Improved measurement of the $2\nu \beta \beta$ half-life of ${}^{136}$Xe with the EXO-200 detector

We report on an improved measurement of the $2\nu \beta \beta$ half-life of ${}^{136}$Xe performed by EXO-200. The use of a large and homogeneous time-projection chamber allows for the precise estimate of the fiducial mass used for the measurement, resulting in a small systematic uncertainty. We also discuss in detail the data-analysis methods used for double-$\beta$ decay searches with EXO-200, while emphasizing those directly related to the present measurement. The ${}^{136}$Xe $2\nu \beta \beta$ half-life is found to be $T_{1/2}^{2\nu \beta \beta }$ = $2.165\pm 0.016\left(\mathrm{stat}\right)\pm 0.059\left(\mathrm{sys}\right)\times {10}^{21}$ yr. This is the most precisely measured half-life of any $2\nu \beta \beta$ decay to date.

Figure 1

Cutaway view of the EXO-200 TPC.

Figure 2

Diagram of the EXO-200 $U$-$V$-$Z$ and $X$-$Y$-$Z$ coordinate systems. Also shown are the hexagonal active region and fiducial region and the circular projection of the Teflon reflector panels.

Figure 3

The EXO-200 installation at the Waste Isolation Pilot Plant.

Figure 4

Visualization of the simulated TPC vessel and internal copper components.

Figure 5

The magnitude of the calculated weighting potential for a single $U$-wire readout channel. The weighting potential peaks to one at the positions of the three wires composing a signal channel ($X=1.5$, 4.5, 7.5 mm, $Z=6$ mm). Example charge drift trajectories are shown by the overlaid red dashed lines; deflections of the trajectories arise from the presence of a $V$-wire channel (diamonds at $X=1.5$, 4.5, 7.5 mm, $Z=12$ mm) situated directly above the $U$-wire channel.

Figure 6

Comparison of the distributions of the pulse rise time (a) and maximum-to-minimum time (b) on $U$ wires between calibration data and simulations using 2D and 3D field maps (see Sec. 4c2) for ${}^{228}$Th data. The long tail in the rise-time distribution is attributable to Compton scatters. Only wire signals above 200 keV are compared, as the values of rise time and maximum-to-minimum time for low-amplitude signals depend strongly on the waveform noise profile. The distributions are normalized to the same total number of events for comparison.

Figure 7

A $U$-wire waveform (a) and the result of the matched filter (b). The horizontal line in (b) is the calculated threshold.

Figure 8

Examples of fits to a $U$ wire (a) and $V$ wire (b) on an expanded vertical scale. One can see that the $V$-wire peaks earlier than the $U$-wire signal.

Figure 9

Distributions of the discriminants described in the text used to identify induction signals, calculated for waveforms generated from ${}^{228}$Th Monte Carlo simulations. The distribution of these values for all $U$-wire signals is shown as the solid histogram, with the cuts used for each value denoted by the vertical dashed lines. $U$-wire signals must satisfy all cuts to be identified as “inductionlike” signals. The cuts are chosen to ensure minimum impact on collection signals (acceptance efficiency $>$$99.9\%$), corresponding to a rejection efficiency of induction signals of 77%, integrated over the $2\nu \beta \beta$ energy spectrum. Also shown are the distributions of simulated induction pulses which were not identified as inductionlike by the cuts (“Not identified”) and simulated pulses containing at least some deposition, but which were identified as inductionlike (“Some deposition”).

Figure 10

The calibration source locations around the TPC vessel as viewed from above. The $XYZ$ coordinates of the source locations are: S2 = (0.0, 0.0, $-$29.5 cm), S5 = (25.5 cm, 0.0, 0.0), S8 = (0.0, 0.0, 29.5 cm), and S11 = (0.0, 25.5 cm, 0.0). Not shown: S17 = (0.0, $-$25.5 cm, 0.0).

Figure 11

The light response function $f(r,\varphi ,z)$ from September 22, 2011, until February 20, 2012, is shown here, indicated by the color coding. For both plots the correction factor ranges from 0.70 (blue) to 1.19 (red). Panels (a)–(h): The function evaluated at eight discrete values of the azimuthal angle $\varphi$ over the full range of $r$ (horizontal axis, $0\mathrm{mm}<r<168\mathrm{mm}$) and $Z$ (vertical axis, $-192\mathrm{mm}<Z<192\mathrm{mm}$). Panels (i)–(q): The function evaluated at nine discrete values of $Z$ over the full range of $X$ (horizontal axis, $-168\mathrm{mm}<X<168\mathrm{mm}$) and $Y$ (vertical axis, $-168\mathrm{mm}<Y<168\mathrm{mm}$). A second response function (not shown here) is used from February 20, 2012, until April 15, 2012.

Figure 12

An example electron lifetime ${\tau }_{\mathrm{e}}$ measurement obtained by fitting a decaying exponential to the ${}^{228}$Th full-absorption peak energies binned by drift time. TPC 2 (negative $Z$) is assigned a negative drift time for convenience in visualization. Fits to separate ${\tau }_{\mathrm{e}}$ for each TPC and the combined fit value are shown. This data are from a single-source calibration run.

Figure 13

The fit of a piecewise polynomial to electron lifetime in TPC 1 [positive $Z$ (a)] and TPC 2 [negative $Z$ (b)]. The colored bands show the 68% confidence interval on the fit. The vertical dashed lines indicate discontinuities in the electron lifetime owing to interruptions in the xenon recirculation or xenon gas feed events. The vertical shaded regions indicate time periods which were excluded from the final data set owing to poor electron lifetime.

Figure 14

Anticorrelation between ionization and scintillation for SS events from a ${}^{228}$Th source. The prominent island at the upper end of the distribution is the 2615-keV $\gamma$ line of ${}^{208}$Tl.

Figure 15

Energy resolutions of ionization and scintillation channels during Run 2a.

Figure 16

Residuals between the calibrated source energies and the true energies for SS and MS events. Also shown is the residual for the ${}^{40}$K peak (cross, MS only), which is obtained from the low-background data set.

Figure 17

(a) The fractional energy resolution ($\sigma /E$) for SS and MS events. The width of the two lines indicates the uncertainty. (b) The absolute energy resolution for SS and MS events. The hatched areas indicate the uncertainty.

Figure 18

Comparison of shape between data (points) and simulation (histograms) for energy and standoff distance distributions. All distributions have been normalized to 1 and, in all cases, the top (bottom) plots are SS (MS) distributions. Panels (a), (c), (e), and (g) are for a ${}^{228}$Th source near the cathode. Panels (b), (d), (f), and (h) are for a ${}^{60}$Co source located near the anode.

Figure 19

Comparison of MS energy distribution between data (points) and simulation (histograms) using ${}^{228}$Th (a) and ${}^{60}$Co (b) sources near the cathode (S5). Note the excellent agreement of the full-energy-deposition $\gamma$-ray peaks all the way up to the summation peaks.

Figure 20

Ratio of ${}^{60}$Co source (at the cathode, S5) calibration spectra to that generated from simulation. Single- and multisite events are shown in (a) and (b), respectively, and linear fits to the data are shown. Ratio plots for ${}^{228}$Th source data and simulation demonstrate the same behavior.

Figure 21

(a) Single-site fraction for ${}^{228}$Th calibration data and simulation. (b) Fractional difference between SS fraction for data and simulation as a function of energy for ${}^{228}$Th and ${}^{60}$Co sources.

Figure 22

History (a) and distribution (b) of rate of events tagged as noise. The drop in noise starting with run 2855 is attributable to a cooling fan change in the electronics box. The unshaded region in (b) indicates the accepted parameter values ranges.

Figure 23

History (a) and distribution (b) of the rate of events that have at least a scintillation and charge cluster. The increase in rate seen after January 13, 2013 (run 3121), came from increased Rn in the system after a Xe feed event. The discontinuity on February 22, 2013 (run 3333), was from an APD electronics change. The unshaded region in (b) indicates the accepted parameter values.

Figure 24

Rate of $2\nu \beta \beta$ versus hexagonal apothem. The vertical dashed line indicates the fiducial cut we have chosen to use at an apothem of 153 mm. The data within that region are consistent with a rate that is proportional to volume.

Figure 25

Drift-time distribution for $\alpha$ events originating from the cathode for events collected in TPC1 (solid histogram) and TPC2 (dashed histogram). Gaussian fits to the distributions and their results are also shown.

Figure 26

Fit results. Data and PDFs for SS energy spectra shown in linear (a), log (b), with residuals (c). The residuals have been normalized by the bin error. To improve visualization of the fit results, the energy bin widths in the plot are 20 keV instead of the 14-keV bin size used during fitting. SS standoff distribution is also shown (inset). Backgrounds have been grouped together according to Rn components and components in or near the TPC vessel. The best-fit counts and errors for each PDF are given in Table 7. There are fewer events in the $0\nu \beta \beta$ region of interest than in Ref. [8] because of the stricter fiducial volume cut.

Figure 27

Projected MS energy spectra (a) and corresponding MS SD distribution (inset) for the final fit results. Residuals are shown in (b). PDF components are as in Fig. 26.

Figure 28

A comparison of this result with EXO-200 (2011) [3] and KamLAND-Zen (2012) [37].

Figure 29

The fit count rate divided by efficiency of $2\nu \beta \beta$ versus energy threshold. The main result is the (red) triangle at 700 keV.

Figure 30

Total $[E_V-{\rho }_E\left(E_U\right)]/{\rho }_E\left(E_U\right)$ for an event, data from Th source runs as well as low-background runs. There is a strong $Z$ dependence for $\left|Z\right|>160$ mm observed, and so the energy relationship between $U$ and $V$ bundles is ignored for bundles in this region.

Figure 31

Visualization of time [Eq. (A4)] PDF used to cluster signal bundles together. The $Z$ direction (color, contour lines) of the plot is the negative log of the indicated PDF: a lower value denotes a higher probability, with 0 (white) being the highest probable state.

Figure 32

As in Fig. 31, but for the position PDF [Eq. (A6)].