Goal

Study models predicting multiple electron/nuclear recoils in NaI(Tl) and the liquid scintillator.

Summary of initial estimates

Potential sensitivity of SABRE (neglecting backgrounds) is comparable to the existing limit from DEAP-3600.
Large-scale scintillator experiments such as SNO+, Borexino have potential to set much stronger limits.

Investigated processes

Heavy elementary DM
Composite DM (Blobs, nuggets, etc.)

Stage 1

Process	Info	Signature	Selection	Background rate	Limits on signal rate	Limits on model parameters	Current limits

Process

Info

Signature

Selection

Background rate

Limits on signal rate

Limits on model parameters

Current limits

Theory

Exp

Theory

Geometric cross-section

Rate is determined by area of detector.
Upper limit on DM mass is determined by flux.
Lower limit on xsec is determined by energy threshold.
Upper limit on xsec is determined by overburden.

‘Track’ in liquid scintillator detector.

Multiple sub-threshold scattering events (~few keV per scatter) , but total energy deposited along track can be above threshold.

I’ll assume scatters are low-energy enough that they generate single photoelectron signals in a scatter.

Simplest selection would be to observe N 1 PE events over a time period consistent with DM crossing the detector.

Crossing time ~3 m / 10^-3 c, so 10 microseconds.

There’s definitely scope for improvement with these selections – the lowest-hanging fruit would be to look for events consistent with a down-going track (top PMTs fire first, bottom ones later).

The dark rate will dominate the event rate at 1 PE. I’ll assume a dark rate of 400 Hz for all PMTs, but can recalculate pretty easily.

The accidental rate will depend upon the N-fold coincidence in ~10 us used for identifying these events.

For 2-fold coincidences, the background rate is 473 Hz.

For 3-fold coincidences, the background rate is 15 Hz.

For 4-fold coincidences, the background rate is 0.3 Hz.

For 5-fold coincidences, the background rate is 4.2 mHz.

For 6-fold coincidences, the background rate is 43 uHz.

For 7-fold coincidences, the background rate is 34 nHz

For 8-fold coincidences, the background rate is 2.2 nHz, which is 0.2 events in 3 years.

NB: the dark count rates for the veto PMTs will be measured soon, so we could flesh this out with more realistic numbers in a couple of months' time.

Assuming 3 years of running and a background entirely due to singles, 90% of experiments would have a difference from the expectation rate of less than:

2.8 mHz for 2-fold coinc.

510 uHz for 3-fold coinc.

72 uHz for 4-fold coinc.

8.5 uHz for 5-fold coinc.

824 nHz for 6-fold coinc.

29 nHz for 7-fold coinc.

8.4 nHz for 8-fold coinc (this gives ~1 count).

These numbers effectively modify the right hand edge of the limit space, depending on which coincidence level we choose, if we assume 100% signal efficiency.

The bottom edge of the limits is set by the average energy deposit required to pass the trigger. This sort of veto event hasn’t been well-studied by SABRE. We claim a 50 keV threshold for two veto PMTs firing within ~few 10’s of nanoseconds. Correcting for a quenching factor of 0.2, 250 keV might be a good first estimate for the 2-fold coincidence threshold. For the higher coincidences, I’ll assume the energy deposit scales linearly (quite rough but a first guess). This would give a threshold of 250*N/2 keV for an N-fold coinc.

With area of 5.3m² and 3 years run time, sensitive to m_DM < 10¹⁹ GeV (assuming zero background).

Sensitive to cross-sections down to ~5x10^-24 (E_th/500keV) cm².