Uncorrelated Background - Background Study

Background Study

5.1 Uncorrelated Background

5.1.1 Accidental Background

The accidental backgrounds are from any double coincidence events, which are acciden-tally passed the IBD selection, and there is no correlation between them. After the distance cut, most accidental backgrounds are suppressed. As shown in Figure 4.15, there still remain some accidental backgrounds. To get more ‘pure’ spectrum, the generated accidental background spectrum are used to be subtracted from the Figure 4.15. Fig-ure 5.1 illustrates the process of generating the accidental background. We first choose a sample of singles from one run and divide it into two parts. The first half is used as the prompt sub-events and the other is used as the delayed sub-events. Those signals are not correlated because they are separated by around ten hours. They are required to pass the relative distance cut since the singles’ rate and spectra are correlated with their vertex positions. For the statistics purpose, we exchange prompt and delayed signals and apply the same IBD cuts again. The generated accidental spectrum is shown in Figure 5.2.

Figure 5.3 shows the process of the accidental background subtraction,

Figure 5.3(c) = Figure 5.3(a) − A · Figure 5.3(b), (5.2)

where Figure 5.3(a) is the spectrum after the 500 mm distance cut, Figure 5.3(b) is the generated accidental spectrum and Figure 5.3(c) is the background subtracted spectrum.

A is the scale factor, which is given by

A = R · T_live NABS−tot

, (5.3)

where R is the random coincidence rate of two single events given by [32]

R = R_s×

R_µ

R_s+ R_µ[1 − e^−(R^s^+R^µ^)T^c] + e^−(R^s^+R^µ^)T^c + R_s

Rs+ Rµ

e^−R^µ^T^c[1 − e^−(R^s^+R^µ^)T^c] − R_s 2Rs+ Rµ

e^−R^µ^T^c[1 − e^−(2R^s^+R^µ^)T^c]

× [R_sT_ce^−R^s^T^c], (5.4)

with R_s is the singles rate and N_ABS−tot is the total number of accidental background

spectrum (ABS).

The number of IBD candidates, N_IBD, is calculated from each bin, i, as

N_IBD,i = N_dis−cut,i− A × N_ABS−tot,i, (5.5)

where N_dis−cut is the number of events after the distance cut.

The ratio of the accidental events which pass the IBD selection, N_ABS−cut to N_ABS−tot is represented by

ε = N_ABS−cut NABS−tot

. (5.6)

So, the subtracted accidental number, N_acc, is R · T_live· ε.

The uncertainty of N_IBD,i is given by

E_IBD,i² = N_dis−cut,i+ A²× N_ABS−tot,i+ E_A² × N_ABS−tot,i² , (5.7)

where E is used to represent the error of each term in Eq (5.5) with the same subscript.

The error of scale factor A, E_A, is related to the uncertainty of singles rate, R_s. Singles rate is defined in the previous chapter, which is the average value of the Nsingles−up and Nsingles−low. Therefore, N_singles−up and Nsingles−low give the intrinsic uncertainties.

There is another pairing method to count the accidental background number. We can move the first N^thsingle events to the end of this singles array, then pairing the prompt and delayed signal with the same IBD selection cuts. After pairing new accidental spectrum, the ε is calculated by Eq (5.6). The N steps random means pairing N times by moving the 1^st, 2^nd... to the N^th single events. The value for ε differs for different step because the singles are the random distribution.

The distance distribution of prompt and delayed signals is used to check the quality of the accidental background subtraction. As shown in Figure 5.5, the black curve is before accidental subtraction, the blue one is from the generated accidental events and the red one is after subtraction. If the subtraction process works well, the entry number should be zero between 2000 mm and 5000 mm, as shown in Figure 5.6.

Figure 5.1: The process of generating accidental background events.

Figure 5.7 shows the delayed energy distribution for each detector. We then fit the 2.2 MeV signals with the Crystal ball function, as shown in Figure 5.8. The fitting results are summarized in the Table 5.2 and 5.9.

The Crystal Ball shape is defined by

f (x; µ, σ, α, n) =







exp[−^(x−µ)_2σ2²], ^x−µ_σ > −|α|

(n/|α|)ⁿexp(−^α₂²)(_|α|ⁿ − |α| − ^x−µ_σ ⁻ⁿ), ^x−µ_σ ≤ −|α|

(5.8)

AD mean ± error sigma ± error 1 2.304021 ± 0.000413 0.138556 ± 0.000373 2 2.306428 ± 0.000417 0.139752 ± 0.000371 3 2.312265 ± 0.000418 0.137387 ± 0.000379 4 2.319766 ± 0.000516 0.137291 ± 0.000465 5 2.312939 ± 0.001500 0.139935 ± 0.001528 6 2.314307 ± 0.001503 0.136600 ± 0.001498 7 2.316229 ± 0.001545 0.141588 ± 0.001562 8 2.321682 ± 0.001928 0.144360 ± 0.002000 Table 5.2: Summary of the nH peak and sigma.

The prompt energy distributions after applying the delayed 3 σ energy cuts are shown in Figure 5.10. These are the IBD candidates. The vertex distribution of IBD candidates

Prompt Energy [MeV]

0 500 1000 1500 2000 2500 3000 3500 4000 4500 103

Figure 5.2: The energy distribution of the generated accidental background for each detector.

Prompt Energy [MeV]

After Distance Cut. Before Accidental Subtraction

(a) Energy distribution after the distance cut

Prompt Energy [MeV]

0 2 4 6 8 10 12

Delayed Energy [MeV]

Accidental background made by singles_1

(b) Generated accidental background

Prompt Energy [MeV]

0 2 4 6 8 10 12

Delayed Energy [MeV]

After accidental background subtraction_1

Figure 5.3: The energy distribution for the process of accidental background subtraction:

(a) − A · (b) = (c).

Prompt Energy [MeV]

0 500 1000 1500 2000 2500 3000 3500 4000 4500 103

Figure 5.4: The energy distribution after the accidental subtraction for each detector.

EH1_AD1

Distance [m]

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Entries/20.00 MeV

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Entries/20.00 MeV

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Entries/20.00 MeV

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Entries/20.00 MeV

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Entries/20.00 MeV

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Entries/20.00 MeV

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Entries/20.00 MeV

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Entries/20.00 MeV

Figure 5.5: The comparison of prompt and delayed signal distributions. Black curve is before accidental subtraction. Blue curve is the generated accidental events. Red curve

EH1_AD1 Entries 256250

Mean 358

RMS 136

Constant -2.037 ± 6.288

Distance [mm]

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Entries/20 mm

Entries 256250

Mean 358

RMS 136

Constant -2.037 ± 6.288

EH1_AD2 Entries 260487

Mean 363.2

RMS 200.2

Constant 0.364 ± 6.420

Distance [mm]

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Entries/20 mm

Entries 260487

Mean 363.2

RMS 200.2

Constant 0.364 ± 6.420

EH2_AD1 Entries 251033

Mean 401.8

RMS 304.1

Constant -2.906 ± 6.308

Distance [mm]

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Entries/20 mm Entries 251033

Mean 401.8

RMS 304.1

Constant -2.906 ± 6.308

EH2_AD2 Entries 160635

Mean 352.4

RMS 133

Constant -2.209 ± 5.116

Distance [mm]

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Entries/20 mm

Entries 160635

Mean 352.4

RMS 133

Constant -2.209 ± 5.116

EH3_AD1 Entries 38535

Mean 439.5

RMS 372.8

Constant -0.6558 ± 6.8505

Distance [mm]

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Entries/20 mm Entries 38535

Mean 439.5

RMS 372.8

Constant -0.6558 ± 6.8505

EH3_AD2 Entries 36060

Mean 443.4

RMS 530.7

Constant 1.906 ± 6.873

Distance [mm]

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Entries/20 mm Entries 36060

Mean 443.4

RMS 530.7

Constant 1.906 ± 6.873

EH3_AD3 Entries 33263

Mean 267.5

RMS 120.2

Constant -4.605 ± 7.135

Distance [mm]

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Entries/20 mm Entries 33263

Mean 267.5

RMS 120.2

Constant -4.605 ± 7.135

EH3_AD4 Entries 23442

Mean 274.8

RMS 472.4

Constant -3.244 ± 5.695

Distance [mm]

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Entries/20 mm Entries 23442

Mean 274.8

RMS 472.4

Constant -3.244 ± 5.695

Figure 5.6: The distribution of distances between prompt and delayed signals after accidental background subtraction for each detector.

EH1_AD1

Figure 5.7: The delayed energy distribution.

EH1_AD1

Entries 464338

Mean 2.283

Entries 464338

Mean 2.283

Entries 469034

Mean 2.285

Entries 469034

Mean 2.285

Entries 441392

Mean 2.29

Entries 441392

Mean 2.29

Entries 290467

Mean 2.299

Entries 290467

Mean 2.299

Entries 64822

Mean 2.29

Entries 64822

Mean 2.29

Entries 64295

Mean 2.287

Entries 64295

Mean 2.287

Entries 65322

Mean 2.292

Entries 65322

Mean 2.292

Entries 43250

Mean 2.293

Entries 43250

Mean 2.293

Figure 5.8: The fitting to 2.2 MeV signal with the crystal ball function.

Ad Number

1 2 3 4 5 6 7 8

nH Peak [MeV]

2.305 2.31 2.315 2.32 2.325

(a) nH mean for each AD

AD Number

1 2 3 4 5 6 7 8

Sigma [MeV]

0.136 0.138 0.14 0.142 0.144 0.146

(b) Sigma for each AD

Figure 5.9: The summary of 2.2 MeV signal peaks and the associated widths.

EH1_AD1

Figure 5.10: The prompt energy distributions for each AD.

2[mm]

R 0 500 1000 1500 2000 2500 3000 3500 4000 4500

103 0 500 1000 1500 2000 2500 3000 3500 4000 4500

103

Figure 5.11: The vertex distribution of IBD candidates in each AD.

are shown in Figure 5.11.

在文檔中大亞灣反應堆微中子實驗—利用慢信號中子被氫捕獲訊號測量微中子振盪混合角 (頁 73-87)