Search for annual and diurnal rate modulations in the LUX experiment

Various dark matter models predict annual and diurnal modulations of dark matter interaction rates in Earth-based experiments as a result of the Earth’s motion in the halo. Observation of such features can provide generic evidence for detection of dark matter interactions. This paper reports a search for both annual and diurnal rate modulations in the LUX dark matter experiment using over 20 calendar months of data acquired between 2013 and 2016. This search focuses on electron recoil events at low energies, where leptophilic dark matter interactions are expected to occur and where the DAMA experiment has observed a strong rate modulation for over two decades. By using the innermost volume of the LUX detector and developing robust cuts and corrections, we obtained a stable event rate of $2.3\pm 0.2\mathrm{cpd}/{\mathrm{keV}}_{\mathrm{ee}}/\mathrm{tonne}$, which is among the lowest in all dark matter experiments. No statistically significant annual modulation was observed in energy windows up to $26{\mathrm{keV}}_{\mathrm{ee}}$. Between 2 and $6{\mathrm{keV}}_{\mathrm{ee}}$, this analysis demonstrates the most sensitive annual modulation search up to date, with $9.2\sigma$ tension with the DAMA/LIBRA result. We also report no observation of diurnal modulations above $0.2\mathrm{cpd}/{\mathrm{keV}}_{\mathrm{ee}}/\mathrm{tonne}$ amplitude between 2 and $6{\mathrm{keV}}_{\mathrm{ee}}$.

Figure 1

Left: Illustration of the FV used in this analysis (black line) in comparison to the density distribution of single scattering events ($<500{\mathrm{keV}}_{\mathrm{ee}}$) in WS2013; the coordinates used are estimated real-world positions corrected based on the S2 positions and the simulated electric field. Right: Illustration of the fiducial cut applied to the drift time and S2 positions along $x_{S2}=0$ at different times, including WS2013 (black circles), early (blue triangles) and late (red squares) WS2014-16. This FV is $\sim 2–3$ times smaller than that used in the LUX WIMP searches [1, 25].

Figure 2

The fiducial mass calculated from the FV geometry (blue dashed line) and from ${}^{83m}\mathrm{Kr}$ calibration data (black squares with error bars). The error includes uncertainties from the ${}^{83m}\mathrm{Kr}$ event selection criteria, from the total active mass, and from the field map interpolations.

Figure 3

The efficiency for the single scatter cut as a function of time evaluated for events between 1.6 and $2.4{\mathrm{keV}}_{\mathrm{ee}}$. The efficiencies were calculated from ${}^3\mathrm{H}$ data taken in December 2013, September 2014, February 2015, September 2015 and February 2016.

Figure 4

The central distribution of ER events in the $\mathrm{S}1\text{−}{\log }_{10}(\mathrm{S}2)$ (position corrected) parameter space, derived from ${}^3\mathrm{H}$ data acquired in December 2013 (black dots), September 2014 (green squares), February 2015 (blue triangles), February 2016 (magenta downwards triangles), and ${}^{14}\mathrm{C}$ data in July 2016 (red circles). Data from WS2014-16 exhibited higher S2 values than WS2013 because of improved high voltage; all WS2014-16 data in the FV were consistent with each other despite the evolving field distortion at large radii. S1s of 50 phd approximately correspond to $11{\mathrm{keV}}_{\mathrm{ee}}$.

Figure 5

The energy spectrum of single scatter ER events in the central 51.4 kg FV of the LUX detector (277 live days total). Both the absolute event counts (axis on the left) and the normalized event rates (axis on the right) are shown. Due to the stringent live-time exclusion criteria, only 32 live days of data from WS2013 were used, and the analysis data set is dominated by WS2014-16 where the $3{\mathrm{keV}}_{\mathrm{ee}}$ event rate excess is less statistically significant.

Figure 6

The observed LUX event rates in the $2–6{\mathrm{keV}}_{\mathrm{ee}}$ energy window (top) and that in the $6–10{\mathrm{keV}}_{\mathrm{ee}}$ window (bottom) from 2013 to 2016. No data exist between 12/2013 and 9/2014 because of detector maintenance. Dashed lines illustrate the best fits to an annual modulation model, determined using the unbinned maximum likelihood method. For the purpose of illustration the live time is folded in the event rate rather than in the fit function; a bin size of 25 days is used.

Figure 7

The evaluated 90% LUX contours for the modulation parameters in the signal region of $2–6{\mathrm{keV}}_{\mathrm{ee}}$ (solid line, purple-filled), and that in the control region of $6–10{\mathrm{keV}}_{\mathrm{ee}}$ (dashed line, blue-filled). The DAMA result (DAMA/NaI and DAMA/LIBRA) for $2–6{\mathrm{keV}}_{\mathrm{ee}}$ [14] (black dot with error bars) and the XENON100 result for $2–5.8{\mathrm{keV}}_{\mathrm{ee}}$ [41] (dotted line, green-filled) are also shown for comparison.

Figure 8

Top: The 90% significance contours in the modulation parameter space for LUX ER events between 10 and $26{\mathrm{keV}}_{\mathrm{ee}}$. Data are grouped using the same $4{\mathrm{keV}}_{\mathrm{ee}}$ bin size as used in the low-energy analysis: 10–14 (solid, purple), 14–18 (dashed, dark red), 18–22 (dotted, pink), and $22–26{\mathrm{keV}}_{\mathrm{ee}}$ (dot-dashed, grey). Bottom: The best-fit modulation amplitude in all LUX ER data below $26{\mathrm{keV}}_{\mathrm{ee}}$. The modulation phase was fixed to be 152 days in the fits for direct comparison with DAMA/LIBRA and XMASS. The dashed line corresponds to the case of zero modulation amplitudes for comparison with data.

Figure 9

The observed ER event rate in the LUX detector as a function of time of the day (presented in hours); the rates were calculated for both solar time, i.e., Mountain time (top), and local sidereal time (bottom).