Energy cut efficiency - Efficiency Study - 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

Efficiency Study

6.3 Energy cut efficiency

× e^−R^s^T^c, (6.2)

where Rµis the effective muon rate, Rsis the singles’ rate and Tcis the coincident windows.

The multiplicity cut efficiency for each run is calculated and shown in Figure 6.1.

Date

Dec-31 Apr-01 Jul-01 Oct-01 Dec-31 Apr-01 Jul-01 Oct-01

Multiplicity Cut Eff

0.98 0.981 0.982 0.983 0.984 0.985

AD1 AD2 AD3 AD4 AD5 AD6 AD7 AD8

Figure 6.1: Multiplicity cut efficiency per day from Dec. 24, 2011 to Nov. 30, 2013.

6.3 Energy cut efficiency

The energy cut efficiency is divided into two parts, the prompt energy cut and the delayed energy cut. Both prompt and delayed energy cut efficiencies, ε_ep and ε_ed, are obtained by simulations.

The Monte-Carlo process is based on the Daya Bay official package, N uW a. The energy cut efficiencies for prompt and delay signals are defined by

ε_p = N (nH capture; E_p > 1.5M eV )

N (total nH capture) (6.3)

εd = N (Ed in 3σ range; Ep > 1.5M eV )

N (nH capture; E_p > 1.5M eV ) (6.4) Correlated uncertainty For nH capture peak, there are slight differences between LS region, Gd-LS region and MC. Both prompt and delayed energies from Monte-Carlo are scaled to the data for calculating the efficiencies. Then, the difference between the data and Monte-Caro gives correlated uncertainties. The results are shown in Table 6.1.

NnH−cap

Ntotal ε_p ε_d

GdLS 0.1563 0.9646 0.9677 LS 0.9582 0.9442 0.6776

After energy rescaling GdLS 0.1563 0.9518 0.9695

LS 0.9582 0.9297 0.6799

Table 6.1: The results on energy cut efficiencies.

Uncorrelated uncertainty The relative difference on nH/nGd ratios¹between AD1 and AD2 are taken as the uncorrelated uncertainty. The average nH/nGd is about one which indicates that the spallation neutrons mainly come from outside of the AD. They have more chances to be captured in the LS region. This is the region where the energy leakage and energy resolution effects are more significant to the 3σ energy cut efficiency.

For normal IBD neutrons induced by reactor neutrinos, they are more uniformly dis-tributed in the AD. Hence it is believed that the difference observed in nH/nGd for different ADs in spallation neutron sample is more severe than IBD neutrons. Therefore, 0.5% is a conservative estimation of the uncertainty in 3σ delayed energy cut efficiency.

Since this uncertainty comes from the measurement of spallation neutrons which enter into the entire detection volume, we assign 0.5% as the uncertainty of energy cut efficiency in both LS and GdLS regions. The final result is shown in Table 6.7.

1nH/nGd ratio: the ratio of the nH signal and nGd signal. nH: The number of the nH signal range within the 3 σ region from the peak. nGd: The number of the nGd signal within 6 MeV and 12 MeV.

6.3.1 nH to nGd ratio by spallation neutron

Assuming the same muon flux for the ADs in the same experimental hall and the same Gd target mass, nGd is a good anchoring point for confirming the identicalness of n-H selection with a floating 3 sigma energy cut. To have a solid measurement of the identi-calness of energy cut efficiency, the nH to nGd ratio is used.

Spallation neutron events selection

Muon identification is different from IBD event selection, which requires that the PMT hit number for IWS or OWS is larger than 20, the charge sum in each AD ( QSumAD ) is larger than 50 MeV. For shower muon, the energy deposits in an AD should be larger than 2.5 GeV. The event selection window is 2500 µs. In the event selection window, the first part is the signals window, which is between 20 µs and 700 µs. The other part is the background window, which is between 700 µs and ∼ 1400 µs. One can get the spallation neutron spectrum by background subtraction.

Fitting methods

In this study, the fitting function consists of two parts, signal and background, as defined in Eq. (6.5). The functions are normalized in the fitting range. The signal plus background is given by

where N₁ is number of signal, N₂ is number of background, f_sig is the signal shape func-tion, fbkg is the background shape function, E+ and E− are upper and lower limits of the fitting range.

For n-H capture, f_sig is the Crystal Ball shape function,

f_sig = f (x; µ, σ, α, n) =

Since this function is composed of a Gaussian and a power low, the parameters, µ, σ, α, n, are defined as usual.

The background shape functions are exponential function, Eq. (6.7), and second order polynomial function, Eq. (6.8).

fbkg = exp(p1· x). (6.7)

fbkg = a1x²+ b1x + 1. (6.8)

For n-Gd capture, there are two kinds of gadolinium isotopes,¹⁵⁵Gd and¹⁵⁷Gd, which capture neutron in ADs. The shape can be described by two crystal ball functions, Eq. (6.9), known as double crystal ball function.

f_dCB(x; µ, σ, α, n) = N¹⁵⁷_Gd · f_CB1(x; µ₁, σ₁, α₁, n₁) + N¹⁵⁵_Gd· f_CB2(x; µ₂, σ₂, α₂, n₂)

= N¹⁵⁷_Gd· f_CB1(x; µ₁, σ₁, α₁, n₁) + N¹⁵⁷_Gd· C_N · f_CB2(x; µ₂, σ₂, α₂, n₂)

= N · [f_CB1(x; µ₁, σ₁, α₁, n₁) + C_N · f_CB2(x; µ₂, σ₂, α₂, n₂)]. (6.9)

Hence, the signal shape function becomes

f_sig = f_CB1(x; µ₁, σ₁, α₁, n₁) + C_N · f_CB2(x; µ₂, σ₂, α₂, n₂) (6.10)

To simplify the fitting function, the relative abundance, neutron capture cross-sections and binding energies of the capture products (or gamma energies) for these isotopes are considered, which were shown in Table 6.2. The relations between parameters are

• The peak position µ: µ1 = µ · 7.94 · S, µ2 = µ · 8.54 · S, where S = 60900 · 0.1480 + 254000 · 0.1565

60900 · 0.1480 · 8.54 + 254000 · 0.1565 · 7.94

• Resolution: σ₁ = σ₂· C_σ, where C_σ =p

8.54/7.94

• α = α1 = α2 and n = n1 = n2.

• C_N = 60900 · 0.1480 254000 · 0.1565

The background shape function for the nGd case is the first order polynomial function,

f_bkg = p₁· x + 1. (6.11)

isotope abundance σ(nth, γ) Eγ 155Gd 14.80 % 60,900 b 8.5364 MeV

157Gd 15.65 % 254,000 b 7.9374 MeV

Table 6.2: Gadolinium isotopes abundance, capture cross-section and energies [33].

The fitting range for nH capture is from 0.8 MeV to 3.5 MeV; for nGd is from 6.0 MeV to 12.0 MeV. The fitting results are shown in Figs. 6.2, 6.3 and 6.4. The neutron capture peak and sigma are summarized in the Tables 6.3, 6.4 and Figure 6.5.

AD number nH Mean (exp) +/- err nH Mean (pol2) +/- err nGd Mean +/- err

1 2.3081 ± 0.0003 2.3090 ± 0.0003 8.0926 ± 0.0004

2 2.3111 ± 0.0003 2.3121 ± 0.0003 8.0909 ± 0.0004

3 2.3170 ± 0.0003 2.3177 ± 0.0003 8.1027 ± 0.0004

4 2.3253 ± 0.0003 2.3260 ± 0.0004 8.1034 ± 0.0005

5 2.3260 ± 0.0007 2.3273 ± 0.0008 8.1232 ± 0.0011

6 2.3273 ± 0.0008 2.3287 ± 0.0008 8.1208 ± 0.0011

7 2.3301 ± 0.0008 2.3315 ± 0.0008 8.1244 ± 0.0011

8 2.3346 ± 0.0010 2.3359 ± 0.0010 8.1253 ± 0.0014

Table 6.3: Summary of neutron capture peak.

AD number nH Sigma (exp) +/- err nH Sigma (pol2) +/- err nGd Sigma +/- err

1 0.1440 ± 0.0003 0.1432 ± 0.0003 0.2958 ± 0.0004

2 0.1451 ± 0.0003 0.1441 ± 0.0003 0.2967 ± 0.0004

3 0.1424 ± 0.0003 0.1418 ± 0.0004 0.2927 ± 0.0004

4 0.1422 ± 0.0004 0.1414 ± 0.0004 0.2928 ± 0.0005

5 0.1443 ± 0.0008 0.1429 ± 0.0010 0.2991 ± 0.0012

6 0.1444 ± 0.0009 0.1425 ± 0.0009 0.3026 ± 0.0012

7 0.1476 ± 0.0008 0.1459 ± 0.0010 0.3048 ± 0.0012

8 0.1504 ± 0.0011 0.1476 ± 0.0012 0.3070 ± 0.0015

Table 6.4: Summary of neutron capture sigma.