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Theory

Theory

Exp

Exp

Exp

Theory

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 3.2 -fold coincidences, the background rate is 15 Hz.

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

For 35-fold coincidences, the background rate is 19 4.2 mHz.

For 46-fold coincidences, the background rate is 102 43 uHz.

For 57-fold coincidences, the background rate is 512 34 nHz.

For 68-fold coincidences, the background rate is 2.5 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:

236 uHz 2.8 mHz for 2-fold coinc.

18 510 uHz for 3-fold coinc.

1.3 72 uHz for 4-fold coinc.

90 nHz 8.5 uHz for 5-fold coinc.

11 824 nHz for 6-fold coinc.

29 nHz for 7-fold coinc.

8.4 nHz for 8-fold coinc (this corresponds to 1 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 coincidencescoincidence threshold. For the higher coincidences, I’m just going to I’ll assume the energy deposit scales linearly (probably incorrect but we’re being quite rough anywaybut 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.

2108.09405

DM-nucleus cross-section scales as A⁴

‘as above’

‘as above’

‘as above for mass reach’.

Cross-section reach is a factor of A⁴ lower:
~10^-28 (E_th/500keV) cm².

2108.09405