Mass hierarchy sensitivity of medium baseline reactor neutrino experiments with multiple detectors

Available online at www.sciencedirect.com

ScienceDirect Nuclear Physics B 918 (2017) 245–256 www.elsevier.com/locate/nuclphysb

Mass hierarchy sensitivity of medium baseline reactor neutrino experiments with multiple detectors Hong-Xin Wang a,∗ , Liang Zhan b , Yu-Feng Li b , Guo-Fu Cao b , Shen-Jian Chen a a Department of Physics, Nanjing University, Nanjing 210093, China b Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China

Received 1 September 2016; received in revised form 23 January 2017; accepted 1 March 2017 Available online 8 March 2017 Editor: Hong-Jian He

Abstract We report the neutrino mass hierarchy (MH) determination of medium baseline reactor neutrino experiments with multiple detectors, where the sensitivity of measuring the MH can be significantly improved by adding a near detector. Then the impact of the baseline and target mass of the near detector on the combined MH sensitivity has been studied thoroughly. The optimal selections of the baseline and target mass of the near detector are ∼12.5 km and ∼4 kton respectively for a far detector with the target mass of 20 kton and the baseline of 52.5 km. As typical examples of future medium baseline reactor neutrino experiments, the optimal location and target mass of the near detector are selected for the specific configurations of JUNO and RENO-50. Finally, we discuss distinct effects of the reactor antineutrino energy spectrum uncertainty for setups of a single detector and double detectors, which indicate that the spectrum uncertainty can be well constrained in the presence of the near detector. © 2017 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3 .

1. Introduction It is reported that the medium baseline reactor neutrino experiment can determine the type of the neutrino mass hierarchy (MH) by precisely measuring the fine structure of the antineutrino * Corresponding author.

E-mail address: [email protected] (H.-X. Wang). http://dx.doi.org/10.1016/j.nuclphysb.2017.03.002 0550-3213/© 2017 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3 .

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energy spectrum from reactors [1–5]. Reactor and accelerator neutrino experiments measured an unexpectedly large value of neutrino mixing angle θ13 in 2012 [6–10], which implies that the MH determination is feasible in the next one or two decades with neutrino oscillation experiments of the new generation. Consequently, experiments using accelerator neutrinos with a long baseline of ∼1000 km [11], atmosphere neutrinos sensitive to the energy range of 1–20 GeV [12,13] and reactor neutrinos at a medium baseline of ∼50 km are proposed to determine the neutrino MH [14–17]. Among the above possibilities, medium baseline reactor neutrino experiments, such as JUNO (Jiangmen Underground Neutrino Observatory) [18–20] and RENO-50 [21–24], have the potential to determine the neutrino MH by using the large liquid scintillator detector (∼20 kton) with energy resolution of unprecedented levels. Key requirements for the MH determination in reactor neutrino experiments are powerful nuclear power plants (NPPs), massive detector and good energy resolution. √ Sensitivity study about JUNO shows that a 20 kton detector with energy resolution of 3%/ Evis (MeV) is mandatory to achieve significance of better than 3σ after 6 years running [18]. Several interesting ideas are proposed to improve the MH sensitivity of reactor neutrino experiments, including combining the mass splitting measurement from accelerator neutrino experiments [18], synergy of different MH probes in reactor and atmospheric neutrino oscillation experiments [25] and using two identical half-size detectors at near and far sites [26,27]. In this work we shall discuss the MH sensitivity improvement by using the near detector (ND) and far detector (FD) in medium baseline reactor neutrino experiments. For the fixed total mass of the ND and FD, the distribution of target mass between the ND and FD and the baseline of the ND can be optimized. The optimization is also applied to the realistic reactor neutrino experiments: JUNO and RENO-50. Then we discuss distinct effects of the reactor antineutrino energy spectrum uncertainty for the setups of a single detector and double detectors, which indicate that the spectrum uncertainty can be well constrained in the presence of the near detector. The remaining parts of this work are organized as follows. In Sec. 2 we introduce the analysis method for the MH sensitivity in medium baseline reactor neutrino experiment. Sec. 3 is devoted to the sensitivity improvement in the presence of the ND, and Sec. 4 is devoted to optimize the baseline and target mass of the ND. Finally, we discuss the impact of the energy spectrum shape uncertainty in Sec. 5 and then conclude in Sec. 6. 2. Analysis method In the quantitative analysis of the neutrino MH sensitivity, the electron antineutrino survival probability in vacuum is adopted as [18,17,28]: Pee = 1 − sin2 2θ13 (cos2 θ12 sin2 31 + sin2 θ12 sin2 32 ) − cos4 θ13 sin2 2θ12 sin2 21    1 2 2 2 = 1 − sin 2θ13 1 − 1 − sin 2θ12 sin 21 cos(2|ee | ± φ) (1) 2 − cos4 θ13 sin2 2θ12 sin2 21 , where ij ≡ 1.267 · m2ij L/E, with m2ij = m2i − m2j (in unit of eV2 ) being the neutrino masssquared difference, L (in unit of meter) being the baseline length and E (in unit of MeV) being the antineutrino energy. In addition,

H.-X. Wang et al. / Nuclear Physics B 918 (2017) 245–256 2 sin(2s 2  ) − s 2 sin(2c2  ) c12 21 12 12 21  12 , 2 2 1 − sin 2θ12 sin 21 2 cos(2c2  ) c2 cos(2s 2 21 ) + s12 12 21 cos φ = 12  12 , 2 2 1 − sin 2θ12 sin 21

247

sin φ =

(2)

and ee ≡ 1.267 · m2ee L/E, with m2ee = cos2 θ12 m231 + sin2 θ12 m232

(3)

being the effective mass-squared difference [29,30]. The positive(negative) sign in Eq. (1) corresponds to the normal(inverted) MH. In our calculation, the neutrino oscillation parameters in Eq. (1) are taken as m221 = (7.53 ± 0.18) × 10−5 eV2 , m2ee = 2.4724 × 10−3 eV2 , sin2 2θ12 = 0.846 ± 0.021 and sin2 2θ13 = 0.085 ± 0.005 [31]. The observed energy spectrum is  F (L, E  ) = R(E, E  )φ(E)σ (E)Pee (L, E)dE, (4) where R(E, E  ) is the detector response function including the energy resolution effect, φ(E) is the reactor antineutrino flux, σ (E) is the inverse beta reaction cross section, Pee (L, E) is the electron antineutrino survival probability. As a quantitative calculation of the MH sensitivity, we adopt similar experimental parameters as those for JUNO, such as a liquid scintillator detector of 20 kton, a baseline of 52.5 km, the total reactor thermal power of 36 GWth , the energy res√ olution of 3%/ Evis (MeV) and six years (2000 days) of data taking. A parameterized reactor fissile antineutrino flux model commonly named ILL-Vogel model [32–35] is used to predict the antineutrino energy spectrum for the inverse beta decay reactions in the detector. To fully explore the fine structure of the antineutrino energy spectrum, the spectrum is divided into 200 equal-size bins between 1.8 MeV and 8.0 MeV. The antineutrino event rate at the detector is calculated to be ∼60/day after assuming a detection efficiency of 80%, which is consistent with the number of JUNO in Ref. [18]. The least squares method is used in the energy spectrum fitting and a standard χ 2 function with proper nuisance parameters and penalty terms is constructed as  Nbin  [Mid − Tid (1 + R + r wr r + d + i )]2 2 χ = Mid d i=1 (5) Nbin 2  2  2   R2 r d i + 2 + + + , 2 2 2 σ σ σR σ r s d r d

i=1

where d is the detector index, i denotes the bin number, M is the measured spectrum, T is the predicted spectrum, ’s with different indices are the nuisance parameters corresponding to different systematic uncertainties, ωr is the fraction of the rth reactor contribution to pull parameter of relative reactor uncertainty, σ ’s with different indices are the standard deviations of nuisance parameters assuming the systematic uncertainty follows the Gaussian form [36]. The systematic uncertainties include the correlated (absolute) reactor uncertainty (σR = 2%), the uncorrelated (relative) reactor uncertainty (σr = 0.8%), the spectrum shape uncertainty (σs = 1%) and the detector-related uncertainty (σd = 1%). Variations of sin2 2θ12 and m221 within their allowed ranges have negligible effects on the best-fit value of χ 2 . Precise measurement of sin2 2θ13 with a 3% uncertainty is expected from

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Fig. 1. Three classes of χ 2 as functions of m2ee for the ND (solid lines), FD (dash lines) and the combined detectors (dot-dash lines) scenarios. The NH is assumed as the true MH and the best-fit values of the IH case (red lines) are the MH sensitivity defined in Eq. (6). (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)

Daya Bay experiment after 2017, and the variation induced to the best-fit value of χ 2 is ∼ 0.2. In minimization process, m2ee is chosen to be the free parameter by convention and other mixing parameters are fixed for fast minimization. Thus, the χ 2 is a function of m2ee and the best-fit 2 can be obtained through scanning m2 . value χmin ee The discriminator of MH can be obtained using both the normal hierarchy (NH) and inverted hierarchy (IH) models to fit the simulant antineutrino spectrum generated by the NH model: 2 2 χ 2 = |χmin (NH) − χmin (IH)|.

(6)

The simulation studies are also accomplished by assuming the IH model as the true one, which gives the consistent conclusion with the assumption of the NH model. In the following, we shall illustrate the simulation results of the NH model. 3. Sensitivity improvement due to near detector Now we want to add a ND and calculate the combined MH sensitivity by adding the antineutrino energy spectrum information of the ND into Eq. (5). To illustrate the improvement of the MH sensitivity, a ND with the target mass of 4 kton and baseline of 12.5 km is assumed as an initial choice and the fitting results are shown in Fig. 1. The solid, dashed and dot-dashed lines in Fig. 1 show the χ 2 as the functions of m2ee for the ND, FD and the combined detectors respectively. The NH is assumed as the true MH to generate the experimental energy spectrum and the black lines are the χ 2 curves after using the NH model to fit the energy spectrum. Therefore, the best-fit (minimal) values of χ 2 for the NH case always keep zero regardless of baselines. On the other hand, the best-fit values of χ 2 for the IH case vary with baselines, which equal to the MH discriminator defined in Eq. (6). In Fig. 1 the best-fit values of χ 2 for the IH case are about 2 2 2 0(ND), 13.9(FD) and 23.6(combination) respectively. Thus we have χcom,min > χ1,min + χ2,min , which demonstrates the improvement of the MH sensitivity by combining the near and far detec2 2 2 tors, where χcom,min , χ1,min and χ2,min are the sensitivities of combined detectors, ND and FD scenarios. The MH sensitivity improvement of the combination of the ND and FD can be explained as follows. Using the standard least squares method, the χ 2 curve is approximatively parabolic and can be expressed as

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Fig. 2. The best-fit value and uncertainty of m2ee as a function of the baseline. The true MH is the NH model and the fitted MH is the IH model. The target mass of detector is 4 kton and other experiment parameters are the same as JUNO.

2 χ 2  χmin +

x − xbest σ

2 (7)

,

where x denotes the variable m2ee , xbest and σ denote the best-fit value and uncertainty of m2ee , 2 is the best-fit (minimal) value of χ 2 . We use χ 2 (i = 1, 2) to represent the χ 2 function for the χmin i 2  χ 2 + χ 2 when ND and FD respectively. The combined χ 2 should be approximated as χcom 1 2 the statistical uncertainty dominates. The combined best-fit value of m2ee can be expressed analytically as xcom,best 

x1,best σ22 + x2,best σ12 σ12 + σ22

.

(8)

The combined best-fit value of the χ 2 is 2 2 2 2 χcom  χ1,min + χ2,min + χext , 2 = χext

(x1,best − x2,best , σ12 + σ22 )2

(9) (10)

2 2 2 is the where χ1,min (χ2,min ) is the sensitivity of the MH determination for the ND (FD) and χext 2 extra MH sensitivity because of the combination. χext > 0 due to different best-fit values of m2ee are shown in Fig. 1. Obviously, the extra MH sensitivity is related to the difference of the best-fit values of m2ee and their uncertainties for the ND and FD scenarios. Consequently, the best-fit value and uncertainty of m2ee as a function of the baseline is shown in Fig. 2. As a conclusion, 2 is large enough even though no the MH sensitivity improvement can be obtained as long as χext direct MH discrimination sensitivity can be obtained from the ND. In our current study, we have neglected some possible detector systematic uncertainties. The main systematic uncertainty for the mass-splitting measurement is the energy scale uncertainty. As one can see from Eq. (10), the reason for the sensitivity improvement is the difference in the best-fit values of m2ee . In the two-detector scenario, the energy scale uncertainties can be divided into the detector uncorrelated and correlated parts. The correlated part does not affect the difference of the best-fit values of m2ee . On the other hand, the uncorrelated part may change the difference of the best-fit values in Eq. (10). The detector energy scale effect includes the detector geometry, liquid scitillator response and electronics. We can suppose that two detectors

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Fig. 3. The contours of the χ 2 , as a function of target mass ratio and baseline of the ND when fixing the total target mass. A maximum value of χ 2 indicates the optimal target mass ratio and baseline for the ND to maximize the MH sensitivity.

have the same liquid scitillator recipe and electronics but different detector geometry due to the target mass difference. Thus the correlated part of the energy scale uncertainty is from liquid scitillator and electronics and the uncorrelated part is from the detector geometry. The latter one will change the difference in the numerator part of Eq. (10), but the whole detector energy scale uncertainty change the denominator of Eq. (10). In our case, the relative difference between two best-fit values of m2ee in Fig. 1 is about 0.7%, therefore the MH sensitivity improvement requires strict control of uncertainties of m2ee , i.e., below the level of 0.5%. 4. Optimization of target mass and baseline For the reactor neutrino experiment of a single detector like JUNO, the baseline was optimized at ∼52.5 km for the MH determination [18]. The sensitivity χ 2 is approximately proportional to the target mass. However the target mass is constrained by the technical challenges and experiment cost, and current selection of the target mass is ∼20 kton. Using a ND as the combination with the FD, the requirement for target mass of the FD can be reduced. A proper selection of target mass and baseline of the ND has the possibility to improve the MH sensitivity even the total target mass of the ND and FD keeps as 20 kton. In the following, we shall first study the optimization of the target mass ratio and baseline in the ideal case where the real reactor core distribution is not taken into account, and then study the optimization for the realistic reactor core distributions of JUNO and RENO-50. The optimal ND location and target mass for JUNO and RENO-50 are provided. 4.1. Ideal case First we consider the ideal case, i.e. a single baseline from the reactor to the detector. Similar to JUNO, we assume the total reactor thermal power to be 36 GWth , and the baseline of the FD is fixed at 52.5 km. For the configuration of a single detector, the sensitivity of MH is χ 2  13.9. Given the total target mass of 20 kton, we change the baseline of ND and target mass ratio between ND and total target mass to calculate the χ 2 for optimization. The result is shown in Fig. 3, where in a large parameter space of the ND target mass ratio and baseline, the MH sensitivity can be improved in comparison to the single detector configuration.

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When the baseline is too small, the double detector could be worse than the single detector 2 2 can not compensate the contribution of adding the  0 and χext configuration, because χ1,min same target mass at the FD. We can propose that the optimal target mass ratio is ∼0.17 and the baseline is ∼12.5 km from Fig. 3. If the total target mass is different, we find the optimal target mass ratio and baseline of the ND have small variations. In all, we propose a target mass ratio of 0.15–0.20 and a baseline of 10–15 km for the ND to be the optimal range for the future reactor neutrino experiments. The optimization result of can be explained by Eq. (9) and Fig. 2. The ND must be close to reactors in order to have enough mismatch in m2ee . On the other hand, the ND must be far from reactors to have a smaller error of m2ee . Considering both effects, we can intuitively find that the possible optimal location of ND is 10–20 km. 4.2. JUNO and RENO-50 In the realistic case, there are multiple reactor cores in one NPP and the baselines from the detector to the reactor cores can not be identical. The difference of multiple baselines will reduce the sensitivity of the MH determination [18]. In this section, we shall study the MH sensitivity improvement due to the ND for JUNO and RENO-50. The selection of the baseline and the target mass of the ND are optimized. There are ten reactor cores in Yangjiang and Taishan NPPs for the JUNO experiment and two NPPs (DYB and HZ) as background. We adopt the power setups of the reactor cores listed in [18]. In our calculation we always adopt 12 baselines even the ND is much close to certain NPP. We obtain χ 2 = 9.87 for actual JUNO configuration (a single 20 kton detector) with the realistic reactor core distribution, while we have χ 2 = 13.9 for the ideal case using the identical baselines (52.5 km) from Yangjiang and Taishan reactors. The distance between Yangjiang and Taishan NPPs is ∼77 km, therefore, there is no proper position for one ND at the baseline of 10–20 km from both the Yangjiang and Taishan NPPs. Thus we consider the ND for Yangjiang and Taishan separately. We adopt some representative candidates to calculate the sensitivity of MH, which are shown in Fig. 4. The candidate sites, their approximate baseline and the χ 2 are given in Table 1. C1 and C2 have the similar baselines, but the difference of χ 2 is about 1. The reduction of the MH sensitivity is because the baseline differences for C2 are larger than those of C1. RENO-50 experiment plans to build a 18 kton detector located at Mt. GuemSeong with a baseline of ∼47 km from the Hanbit NPP of Yonggwang with the total thermal power of √ 16.5 GW [22]. Assuming energy resolution of 3%/ Evis (MeV), we calculate the MH sensitivity for RENO-50 and obtain χ 2  5.86 for six years of data taking. It implies that more than 3σ significance can be obtained from data of ∼10 years, and this conclusion is consistent with the calculation in Ref. [24]. The candidates of ND for RENO-50 are shown in Fig. 5. The properties of candidates and combined MH sensitivity are listed in Table 1. 5. Impact of the energy spectrum shape uncertainty Recently, the measured IBD positron(antineutrino) energy spectrum show an event excess in the 4–6 (5–7) MeV region relative to the prediction [37–39]. The new observed event excess and re-evaluations of the reactor neutrino flux [40–42] indicate that the shape uncertainty of reactor antineutrino energy spectrum could be underestimated. The shape uncertainty of reactor antineutrino energy spectrum derived from the most commonly used model (Huber–Mueller or

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Fig. 4. The geographic map of the optimal candidates near the Yangjiang NPP (YJ NPP) and the optimal range near the Taishan NPP (TS NPP) identified for the ND of the JUNO experiment. Table 1 The properties of candidates of ND. The mass of ND is fixed as the optimal 4 kton. Experiment

JUNO

Candidate

C1

C2

C3

C4

C5

C1

RENO-50 C2

Baseline (km) χ 2

10 15.5

10 14.6

17 14.7

10 15.7

15 15.3

9 8.7

12 9.2

ILL-Vogel fissile antineutrino model) could be 4% or even larger. As the primary uncertainty, shape uncertainty dramatically affects the MH sensitivity for a single detector case, therefore it must be effectively controlled. However, the two-detector configuration can significantly reduce the impact of the shape uncertainty relative to the one-detector configuration because the ND with great statistics can be used to constrain the shape uncertainty. To illustrate the ND effects on the energy spectrum shape uncertainty, we compare the one detector configuration with a FD of 24 kton at the baseline of 52.5 km and the two detector configuration with a ND of 4 kton at the baseline of 12.5 km and a FD of 20 kton at the baseline of 52.5 km, where the reactors distribution is marginalized. The MH sensitivity as a function of the reactor shape uncertainty is shown in Fig. 6. The solid black line shows the sensitivity of the one detector configuration, and the dash red line is the sensitivity of the two detector configuration. With the increase of the shape uncertainty, χ 2 of the one detector configuration reduces rapidly, while the χ 2 of the two detector configuration first reduces and then becomes stable. In the limit of the shape uncertainty goes to infinity, χ 2 for the one detector configuration will be close to zero, but the two detector configuration can determine the MH with a high sensitivity because of the ND constraint on the shape uncertainty. For 4% or even larger shape uncertainty, we can obtain a best χ 2 of ∼8.4 for a single 24 kton detector configuration, while a almost stable χ 2 of ∼17.2 can be obtained for the two-detector configuration with the same 24 kton target mass.

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Fig. 5. The geographic map of the optimal range and candidates identified for the ND of the RENO-50 experiment.

Fig. 6. The MH sensitivity as a function of the reactor shape uncertainty for both the single (solid line) and double (dashed line) detector configurations.

As the shape uncertainty changes, the uncertainty of m2ee in the ND shown in Fig. 2 will 2 and the optimization of the change accordingly. Therefore, the shape uncertainty will affect χext ND baseline. Following the same FD setup as in Sec. IV-A, we take the ND target mass as 10 kton and illustrate the relation between the optimal ND baseline and the size of the reactor shape uncertainty in Fig. 7. The top panel shows the χ 2 as a function of the baseline for different reactor shape uncertainties, and the bottom panel shows the optimal baseline of the ND as a function of the reactor shape uncertainty. The optimal baseline varies between 10–20 km and it will increase when the reactor shape uncertainty becomes larger. The variation of the optimal ND baseline can be explained intuitively as follows. First, we must guarantee the measurement of m2ee at the ND is roughly as accurate as that of the FD

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Fig. 7. The combined MH sensitivity as a function of the ND baseline for different reactor shape errors (top panel), and the optimal baseline (Lbest ) of the ND as a function of the shape uncertainty (bottom panel).

which, according to Fig. 2, requires several cycles of m2ee oscillations in the ND. Second, if the reactor shape uncertainty increases, more cycles of m2ee oscillations are needed to obtain a comparable measurement of m2ee . The optimal baseline is directly related to the number of oscillation cycles. The larger baseline, the more cycles. 6. Conclusion In this work we have studied the MH measurement of medium baseline reactor neutrino experiments with multiple detectors, where the MH sensitivity can be improved by combining the near and far detectors. We present the optimization results both in the ideal case with the identical baseline, and the realistic cases for the specific configurations of JUNO and RENO-50. In addition, due to the constraint of the near detector in the reactor antineutrino energy spectrum measurement, the double detector configuration can reduce the impact of the shape uncertainty from the reactor antineutrino flux prediction. The impact of different shape uncertainties on the optimal near detector baseline is also studied. Our work is relevant to the design of future medium baseline reactor neutrino experiments and might be useful if an additional near detector is considered at JUNO or RENO-50. Acknowledgements This work was supported by the National Natural Science Foundation of China under Grant Nos. 11390383, 11135009, 11205176 and 11305193, by the Youth Innovation Promotion Association CAS under Grant No. 2016009, by the Strategic Priority Research Program of the Chinese Academy of Sciences under Grant No. XDA10010900. References [1] S.T. Petcov, M. Piai, The lma msw solution of the solar neutrino problem, inverted neutrino mass hierarchy and reactor neutrino experiments, Phys. Lett. B 533 (2002) 94–106.

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