Nuclear recoil response of liquid xenon and its impact on solar 8B neutrino and dark matter searches

Knowledge of the ionization and scintillation responses of liquid xenon (LXe) to nuclear recoils is crucial for LXe-based dark matter experiments. Current calibrations carry large uncertainties in the low-energy region below $\sim 3{\mathrm{keV}}_{\mathrm{nr}}$ where signals from dark matter particles of $<10\mathrm{GeV}/{\mathrm{c}}^2$ masses are expected. The coherent elastic neutrino-nucleus scattering ($\mathrm{CE}\nu \mathrm{NS}$) by solar ${}^8\mathrm{B}$ neutrinos also results in a continuum of nuclear recoil events below $3.0{\mathrm{keV}}_{\mathrm{nr}}$ (99% of events), which further complicates low-mass dark matter searches in LXe experiments. In this paper, we describe a method to quantify the uncertainties of low-energy LXe responses using published calibration data, followed by case studies to evaluate the impact of yield uncertainties on ${}^8\mathrm{B}$ searches and low-mass dark matter sensitivity in a typical ton-scale LXe experiment. We conclude that naively omitting yield uncertainties leads to overly optimistic limits by factor $\sim 2$ for a 6 GeV weakly interacting massive particle mass. Future nuclear recoil light yield calibrations could allow experiments to recover this sensitivity and also improve the accuracy of solar ${}^8\mathrm{B}$ flux measurements.

Figure 1

The neutrino flux that can induce observable $\mathrm{CE}\nu \mathrm{NS}$ events in a LXe detector. The gray area corresponds to an energy region that produces 0 observable quanta (photons and electrons) according to the NEST NR yield model, and is beyond the reach of a LXe detector. The diffused supernova neutrino background (DSNB) spectra are shown at various Fermi-Dirac temperatures in units of MeV [10]. Because the sub-GeV atmospheric neutrino remains unexplored by current experiments, the sub-GeV spectrum for dark matter experiments are based on FLUKA simulation. The low-energy cut off is caused by the lack of low-energy cosmic ray data and interaction uncertainties between cosmic rays and air nuclei as the simulation inputs [11, 12]. The top x-axis is the maximum recoil energy from a neutrino back-scattering on a ${}^{131}\mathrm{Xe}$ nucleus.

Figure 2

The $\mathrm{CE}\nu \mathrm{NS}$ energy spectrum for all neutrino backgrounds that are relevant to for LXe dark matter experiments. The dashed and dotted spectra are 6 GeV ($4\times {10}^{-45}{\mathrm{cm}}^2$) and 100 GeV ($3\times {10}^{-49}{\mathrm{cm}}^2$) WIMPs whose spectrum shapes degenerate with those of ${}^8\mathrm{B}$ and atmospheric neutrinos. The gray area corresponds to an energy region that produces 0 observable quanta (photons and electrons) according to the NEST NR yield model. The $1\sigma$ uncertainties associated with each neutrino source (transparent color bands) are the neutrino flux uncertainties.

Figure 3

A summary of all NR $L_y$ and $Q_y$ measurements at various electric fields published in the past decade. The default NEST v2.1 curves come from a global fit taking into account all available data extending up to $100{\mathrm{keV}}_{\mathrm{nr}}$. Bottom: the detected energy spectra for various low-mass WIMPs computed using NEST v2.1 yield and the detector parameters in [14]. The solid spectra are for a detector threshold with 3-fold S1 coincidence and $\ge 5$ electron S2 requirement. The dashed spectra are for a 2-fold 5 electron detector threshold.

Figure 4

The Brazilian flag uncertainty bands for the yield curves. Top: The bands represent the 1 and 2 sigma uncertainties for $Q_y$ propagated from the $(a^{\mathrm{Qy}},b^{\mathrm{Qy}})$ model. The Livermore data at $220\mathrm{V}/\mathrm{cm}$ has the smallest uncertainties for $Q_y$. The $*$ superscript indicates the $Q_y$ data points are adjusted to $220\mathrm{V}/\mathrm{cm}$ before the fit. The gray shadow marks the region where a sharp fall-off in NEST is enforced. Bottom: same as the top but for $L_y$. The LUX Run 4 data at equivalent $400\mathrm{V}/\mathrm{cm}$ has the smallest uncertainties for $L_y$. The $*$ superscript indicates that the LUX Run 3 $L_y$ data points are adjusted to $400\mathrm{V}/\mathrm{cm}$ before the fit.

Figure 5

Top: the median NR detection efficiency (dashed) as a function of true recoil energy for two sets of $\mathrm{S}1+\mathrm{S}2$ detector thresholds. The two shaded color bands are the 68% and 95% uncertainties from $L_y$. On the same plot, we show differential rate spectra for solar ${}^8\mathrm{B}$ $\mathrm{CE}\nu \mathrm{NS}$ surviving the detection thresholds, whose normalization is indicated by the y-axis on the right. The shaded blue and red bands are derived from the $1\sigma$ uncertainty in detection efficiencies. The region between two vertical dotted lines indicate where the central 68% of the events are. Bottom: the fractional uncertainties, defined as the difference from the $\pm 1\sigma$ probability to the median probability divided by the median probability, as a function of energy.

Figure 6

Top: the mock data generated for a $15.3\mathrm{t}\times \mathrm{yr}$ exposure using the nominal ${}^8\mathrm{B}$ flux ($\mathrm{\Phi }=5.25\times {10}^6{\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}$) [28] and the default NEST $L_y$ and $Q_y$ curves. The detector thresholds for S1 is 3-fold coincidence and for S2 is 5 ${\mathrm{N}}_{ee}$. The error bars are Poissonian. The ER component combines all background labeled as “ER” in Table IV of [14]. The NR combines all “NR” labeled background except for solar $hep$ neutrino. The bin width is $0.05\log (phd)$. Bottom: projections of the 90% confidence volumes in ${\theta }_{Ly}$ and $\mathrm{\Phi }$ parameter space. Green (blue) stripe shows the confidence interval for a $15.3\mathrm{t}\times \mathrm{yr}$ ($50\mathrm{t}\times \mathrm{yr}$) exposure without any constraints of $L_y$ and $Q_y$. The orange (red) contour shows the interval for a $15.3\mathrm{t}\times \mathrm{yr}$ ($50\mathrm{t}\times \mathrm{yr}$) exposure with $L_y$ and $Q_y$ constrained to the calibration data using the model in Sec. 2c. The solid black line is a $50\mathrm{t}\times \mathrm{yr}$ exposure where we artificially reduce $L_y$ and $Q_y$ uncertainties to half.

Figure 7

Top: The projected median sensitivity (90% confidence limit) for a $15.3\mathrm{t}\times \mathrm{yr}$ of LXe exposure as a function of WIMP mass. The solid curves assume the standard 3-fold $5{\mathrm{N}}_{ee}$ detector threshold for the LZ-like detector, and dashed curves assumes a relaxed 2-fold threshold $5{\mathrm{N}}_{ee}$ detector threshold. The black curves are the baseline scenario where neither $L_y$ nor $Q_y$ uncertainty is included. Green curves include $Q_y$ uncertainty only, orange curves include $L_y$ uncertainty derived from the single parameter model (Sec. 2c), red curves include $L_y$ uncertainty derived from $(a,b)$ models (Sec. 2b). Bottom: the ratio, computed by taking the colored curves from the top plot, divided by the black curves (baseline).

Figure 8

The projected $6\mathrm{GeV}/{\mathrm{c}}^2$ WIMP sensitivity (the median 90% exclusion limit) for a 5.6-ton LZ-like detector as a function of live days. The solid curves are the detector threshold of 3-fold S1 coincidence and $5{\mathrm{N}}_{ee}$ S2 requirement, and the dashed curves are a relaxed 2-fold $5{\mathrm{N}}_{ee}$ detector threshold. The black curves are the naive scenario where yield uncertainty is not included. The shaded bands are the 68% overall uncertainties from PLR calculation.

Figure 9

Calibration requirement of the $L_y$ uncertainties for the ${}^8\mathrm{B}$ rate at two different thresholds. The dashed lines are the corresponding levels of Poisson uncertainties for ${}^8\mathrm{B}$ neutrino in a projected $15.3\mathrm{t}\times \mathrm{yr}$ exposure. The dotted lines are for a $50\mathrm{t}\times \mathrm{yr}$ exposure.

Figure 10

The Brazilian flag 1 and 2 sigma error bands for $Q_y$ and $L_y$ propagated from the single parameter model, similar to Fig. 10.