The SIMPLE Phase II dark matter search

Phase II of SIMPLE (Superheated Instrument for Massive ParticLe Experiments) searched for astroparticle dark matter using superheated liquid ${\mathrm{C}}_2{\mathrm{ClF}}_5$ droplet detectors. Each droplet generally requires an energy deposition with linear energy transfer (LET) $\gtrsim 150\mathrm{keV}/\mu \mathrm{m}$ for a liquid-to-gas phase transition, providing an intrinsic rejection against minimum ionizing particles of order ${10}^{-10}$, and reducing the backgrounds to primarily $\alpha$ and neutron-induced recoil events. The droplet phase transition generates a millimetric-sized gas bubble that is recorded by acoustic means. We describe the SIMPLE detectors, their acoustic instrumentation, and the characterizations, signal analysis and data selection, which yield a particle-induced, “true nucleation” event detection efficiency of better than 97% at a 95% C.L. The recoil-$\alpha$ event discrimination, determined using detectors first irradiated with neutrons and then doped with alpha emitters, provides a recoil identification of better than 99%; it differs from those of COUPP and PICASSO primarily as a result of their different liquids with lower critical LETs. The science measurements, comprising two shielded arrays of fifteen detectors each and a total exposure of 27.77 kgd, are detailed. Removal of the 1.94 kgd Stage 1 installation period data, which had previously been mistakenly included in the data, reduces the science exposure from 20.18 to 18.24 kgd and provides new contour minima of ${\sigma }_p=4.3\times {10}^{-3}\mathrm{pb}$ at $35\mathrm{GeV}/{\mathrm{c}}^2$ in the spin-dependent sector of astroparticle dark matter–proton interactions and ${\sigma }_N=3.6\times {10}^{-6}\mathrm{pb}$ at $35\mathrm{GeV}/{\mathrm{c}}^2$ in the spin-independent sector. These results are examined with respect to the fluorine spin and halo parameters used in the previous data analysis.

Figure 1

Phase diagram of the fabrication protocol for a ${\mathrm{C}}_2{\mathrm{ClF}}_5$ SDD. The indicated sol-gel transition denotes the onset of a gel-like diphasic system containing both liquid and solid phases whose morphology is a continuous polymer network.

Figure 2

Science ${\mathrm{C}}_2{\mathrm{ClF}}_5$ SDD during installation; the bottle is a squared $10\times 10{\mathrm{cm}}^2$ base, 12 cm tall Schott glass containing $\sim 900\mathrm{ml}$ of $\text{freon}+\text{gel}$ covered by a 6 cm glycerin layer. The cap contains the microphone and feedthroughs for the pressure (horizontal) and microphone (vertical) electronics.

Figure 3

Temperature variation of the threshold recoil energy with pressure for the three ${\mathrm{C}}_2{\mathrm{ClF}}_5$ constituents and ${}^4\mathrm{He}$ ions at 2.00 (solid), 2.50 (dotted), and 3.00 (dash dot) bar, calculated with $\mathrm{\Lambda }=1.40$. The vertical line denotes the standard operating temperature of the SDD; the horizontal line denotes the 8 keV recoil threshold energy for 2 bar in the measurements.

Figure 4

A partial gallery of the PSDs of a “true nucleation” event (a), in comparison with typical gel-associated background acoustic events: (b) fracture, (c) ${\mathrm{N}}_2$ release, and (d) microleak, as well as typical acoustic backgrounds such as (e) water input bubbles and (f) ventilation system operation. Although the ${\tau }_0$, $\mathcal{F}$ parameters vary with each, the characteristic PSD is preserved.

Figure 5

SRIM-calculated LET for 100 keV fluorine recoil ions in ${\mathrm{C}}_2{\mathrm{ClF}}_5$ as a function of penetration depth. The conditions for bubble nucleation are satisfied only over $\sim 0.4\mu \mathrm{m}$ of liquid penetration.

Figure 6

Amplitude analysis of recoil events generated by neutron irradiation (solid), in comparison with a droplet size distribution (dashed) generated by the “standard fabrication protocol” of Sec. 2a when scaled as $\mathcal{A}\to {\mathrm{gr}}^3$. The Gaussian fit to the irradiation data yields a mean of 5.8, $4.4\sigma$ below $\ln ({\mathcal{A}}^2)=9.2$.

Figure 7

Scatter plot of the response-corrected first 250 recorded event amplitudes in the SDD neutron irradiation of Fig. 6, yielding a recoil distribution with mean $3.5\sigma$ below $\ln (\mathcal{A}{)}^2=9.2$, indicating the exposure-dependent populating of the eventual recoil distribution with a bias to largest events first.

Figure 8

A typical reanalysis of monochromatic neutron (54 and 149 keV) SDD irradiation data at 2 bar, including all neutron-liquid interactions weighted by Eq. (7) with $\mathrm{\Gamma }$ being a free parameter; the shaded region corresponds to $\mathrm{H}({\mathrm{E}}_c)$ with $\mathrm{\Gamma }=4.2\pm 0.3$.

Figure 9

Experimental results obtained with a single ${\mathrm{C}}_2{\mathrm{ClF}}_5$, standard fabrication detector at 2 bar and $9°\mathrm{C}$, first irradiated with Am/Be neutrons, and then doped with ${\mathrm{U}}_3{\mathrm{O}}_8$ $\alpha$’s, yielding 867 $\alpha$ and 1280 recoil events. The indicated gap corresponds to a separation of 20 mV, which is readily resolved with the 0.3 mV of the acquisition electronics. The asymmetry in the $\alpha$ response is due to the relationship between droplet size distribution and the Bragg curve above ${\mathrm{LET}}_c$ of the $\alpha$’s in the liquid, as discussed in the text. The central peak represents the first 15 events of the neutron irradiation, amplified by a factor 50 for visibility.

Figure 10

Bragg curves for 5.5 MeV $\alpha$s in ${\mathrm{C}}_2{\mathrm{ClF}}_5$ (solid), ${\mathrm{C}}_4{\mathrm{F}}_{10}$ (dashed), and ${\mathrm{CF}}_3\mathrm{I}$ (blue dotted) as a function of penetration depth, with the ${\mathrm{LET}}_c$ of each at the operating temperatures and pressures indicated in Refs. [1, 2, 3]. The Bragg peak in ${\mathrm{C}}_2{\mathrm{ClF}}_5$ above the ${\mathrm{LET}}_c$ of $176\mathrm{keV}/\mu \mathrm{m}$ is achieved with $32–40\mu \mathrm{m}$ penetration of the liquid. The $\mathrm{\Lambda }$ for the ${\mathrm{C}}_4{\mathrm{F}}_{10}$ and ${\mathrm{CF}}_3\mathrm{I}$ are obtained from the phenomenological $\mathrm{\Lambda }=4.3({\rho }_v/{\rho }_l{)}^{1/3}$, which is not verified for either; both [2, 3], however, claim larger $\mathrm{\Lambda }$, which reduces the respective ${\mathrm{LET}}_c$ relative to that indicated.

Figure 11

Phase space estimate of the containment probability that a droplet of diameter 2r contains an $\alpha$ trajectory above ${\mathrm{LET}}_c$, as described in the text.

Figure 12

Sample distribution of 522 ${\mathrm{C}}_2{\mathrm{ClF}}_5$ droplet sizes taken from the standard fabrication protocol of Sec. 2a2, together with a Gaussian fit to the distribution with ${\chi }_r^2=4.6$.

Figure 13

Schematic (not to scale) of the Phase II experiment Stage 2 disposition in the GESA facility of the LSBB.

Figure 14

Pressure evolution of the two SDD sets over each of Stage 1 and 2 measurements (same scale), with the dotted lines indicating the 2.00–2.15 bar region. The letter identifications in each correspond to the SDD. The pressures of the SDDs in Stage 2 were slowly increased to above 3 bar, permitting an in situ measurement of $\mathrm{\Lambda }$. The failure of detectors I, L, M in Stage 2 occurred early in the measurement, and the records were not used in the analysis; K ran until day 48.

Figure 15

Scatter plots of the corrected Stage 1 (left) and 2 (right) single event signals with respect to decay constants and frequency. The indicated boxes isolate the events exhibiting particle-induced characteristics. Identification of the event origins follows from comparison of their PSD structures with those of calibration templates.

Figure 16

Scatter plots of the corrected Stage 1 (left) and 2 (right) single event signals with respect to $\mathcal{A}$ and $\mathcal{F}$. Identification of the event origins follows from comparison of their PSD structures with those of calibration templates.

Figure 17

New ${\mathrm{S}}_p\mathrm{D}$ exclusion contour (SIMPLE-2014) resulting from correction of the Stage 1 results, together with its variations from the use of the strict Feldman-Cousins application (F-C only), Divari fluorine spin values (Divari), the canonical SHM ${\mathrm{v}}_0$, ${\mathrm{v}}_{\text{esc}}$ parameters (canonical), and $\text{canonical}+{\rho }_0=0.40\mathrm{GeV}/{\mathrm{c}}^2$ (canonical, $\rho$); the previous “merged” contour, reported in Ref. [1] using the Pacheco-Strottman $⟨{\mathrm{S}}_{p,n}^F⟩$ [52] and Lewin-Smith SHM parameters, is also shown (SIMPLE-2012) for comparison. The region in gray denotes the area suggested by CMSSM [55].

Figure 18

New $S_n\mathrm{D}$ exclusion contour (SIMPLE-2014) resulting from the corrected Stage 1 results, together with that of the 2012 report (SIMPLE 2012). Also shown are contours for the Divari only and canonical only.

Figure 19

New SI exclusion contour (SIMPLE-2014) resulting from correction of the Stage 1 results, together with its variations, using a strict Feldman-Cousins application (FC only), the canonical SHM parameters (canonical), and $\text{canonical}+\rho =0.40\mathrm{GeV}/{\mathrm{c}}^2$ (canonical, $\rho$); the previous merged contour, reported in Ref. [1] using Lewin-Smith SHM parameters, is also shown (SIMPLE-2012) for comparison.