Sterile neutrinos, coherent scattering, and oscillometry measurements with low-temperature bolometers

Coherent neutrino-nucleon scattering offers a unique approach in the search for physics beyond the standard model. When used in conjunction with monoenergetic neutrino sources, the technique can be sensitive to the existence of light sterile neutrinos. The ability to utilize such reactions has been limited in the past due to the extremely low-energy threshold (10–50 eV) needed for detection. In this paper, we discuss an optimization of cryogenic solid-state bolometers that enables reaching extremely low kinetic energy thresholds. We investigate the sensitivity of an array of such detectors to neutrino oscillations to sterile states. A recent analysis of available reactor data appears to favor the existence of such a sterile neutrino with a mass splitting of $|\Delta m_{\mathrm{sterile}}{|}^2\ge 1.5{\mathrm{eV}}^2$ and mixing strength of ${sin}^{2}2{\theta }_{\mathrm{sterile}}=0.17\pm 0.08$ at 95% confidence level. An array of such low-threshold detectors would be able to make a definitive statement as to the validity of the interpretation.

Figure 1

Schematic of bolometer model. The refrigerator acts as a cold bath at temperature $T_b$. The Si heat capacity is connected by a thermal conductance $G_{\mathrm{pb}}$ to the bath. The TES is connected by the electron-phonon conductance $G_{\mathrm{ep}}$ to the Si. A potential excess heat capacity with its coupling are shown in dashed outlines. For this study we have assumed $C_{\mathrm{excess}}$ and/or $G_{\mathrm{excess}}$ can be made small enough to become negligible.

Figure 2

Calculation of threshold for Si and Ge targets from 20–100 g at different operating temperatures. The lowest line for each target material is the 20 g line. The model (see Fig. 1) takes into account the heat capacity of the TES and the target, the internal thermal fluctuation noise between the target and the TES thermometer, the electronics noise, the Johnson noise from the TES and its bias resistor, and the phonon noise between the target to the bath. The volume of the TES was scaled to give the best energy resolution at 15 mK. The horizontal dashed line marks the desired 10 eV threshold, corresponding to an energy resolution $\Delta E_{\mathrm{FWHM}}=3.14\mathrm{eV}$. The vertical dashed line marks the desired operating temperature of 15 mK. For Si, a 50 g target meets the requirements. For Ge, a 20 g target meets the requirements.

Figure 3

Zoom-out of Fig. 2. Our desired operating point is designated by the vertical and horizontal dashed lines. The legend for both plots are the same. The ovals designate the region of operation for the following low-temperature experiments: CUORE [28], EDELWEISS [40], CRESST [53], CDMS [31], X-ray microcalorimeters for astrophysics [42], and MARE (proposed) [29]. Note that these experiments use different combinations of thermal or athermal measurements, TES or NTD thermometry, and mass per detector unit, so cannot be directly compared to the design presented in this paper.

Figure 4

Simulated current readout for 10–50 eV recoils using the model parameters in Table . The current has been multiplied by $-1$ to make the pulses positive. Noise sources modeled are: the phonon noise between the target to the bath, the internal thermal fluctuation noise between the target and the TES thermometer, the Johnson noise from the TES and its bias resistor, and the electronics noise. The modeled 10 eV pulses are clearly separated from the noise.

Figure 5

Conceptual schematic of the experimental setup for a bolometric measurement of coherent scattering from a high-intensity ${}^{37}\mathrm{Ar}$ neutrino source. An array of 10 000 Si bolometers is arranged in a column of dimensions $0.42(\mathrm{dia}.)\times 2.0(\mathrm{\text{lenghth}})$ meters (shown in green) inside a dilution refrigerator suspended from a vibration isolation mount. Each Si bolometer has a mass of 50 g for a total active mass of 500 kg. Appropriate passive or active shielding surrounds the refrigerator. A cylindrical bore in the shield allows the ${}^{37}\mathrm{Ar}$ source, mounted on a translation mechanism, to be moved to different positions along the side of the array. Periodic movement of the source throughout the measurement sequence allows each detector to sample multiple baselines, enables cross-calibration among detectors, and aids in background subtraction. The minimum distance from the source to a bolometer is assumed to be $\sim 10\mathrm{cm}$.

Figure 6

Plot of the relative signal error versus signal-to-noise ratio $\frac{S}{\sqrt{B}}$ ($S$ represents signal strength, $B$ represents background counts) for a 500-kg Si array exposed to a 5 MCi ${}^{37}\mathrm{Ar}$ for 300 days. This array configuration and source intensity yields approximately $S\simeq 54,000$ total signal events. Arrow indicates signal-to-noise ratio corresponding to 1 background event/kg/day.

Figure 7

Distribution of events on a 500 kg Si array as a function of time of source deployment. Source considered here is a 5 MCi ${}^{37}\mathrm{Ar}$ electron-capture source.

Figure 8

Left: Ratio of data and Monte Carlo for a simulated neutrino oscillation signal ($\Delta m_S^2=1.5{\mathrm{eV}}^2$, $\sin (2{\theta }_S{)}^2=0.15$) as a function of source distance from a 5 MCi ${}^{37}\mathrm{Ar}$ neutrino source and a 500 kg Si array. Right: Likelihood contour curves for same signal after 300 days of data taking. Contour levels are shown at 90% (blue), 95% (green), and 99% (red).

Figure 9

Likelihood contours for a 300-day run on a 500 kg Si array (left) and 200 kg Ge (right) array exposed to a 5 MCi ${}^{37}\mathrm{Ar}$ (top) and ${}^{51}\mathrm{Cr}$ (bottom) source, using both shape and rate information. Confidence levels in all plots are shown at 90% (blue), 95% (green), and 99% (red). Statistical and systematic errors are included in the signal analysis.

Figure 10

Likelihood contours for a 300-day run on a 500 kg Si array and a 5 MCi ${}^{37}\mathrm{Ar}$ source, using only shape information. Contour curves use same scheme as in Fig. 8.