Signal yields, energy resolution, and recombination fluctuations in liquid xenon

This work presents an analysis of monoenergetic electronic recoil peaks in the dark-matter-search and calibration data from the first underground science run of the Large Underground Xenon (LUX) detector. Liquid xenon charge and light yields for electronic recoil energies between 5.2 and 661.7 keV are measured, as well as the energy resolution for the LUX detector at those same energies. Additionally, there is an interpretation of existing measurements and descriptions of electron-ion recombination fluctuations in liquid xenon as limiting cases of a more general liquid xenon recombination fluctuation model. Measurements of the standard deviation of these fluctuations at monoenergetic electronic recoil peaks exhibit a linear dependence on the number of ions for energy deposits up to 661.7 keV, consistent with previous LUX measurements between 2 and 16 keV with ${}^3\mathrm{H}$. We highlight similarities in liquid xenon recombination for electronic and nuclear recoils with a comparison of recombination fluctuations measured with low-energy calibration data.

Figure 1

Single-scatter events identified in the LUX 2013 WIMP-search data. The labels indicate the source isotopes and their energies. Only radial and drift-time fiducial cuts ($r_{S2}<20\mathrm{cm}$; $38\mu \mathrm{s}<t_d<305\mu \mathrm{s}$) have been applied to make this plot; additional cuts are applied to maximize signal to background for each peak individually in the following measurements.

Figure 2

Single-scatter events satisfying radial and drift-time fiducial cuts ($r_{S2}<20\mathrm{cm}$; $38\mu \mathrm{s}<t_d<305\mu \mathrm{s}$) prior to May 12 in the LUX 2013 WIMP-search data. The error bars represent statistical uncertainty. The dashed red lines indicate the true peak energies of the 5.2- and 33.2-keV, $L$- and $K$-shell, electron captures (ECs) of ${}^{127}\mathrm{Xe}$. The 33.2-keV $K$-shell peak emerges clearly when data collected in the 24 h following each ${}^{83\mathrm{m}}\mathrm{Kr}$ injection are excluded. ${}^{127}\mathrm{Xe}$ was cosmogenically produced while in storage above ground, and it began decaying away once the LUX xenon was moved underground. These EC sources became negligibly weak by the end of the WIMP-search data acquisition.

Figure 3

Fiducial single-scatter events ($r_{S2}<20\mathrm{cm}$; $38\mu \mathrm{s}<t_d<305\mu \mathrm{s}$) from an August 2013 ${}^{137}\mathrm{Cs}$ calibration of the LUX detector. The dashed red line indicates the true energy of the photopeak at 661.7 keV.

Figure 4

The $S1$ and $S2$ (corrected pulse areas) from events including 410-keV ${}^{127}\mathrm{Xe}$ decays.

Figure 5

The measured light yield at peak energies in the LUX ER energy spectrum for (a) single- and (b) multiple-site energy depositions. Also in (a), the dashed blue line is the mean response predicted by NEST for an applied field of $180\mathrm{V}/\mathrm{cm}$, and the shaded blue region shows its 5% uncertainty. The red circles (and shaded band) show LUX measurements (and uncertainty) from an injected ${}^3\mathrm{H}$ beta source also under a mean applied field of $180\mathrm{V}/\mathrm{cm}$ [9]. In (b), the NEST predictions for multicomponent decays of ${}^{83\mathrm{m}}\mathrm{Kr}$, ${}^{127}\mathrm{Xe}$, and ${}^{129\mathrm{m}}\mathrm{Xe}$ are made by summing the mean photons expected from the constituent scatters and dividing by the total energy. The light yield of 33.2-keV ${}^{127}\mathrm{Xe}$ is lower than the NEST prediction, where the recombination models transition.

Figure 6

The measured charge yield at peak energies in the LUX ER energy spectrum for (a) single- and (b) multiple-site energy depositions. In (a), the dashed blue line is the mean response predicted by NEST for an applied field of $180\mathrm{V}/\mathrm{cm}$, and the shaded blue region shows its 5% uncertainty. The red circles (and shaded band) show LUX measurements (and uncertainty) from an injected ${}^3\mathrm{H}$ beta source also under a mean applied field of $180\mathrm{V}/\mathrm{cm}$ [9]. Charge yields measured at 33.2 and 5.2 keV in a dedicated two-S2 ${}^{127}\mathrm{Xe}$ LUX analysis (green) [26] agree with these one-S2 measurements (black). In (b), the NEST predictions for multicomponent decays of ${}^{83\mathrm{m}}\mathrm{Kr}$, ${}^{127}\mathrm{Xe}$, and ${}^{129\mathrm{m}}\mathrm{Xe}$ are made by summing the mean electrons expected from the constituent scatters and dividing by the total energy.

Figure 7

The recombination probability calculated at peak energies in the LUX ER energy spectrum for (a) single- and (b) multiple-site energy depositions. In (a), the dashed blue line is the mean recombination predicted by NEST for an applied field of $180\mathrm{V}/\mathrm{cm}$, and the shaded blue region shows its 5% uncertainty. The red circles (and shaded band) show LUX measurements (and uncertainty) from an injected ${}^3\mathrm{H}$ beta source also under a mean applied field of $180\mathrm{V}/\mathrm{cm}$ [9].

Figure 8

The measured energy resolution at known energy peaks in the LUX ER backgrounds. The detector is optimized for low-energy sensitivity, and variable amounts of PMT saturation and single-electron contributions affect S2 pulses and hamper the energy resolution at high energy, as discussed in the text. Data from the PIXeY (blue x; [27]), MiX (red triangle; [28]), ZEPLIN-III (green star; [29]), and XENON100 (magenta square; [30]) are shown for comparison.

Figure 9

The ER and NR calibration data (cyan and orange, respectively) form characteristic recoil bands. Large filled circles show the fitted band Gaussian mean and small filled circles indicate the fitted Gaussian $\pm 1\sigma$. Power law fits to the means and $\pm 1\sigma$ are shown with solid and dashed lines.

Figure 10

The measured Gaussian recombination fluctuations [as described in approach (a)] scale linearly with the number of ions. The solid (dashed) red lines are the linear best fit ($\pm 1\sigma$) calculated to be ${\sigma }_r=(0.059\pm 0.003)n_i$. The other solid lines show the NEST model [approach (b)] for five choices of $\omega$, where the line color changes with $\omega =0.0025$ (black), 0.005, 0.0075, 0.01, 0.0125 (lightest gray).

Figure 11

The ER band width is plotted with the best-fit NEST ER band width. Note that NEST here has been customized for these low energies as in [9]. The data points with full opacity are used for the fit of $\omega$. NEST’s Poisson implementation of fluctuations breaks down below $S1=5\mathrm{phd}$, and lower ${}^3\mathrm{H}$ statistics above $S1=65\mathrm{phd}$. The solid blue line is the NEST prediction for $\omega =0.0075$, while the shaded blue region shows the variation for the range of uncertainty in $\omega$.

Figure 12

The NR band width is plotted with the best-fit NEST NR band width. Note that NEST here is a modified version of [8] as in [4]. The data points with full opacity are used for the fit of $\omega$, while the semitransparent points are excluded due to limited statistics and large variation in the fit values from the midrange energies of the D-D recoil spectrum with lower event rate (begins near $S1=35–40\mathrm{phd}$). The solid blue line is the NEST prediction for $\omega =0.0065$, while the shaded blue region shows the variation for the range of uncertainty in $\omega$.