaluated for WIMP masses of $400\mathrm{GeV}/{\mathrm{c}}^2$, $1000\mathrm{GeV}/{\mathrm{c}}^2$, and $4000\mathrm{GeV}/{\mathrm{c}}^2$, for values of the mass splitting $\delta$ of 0 keV (purple), 50 keV (blue), 100 keV (green), 150 keV (yellow), 200 keV (orange), and 250 keV (red). Circular data points represent the $1000\mathrm{GeV}/{\mathrm{c}}^2$ inelastic limits from the LUX WS2014-16 NREFT search [9].

Figure 10

The 90% confidence limit (solid lines) of the dimensionless isovector WIMP-nucleon couplings for each of the fourteen NREFT interactions. The dotted lines show the medians of the sensitivity projection and the shaded bands correspond to the $1\sigma$ sensitivity band. The upper limit is evaluated for WIMP masses of $400\mathrm{GeV}/{\mathrm{c}}^2$, $1000\mathrm{GeV}/{\mathrm{c}}^2$, and $4000\mathrm{GeV}/{\mathrm{c}}^2$, for values of the mass splitting $\delta$ of 0 keV (purple), 50 keV (blue), 100 keV (green), 150 keV (yellow), 200 keV (orange), and 250 keV (red).

Figure 11

The 90% confidence limit of the dimensionless isoscalar NREFT ${\mathcal{O}}_1$ WIMP-nucleon couplings from various LXe direct detection experiments. Solid lines represent the limit on ${\mathcal{O}}_1$ isoscalar from NREFT analyses: LZ—this work (black), PandaX-II 2019 (blue), XENON100 (magenta), and LUX WS2014-16 (brown point). Dotted lines represent recast SI limits; LZ—this work (black dotted), PandaX-4T 2021 (blue dotted), XENONnT (yellow dotted), and LUX full exposure (brown dotted). The normalizations applied for the recast limits are given in Table 3.