Background Study
5.2 Correlated Background
5.2.1 Fast neutron
Energetic neutrons can be produced by cosmic muons via spallation. Before neutron is thermalized, it deposits energy by the elastic scattering with proton. This process gives the prompt-like signal and the thermalized neutron captured on gadolinium or hydrogen gives the delayed signal. These prompt and delayed signals mimic IBD events.
There are timing relations between muons and the neutron produced in the detector.
It is easy to remove such neutron background in the detector by the timing coincidence.
Some of the neutrons which enter the detector are produced in the rock surrounding the water pool. The parent muons in such a case are tagged by the water veto system.
Such neutrons are referred to as fast neutrons which do not satisfy the above timing coincidence. One can estimate the number of fast neutrons from the IBD candidates by the extrapolation method. The event selection is the same as IBD selection except that the prompt energy cut is set at 100 MeV. We then fit the prompt energy spectrum from 20 MeV to 100 MeV and then extrapolate the fitted function to lower energies. We calculate the area of the fitted function between 1.5 MeV and 12 MeV for estimating the event number of fast neutrons.
The fitting function is
f (E; λ) = Npow· Eλ R12
1.5EλdE, (5.9)
where Npow is the event number of fast neutrons, E is energy and λ is the power law constant. The fitting results are shown in Figure 5.12. The fast neutron rate can be calculated by Eq (5.1).
On the other, the first order polynomial, Eq (5.10), is used to estimate the systematic error, which is the difference between errors from Npow and Npol1. The total error is q
σN2pow + σsys2 .
f (E; S) = Npol1· (S · E + 1) R12
1.5(S · E + 1)dE. (5.10)
powerlaw_EH1
Entries 442921
Mean 3.83
Entries 442921
Mean 3.83
Entries 442921
Mean 3.83
Entries 442921
Mean 3.83
Entries 349071
Mean 3.764
Entries 349071
Mean 3.764
Entries 349071
Mean 3.764
Entries 349071
Mean 3.764
Entries 211050
Mean 2.924
Entries 211050
Mean 2.924
Entries 211050
Mean 2.924
Entries 211050
Mean 2.924
Figure 5.12: Fast neutron fitting results. The red curve is the fitting range and the blue one is the extrapolated curve.
EH1 EH2 EH3
N6AD Eq (5.9) 601.899 ± 75.2179 226.807 ± 45.9474 83.6951 ± 29.0545 Pol1 462.604 ± 91.0539 141.283 ± 55.5341 53.4328 ± 33.8179 λ -0.5585 ± 0.0678 -0.5524 ± 0.1098 -0.5954 ± 0.1864 Rate 2.0193 ± 0.2579 1.4578 ± 0.3017 0.1523 ± 0.0536 N8AD Eq (5.9) 1320.95 ± 111.894 1347.98 ± 128.321 184.718 ± 41.062
Pol1 800.702 ± 133.678 630.799 ± 123.6 122.303 ± 48.8155 λ -0.5631 ± 0.0460 -0.6997 ± 0.0511 -0.5415 ± 0.1205 Rate 2.2571 ± 0.1948 2.1706 ± 0.2068 0.1282 ± 0.0290 N6+8
Eq (5.9) 1922.84 ± 134.805 1567.15 ± 134.961 268.149 ± 50.1711 Pol1 1265.72 ± 161.749 771.855 ± 135.455 175.806 ± 59.4557 λ -0.5617 ± 0.0381 -0.6733 ± 0.0464 -0.5572 ± 0.1014 Rate 2.1768 ± 0.1556 2.0179 ± 0.1738 0.1348 ± 0.0256 Table 5.3: Summary of the fast neutron number and rate estimation
5.2.1.1 Verification of the fast neutron spectrum shape
Eq (5.9) can be verified by the fast neutron spectrum, shown in Figure 5.14. The fast neutron events are selected from muons tagged only by outer water pool (OWP) with the following additional requirements:
• There is no any IWS or AD muon events 10 µs before an OWS muon;
• There is no any IWS or AD muon between the OWS muon and the AD signal in a time window.
The muon types are classified as follows:
• Both OWP and IWP Muon: the number of PMT hit is greater than 20.
• AD muon: the total visible energy deposit is more than 100 MeV in an AD
• Shower muon: the total visible energy deposit is more than 2.5 GeV in an AD The selection criteria of fast neutron events are as follows:
• The same as IBD selection except the prompt energy cut which is set at 100 MeV.
• The AD re-trigger cut: time to previous AD muon greater than 12 µs.
• Double muon cut: A muon passing through the detector can induce one or more neutrons. These neutrons can be captured by Gd or H, as shown in Figure 5.13(b).
The double muon events are shown when the time interval is greater than 0.6 µs.
To remove these, it requires that the prompt signal to previous OWS muon is less than 0.6 µs.
• Stop muon cut: The low energy muon which enters into the detector and decays there is called ”stop muon”. Figure 5.13(c) is the delayed events versus the delayed time to previous OWS tagged muon. There are a lot of events with energy larger than 20 MeV and extending to 60 MeV when the time interval is less than 10 µs.
These are mainly from the stop muon events. To remove these events, one requires that the delayed signal to previous OWS muon is greater than 10 µs.
5.2.2 8He/9Li
In addition to neutrons, cosmic muons also produce radioactive isotopes via their interac-tions with nuclei in the liquid scintillatior. It is worth noting that the long-lived radioiso-topes, 9Li(τ1/2 = 178.3ms, Q = 13.6M eV ) and 8He(τ1/2 = 118.5ms, Q = 10.7M eV ), can give correlated beta-neutron signals and fake IBD events.
The time distribution of9Li decays can be described by an exponential function
f0(t) = λLie−λLit, (5.11)
where t is the time to the last muon which produces 9Li, and λLi = (1/257.2) · ms−1 is the decay constant.
The probability density function (p.d.f) of9Li decays after a muon that produces this
9Li is given by
f1(t) = λLie−λLit· e−λµt, (5.12) where t is time to the last muon and e−λµt is the probability for not having additional muons between the last muon and time t.
If the 9Li event is not from the previous muon, but from the muon which is earlier than the previous muon with the time between these two muons as t1, the p.d.f of 9Li decays is given by
f2(t) = Z ∞
0
λµdt1· λLie−λLi(t+t1)· e−λµt = λµ× λLi/(λµ+ λLi)e−(λLi+λµ)t (5.13)
1
(a) Energy distribution for OWS tagged muon induced events.
Prompt Signal Time to Previous Osw Muon [s]
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
(b) Prompt events versus the prompt time to previous OWS tagged muon
Delayed Signal Time to Previous Osw Muon [s]
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
(c) Delayed events versus the prompt time to previous OWS tagged muon
hMergEpVsEd_EH0_px
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Mean 28.04
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Mean 28.04
Figure 5.14: Fittings to fast neutrons from muons tagged only by outer water pool (OWP).
Obviously,9Li can be produced by even earlier muons. Hence one should sum over an infinite series of pdf. It can be shown that
fLi(t) ≡ f1(t) + f2(t) + f3(t) + ... = (λLi+ λµ)e−(λLi+λµ)t. (5.14)
On the another hand, for the IBD and accidental events, the p.d.f of such events is given by
fIBD+Acc(t) = λµ· e−λµt, (5.15)
where t is the time to the last muon.
At time t, the number of9Li, IBD and accidental events can then be written as
Nevent(t) = NLi(λLi+ λµ) · e−(λLi+λµ)t+ NIBD+Accλµ· e−λµt. (5.16)
To estimate the number of 9Li events, we vary t and fit the event counts for different t using Eq (5.16), shown in Figure 5.15. The 9Li events are selected by the tagged muon which requires at least one trigger with energy larger than 1.8 MeV within the 20 µs and 200 µs after an AD muon.
5.2.3 241Am −13 C source
As mentioned in the previous chapter, the calibration sources are stored in the ACUs on the top of each detector. The neutron source, 241Am −13 C, emits neutrons which inelastically scatter with steel and then captured by nuclei, such as Fe, Cr, Mn or Ni.
This process emits many gammas and mimics IBD events. From the Figure 5.16, which shows the z distribution of the neutron-like signal, the asymmetric feature can be used to estimate the background rate from 241Am −13C source.
Figure 5.17 shows the neutron-like spectrum within the 6 and 12 MeV. The spectrum difference (red) between the top half (blue) and the bottom half (green) of the detector is the contribution from the AmC source. The correlated AmC background can be estimated by
Bkgs(normal) = F (strong AmC) · Nn−like, (5.17)
where Nn−likeis the number of subtracted results within the 6 MeV to 12 MeV, F (strong AmC) =
Figure 5.15: 9Li fitting results for each experimental hall.
Z (m)
-3 -2 -1 0 1 2 3
Entries / 0.03m
1 10 102
103
Figure 5.16: The distribution of the neutron-like signals on the Z direction from the normal physics run. The center of the detector is at Z = 0 m [27].
3.36854×10−4 is the scaling factor which is from the strong AmC source study. The study of strong AmC source has been done by our collaborator.
Table 5.5 is the summary of the background rates for each detector.
AD1 AD2 AD3 AD4 AD5 AD6 AD7 AD8
N6AD 37156 ± 351.377 35184 ± 348.525 40280 ± 326 35810 ± 211.367 34150 ± 208.355 33792 ± 205.811
R6AD 0.0838 0.0797 0.0872 0.0658 0.0628 0.0622
N8AD 55327 ± 473.406 58837 ± 477.706 53318 ± 431.771 62554 ± 440.831 18704 ± 185.844 14265 ± 174.118 13592 ± 172.945 23372 ± 199.244
R8AD 0.0636 0.0679 0.0578 0.0679 0.0175 0.0133 0.0127 0.0219
N6+8 92483 ± 589.558 94021 ± 591.332 93598 ± 541.019 62554 ± 440.831 54514 ± 281.45 48415 ±271.531 47384 ± 268.827 23372 ±199.244
R6+8 0.0704 0.0718 0.0676 0.0679 0.0338 0.0300 0.0294 0.0219
Table 5.4: The summary of the 241Am −13C background number and rates for each AD and data taking period.
5.3 Summary
Table 5.5 is the summary of the background rates for each detector.
Delayed Energy [MeV]
All Z range: 347579.0 Z > 0: 220031.0
All Z range: 349673.0 Z > 0: 221847.0
All Z range: 292702.0 Z > 0: 193150.0
All Z range: 194332.0 Z > 0: 128443.0
All Z range: 79214.0 Z > 0: 66864.0
All Z range: 73729.0 Z > 0: 61072.0
All Z range: 72268.0 Z > 0: 59826.0
All Z range: 39698.0 Z > 0: 31535.0
Figure 5.17: The spectrum of neutron-like signals with different selections on Z-position.
The black points are total signals without position cuts. The blue points are from the
RateDataSetAD1AD2AD3AD4AD5AD6AD7AD8 RAcc.6AD64.96±0.1364.06±0.1357.62±0.11-62.10±0.0664.05±0.0668.20±0.07- 8AD58.91±0.1158.07±0.1154.06±0.0952.71±0.0952.64±0.0452.83±0.0456.73±0.0556.74±0.05 RFastN6AD2.09±0.272.09±0.271.37±0.29-0.10±0.040.10±0.040.10±0.04- 8AD2.18±0.762.18±0.762.02±1.032.02±1.030.14±0.060.14±0.060.14±0.060.14±0.06 R9Li6AD5.81±1.395.81±1.393.57±1.13-0.54±0.120.54±0.120.54±0.12- 8AD1.70±0.731.70±0.731.46±0.721.46±0.720.15±0.050.15±0.050.15±0.050.15±0.05 RAmC(1/d)6AD0.09±0.030.09±0.030.09±0.03-0.06±0.020.06±0.020.06±0.02- 8AD0.08±0.040.08±0.040.07±0.040.08±0.040.02±0.010.02±0.010.01±0.010.02±0.01
Table 5.5: The summary of the background rates. Data set: ‘6AD’ is from Dec 24, 2011 to Jul 28, 2012. ‘8AD’ is from Oct 19, 2012 to Nov 30, 2013.