RN.eps
A unified analysis of the reactor neutrino program
towards the measurement of the θ13 mixing angle
G. Mention
(a), Th. Lasserre (a,b), D. Motta (a)
(a)DAPNIA/SPP, CEA Saclay, 91191 Gif sur Yvette, France
(b) Laboratoire Astroparticule et Cosmologie (APC), Paris, France
November 9, 2018
Abstract
We present in this article a detailed quantitative discussion of the measurement of the leptonic
mixing angle θ13 through currently scheduled reactor neutrino oscillation experiments. We thus focus
on Double Chooz (Phase I & II), Daya Bay (Phase I & II) and RENO experiments. We perform a
unified analysis, including systematics, backgrounds and accurate experimental setup in each case. Each
identified systematic error and background impact has been assessed on experimental setups following
published data when available and extrapolating from Double Chooz acquired knowledge otherwise.
After reviewing the experiments, we present a new analysis of their sensitivities to sin2(2θ13) and study
the impact of the different systematics based on the pulls approach. Through this generic statistical
analysis we discuss the advantages and drawbacks of each experimental setup.
1 Experimental context
Over the last years the phenomenon of neutrino flavor conversion induced by nonzero neutrino masses
has been demonstrated by experiments with solar [1, 2, 3], atmospheric [4], reactor [5, 6] and accelerator
neutrinos [7, 8]. Neutrino oscillation, that can be described by the Pontecorvo–Maki–Nakagawa–Sakata
(PMNS) mixing matrix [11], is the current best mechanism to explain the data. Considering only the three
known families, the neutrino mixing matrix is parameterized by the three mixing angles (θ12, θ23, θ13) and a
possible δ CP violation phase. The angle θ12 has been measured to be large (sin
2(2θ12) ≃ 0.8), the angle θ23
has been measured to be close to maximum (sin2(2θ23) & 0.9); but the last angle θ13 has only been upper
bounded sin2(2θ13) . 0.15 at 90 % C.L., by the CHOOZ reactor experiment [9, 12]. These achievements
have now shifted the field of neutrino oscillation physics into a new era of precision measurements. Next
generation experiments are underway all around the world to further pin down the values of the oscillation
parameters of both solar and atmosheric driven oscillations. Currently the most important task, for the
experimentalists, is the determination of the last oscillation through the measurement of the unknown
mixing angle θ13. An improved sensitivity on θ13 is not only important for the understanding of neutrino
oscillations, but also to open up the possibility of observing CP-violation in the lepton sector if the θ13 driven
oscillation is discovered by the forthcoming experiments.
In order to improve the CHOOZ constraint on θ13 at least two identical unsegmented liquid scintillator
neutrino detectors close to a nuclear power plant (NPP) are required. The near detector(s) located a few
hundred meters away from the reactor cores monitor the unoscillated νe flux. The far detector(s) is(are)
located at a distance between 1 and 2 km, searching for a departure from the 1/L2 behavior induced by
oscillations. Experimental errors are being partially cancelled when using identical detectors. The goal is
to achieve an overall effective systematic error of less than 1 % [19, 34].
Three experiments have received partial or full approval to perform such a measurement in a near future:
Double Chooz in France [24], Daya Bay in China [25] and RENO in Korea [26]. In addition, a project is
http://arxiv.org/abs/0704.0498v2
under study at the Angra power plant in Brazil to further improve the sensitivity of the measurement on a
longer time scale [29]. Furthermore the Japanese KASKA collaboration is promoting the reactor neutrino
oscillation physics [28].
2 Neutrino oscillation at reactor and θ13
Fission reactors are prodigious sources of electron antineutrinos which have a continuous energy spectrum
up to about 10 MeV. For Eνe > Ethr = 1.806 MeV they can be detected though the νe+p → e++n reaction
using the delayed coincidence technique, where an electron antineutrino interacts with a free proton in a
tank containing a target volume filled with Gd loaded liquid scintillator. The positron and the resultant
annihilation gamma-rays are detected as a prompt signal while the neutron slows down and then thermalizes
in the liquid scintillator before being captured by a hydrogen or gadolinium nucleus. The excited nucleus
then emits gamma rays which are detected as the delayed signal. Electron antineutrinos energy is derived
from the measured visible energy from positron energy loss and annihilation,
Evis = Ee+ +me ≃ Eν − Ethrν + 2me . (1)
The νe spectrum is calculated from measurements of the beta decay spectra of
235U, 239Pu and 241Pu [15]
after fissioning by thermal neutrons and theoretical 238U spectrum, since no data are available for 238U 1.
As a nuclear reactor operates, the fission element proportions evolve in time (the so-called burn-up). Since
we are interested here on long term interpretation of the data for oscillation search, we will use an average
fuel composition for a reactor cycle corresponding to
235U (55.6 %), 239Pu (32.6 %), 238U (7.1 %) and 241Pu (4.7 %) . (2)
The mean energy release per fission, 〈Ef 〉, is then 205 MeV and the energy weighted cross section for
νep → e+n amounts to 〈σf 〉 = 6 10−43 cm2 per fission. Let us introduce a new luminosity unit, called the
r.n.u. (for reactor neutrino unit) and defined as 1 r.n.u. = 0.197 1060 MeV. With this unit, an experiment
taking data for T years with a total NPP (nuclear power plant) thermal power of P GW and with N 1030 free
protons inside the target has a luminosity L = T P N r.n.u.. The event number, N(L), at a distance L from
the source, assuming no - oscillation, can be quickly assessed with
N(L) =
〈σf 〉
4π 〈Ef 〉
≃ 4.6 109
1 GWth
For the full antineutrino reactor energy spectra simulation, we follow Vogel’s analytical parameteriza-
tion [16], based on second order Eν polynomials. Higher order parameterizations [18] give very comparable
results and do not require a specific attention for our aim in this article. The antineutrino event rates
per energy range is then computed according to the mean reactor core composition (2) and experimental
site specifications (reactor and detector locations, average efficiencies and running time as described in
section 6).
Reactor neutrino experiments measure the survival probability Pee which does not depend on the Dirac
δCP phase. In addition, the oscillation of MeV’s reactor neutrinos studied over a distance of a few kilome-
ters is not affected by the modification of the coherent forward scattering from matter electrons [32, 33].
Expanding the full three flavors νe oscillation probability as a function of (∆m
21/∆m
2 ≃ 1/302 ratio
and sin2(2θ13), Pee measurements from reactor experiments on the kilometer scale may be described by the
simplest two flavors oscillation formula:
Pee ≃ 1− sin2(2θ13) sin2
∆m231L
. (4)
as long as sin2(2θ13) & 10
−3. We assume that in eq. (4), ∆m231 is measured by other experiments (MINOS [8],
K2K [7] and super-K [4]). With a determination of ∆m231 better than 10 %, the impact on sin
2(2θ13)
1238U fissions only with fast neutrons. Theoretical predictions are computed by summing all known beta decay processes
contributing.
determination can be neglected [34]. All results within this study are, unless otherwise stated, computed
for a representative value of ∆m231 [13]:
∆m231 = 2.5
+0.25
−0.25 10
−3 eV2 at 68 % C.L.. (5)
3 Generic analysis of θ13 sensitivity
The calculation of event rates is a convolution of the νe flux spectrum, the cross section, the oscillation
probability, the detector efficiency with the energy response function.
The detector energy response simulation, as well as its correction through detector callibrations are specific
to each experiment. The details of the corrections are thus beyond the scope of this article. We therefore
assume in the following that the reconstructed energy is identical to the true deposited energy. We will
implement, anyway, a simple energy scale systematic uncertainty (section 6.1).
We based our event rates computations on an extended version of the numerical code developed for Dou-
ble Chooz [34, 24]. These computations take into account the characteristics of each experimental setup as
the number of reactors, detectors, locations, overburdens, efficiencies, operating time, and so on which will
be described in section 6.
The resulting event rates, then, form the basis for a χ2 analysis, where systematic uncertainties are properly
included. Since event rates in the disappearance channel of reactor experiments are quite large, we can use
a Gaussian χ2, which has the advantage of allowing a natural inclusion of systematic errors through the
so-called “pull-approach” [14]:
χ2 = min
i=1,...,Nb
D=D1,...,DN
∆Di −
k,k′=1
k,k′αk′
. (6)
This generic χ2 definition encompasses all the spectral information (i index) from each detector (D index)
and systematics parameterization through αk and S
i,k. For S
i,k = 0, we recover the classical χ
2 definition,
χ2no syst =
, through
∆Di =
i −NDi
/UDi (7)
where we assume that the simulated data event numbers, N
i , are uncorrelated between bins and detectors.
In the absence of real data, they are computed for fixed given values of ∆m231
⋆ and sin2(2θ13)
⋆. On the
other hand NDi , the theoretical model, relies on the searched sin
2(2θ13) value. We assume an uncorrelated
weight error UDi which, in the absence of systematic uncertainty, is simply expressed as the statistical error:
UDi =
NDi .
Systematic uncertainties are included in the χ2 definition (6) through αk and S
i,k coefficients. The S
coefficient represents the shift of the ith bin of detector D spectrum due to a 1 σ variation in the kth
systematic uncertainty parameter αk. Following this definition, we introduce bin, detector and reactor
correlations in the systematic errors through SDi,k definitions whereas systematic parameter correlations are
gathered in Wk,k′ (we refer to the appendix for details). Eventually, some fully uncorrelated systematic
uncertainties may be included through the UDi definition, by adding quadratically all their effects together
with the statistical uncertainty. We will use this property to include background shape uncertainties in
our analysis as described in section 5. We refer to the appendix for the proper inclusion and definition of
systematic coefficients SDi,k and αk inside the χ
2 definition (6).
We define the sensitivity or sensitivity limit sin2(2θ13)lim as the largest value of sin
2(2θ13) which fits the
true value sin2(2θ13)
⋆ = 0 at the chosen confidence level. We therefore determine the sin2(2θ13) sensitivity
at 90 % C.L. of an experiment as the value of sin2(2θ13) for which
∆χ2 = χ2(sin2(2θ13))− χ2min = 2.71 . (8)
4 Generic overview of systematic error inputs
Systematic errors can be classified into three main categories: reactor, detector and data analysis induced
uncertainties. In this section we provide a brief and generic description of the systematic uncertainties
included in our modelization. Details concerning specific experimental cases are given in sections 6, 7.
The dominant reactor induced systematic error comes from our limited knowledge of the physical processes
which produce electron antineutrinos in nuclear reactors. This leads to an overall normalization error on
the production rate of 1.9 % [9]. Similarily we include a 2.0 % uncertainty on the antineutrino spectral
shape [15], with the conservative hypothesis that the energy bins are not correlated among themselves.
Furthermore, even at a perfectly defined thermal power and with an absolute knowledge of the number of
antineutrinos emitted for each fission, an underlying uncertainty remains since the nuclear energy released
per fission is known to about 0.5 % [9]. In our model the last three uncertainties are taken to be fully
correlated between the nuclear cores.
We included another group of reactor induced systematics, taken to be uncorrelated between the reactor
cores: the uncertainty on the determination of the thermal power of each nuclear core, within 0.6 – 3 % and
the uncertainty on the isotopic composition of the nuclear core fuel elements, within 2 – 3 %. Also, finite
size and solid angle effects, distances bias between reactors and detectors, as well as displacements of the
neutrino production barycenter might affect the fluxes at the near detector(s) if they are close to the power
plants (below 200 m) up to a level of 0.1 %.
We did not implemented the uncertainty coming from neutrinos produced in the spent fuel pools, often
located within tens of meters from the nuclear cores since we could not gather all the relevant information
for the different sites. We thus neglect this effect in our simulation, whithout any justification except in
the case of Double Chooz, since a detailed evaluation has shown that this uncertainty does not affect its
sensitivity [24]. We point out that in particular cases this additional neutrino source slightly affects the
antineutrino spectrum, and is thus relevant for experiments aiming at high sensitivities, e.g. sin2(2θ13) ∼
0.01. We could also have introduced a specific error on the inverse-beta decay neutrino cross section of
0.1 % [9, 36]. However, being fully correlated between the detectors, the latter can be gathered into a global
uncertainty, adding up to the overall neutrino rate knowledge.
The basic principle of the multi-detector concept is the cancellation of the reactor induced systematics;
additional contributions would not modify significantly the sensitivities of the forthcoming experiments.
Let us now focus on the uncorrelated errors between detectors that could affect strongly the experimental
results.
The uncorrelated errors between detectors directly contribute to the relative normalization of the mea-
sured antineutrino energy spectrum of each detector. One of the major improvement with respect to the
CHOOZ experiment relies on the precise measurement of the number of free protons inside target volumes,
proportional to the antineutrino rates. Experimentally the target mass will be determined at 0.2 %. An
uncertainty on the fraction of free hydrogen per unit volume remains, at the level of 0.2 – 0.8 %, if different
batches of liquid scintillator are used to fill the detectors of a given experiment. This complex case diserve a
special treatment as described in section 7.2. We did not include any error associated with the measurement
of the live time of the experiments.
The last set of systematics concerns the selection cuts applied to extract the antineutrino signal and reject
the backgrounds. Neutrino events are identified as positrons followed in time by a single neutron captured on
a gadolinium nucleus. New detector designs have been proposed in order to simplify the analysis, reducing
the systematic errors while keeping high statistics and high detection efficiency. We accounted for three
uncertainties for both positron and neutron associated to a candidate event: the possibility of missing the
particle as it escapes the target (escape), the uncertainty related to the particle interactions2 (capture) and
2Note that it affects essentially the neutrons, since the Gd concentration might differ between the detectors if they are not
the identification cut based on the energy deposited in the detector active region (identification). Finally
we take into account the uncertainty on the efficiency of the delay cut and an error on the neutron unicity
of the event selections, whereas we do not consider any position vertex reconstruction. We provide in
section 6.1 (Table 1) the detailed systematic inputs necessary for our simulations. The uncertainty on these
efficiencies have been treated, otherwise stated, as uncorrelated between detectors. Uncertainties induced
by the background subtractions are discussed in sections 5 and 6.3.
5 Backgrounds: description and modelization
In this section we briefly review the three main kinds of background for the next generation of reactor
neutrino experiments: accidental coincidences, fast neutrons and the long-lived muon induced isotopes
9Li/8He. We then describe our simplified background modelization.
Naturally occurring radioactivity mostly creates accidental background, defined as a coincidence of a prompt
energy deposition between 0.5 and 10 MeV, followed by a delayed neutron-like event in the fiducial volume
of the detector within a few hundredths of a millisecond. Selection of high purity materials for detector
construction (scintillator, mineral oil, PMT’s, steel, etc.) and passive shielding provide an efficient handle
against this type of background. We assume that the accidental background rate can be measured in situ
with a precision of 10 %.
Cosmic ray muons will be the dominating trigger rate at the depth of all near detector sites. Even though the
energy deposition corresponds to about 2 MeV per centimeter path length (providing a strong discrimination
tool) they induce the main source of background.
Muon induced production of the radioactive isotopes 8He, 9Li and 11Li can not be correlated to the primary
muon interaction since their lifetimes are much longer than the characteristic time between two subsequent
muon interactions. The characteristic signature of this last class of events consists in a four-fold coincidence
(µ → n → β → n). The initial muon interaction is followed by the capture of spallation neutrons within
about 1 ms. The time scale of the decay of the considered isotopes is on the order of a few 100 ms, again
followed by a neutron capture. This background mimics the νe signal and is considered among the most
serious difficulty to overcome for the next generation reactor neutrino experiments. In our simulation we
will assume that it can be estimated to within 50 %.
A further source of background are neutrons that are produced in the surrounding rocks by radioactivity
and in cosmic ray muon induced hadronic cascades. In the latter case, which is dominant at shallow depth,
the primary cosmic ray muon may not penetrate the detector, being thus invisible. Fast neutrons may
then enter the detector and create recoil protons and be captured by hydrogen or gadolinium nuclei after
thermalization. Such a sequence can mimick a νe event. In the case of Double Chooz far detector (depth of
300 m.w.e.), muon induced neutron production can be fairly well estimated from the results of the CHOOZ
experiment, since it was the dominating backgroundmonitored during reactor off periods [9]. We will assume
that this background rate can be estimated within a factor of two. Figure 1 illustrates the background
spectra that we implemented in our modelization. We used the CHOOZ reactor off data [9] to estimate the
fast neutron background spectral shape, measured to be flat. We used a simple approximate exponential
shape for accidental backgrounds. Finally we implemented the spectra of 8He and 9Li based on nuclear data
information; we weighted them in the ratio 0.2/0.8, respectively. We checked that slight modifications of
the background shapes do not change the results of our simulations for sin2(2θ13) sensitivities above 0.01.
Background rates are adjusted to match to the predictions at each detector location. Afterward they are
subtracted from the total Evis spectrum in each detector. These three backgrounds, Bn, have rates and
shapes known at σBD
and σshp,BD
, respectively. We take the conservative assumption that these shape
uncertainties are fully uncorrelated between bins. Thus, the σshp,BD
contributions may be directly included
inside UDi (eq. (7)). These generic uncorrelated errors will then take into account the statistical and the
background shape subtraction uncertainties:
filled with a single batch of liquid scintillator.
0 1 2 3 4 5 6 7 8 9 10
Evis (MeV)
Proton recoils
Accidentals
Cosmogenics
Figure 1: Energy spectrum of the backgrounds from spallation neutrons, accidentals, and cosmogenic
20 % 8He and 80 % 9Li. Each curve is normalized to unity.
UDi =
NDi +
BDn,i + σ
shp,BD
BDn,i
As the background rate uncertainties are correlated between bins, we treat them with additional pull terms,
, in eq. (6), with weights σBD
included in SDi,k (see the appendix).
6 Comparison of the current proposals
Several sites are currently being considered for new reactor experiments to search for θ13: Angra dos
Reis (Angra, Brazil), Chooz (Double Chooz, France, and possibly Triple Chooz), Daya Bay (Daya Bay,
China), Kashiwazaki (KASKA, Japan) and Yonggwang (RENO, Korea). All these experiments may be
classified in two generations. The first aims to probe the value of sin2(2θ13) till 0.02 – 03, and the second to
track sin2(2θ13) down to 0.01 (90 % C.L.). The first phase concerns Double Chooz, RENO, and possibly
Daya Bay (with its phase I). This phase should end by 2013. Angra, Daya Bay (nominal setup with
8 detectors), KASKA and possibly Triple Chooz are focusing on the second phase. For these second
generation experiments, a significant R&D effort is required since the effective Gd-scintillator mass will be
increased by, at least, one order of magnitude, and systematics, as well as backgrounds uncertainties, have
to be further reduced with respect to the first phase experiments. In the following comparisons we will not
include Angra, KASKA and Triple Chooz. We will only focus on Double Chooz, Daya Bay and RENO.
In the next sections we first introduce a generic discussion on systematics, scintillator composition and
backgrounds (sections 6.1 to 6.3). We will then shortly describe each setup and compute the associated
baseline sensitivity (sections 7.1 to 7.3). We then perform a comparative analysis of the setups in section 8
to highlight advantages and drawbacks of each setup.
6.1 Detailed systematics review
The two Double Chooz [24] and Daya Bay [25] proposals take a careful inventory of systematics, compiled
in Table 1 for comparison. Double Chooz and Daya Bay estimates for the case of no additional R&D are
at hand. We decided to strictly use the systematic errors (Table 1) and background values quoted by the
collaborations [24, 25, 26]. However, we could not find any detailed background estimate for the RENO and
Daya Bay Mid site setups. In the latter cases we use a simple model to estimate the background subtraction
uncertainties from the scaling of the Double Chooz far detector (see section 6.3).
Error Description CHOOZ Double Chooz Daya Bay
No R&D R&D
Absolute Absolute Relative Absolute Relative Relative
Reactor
Production cross section 1.90 % 1.90 % 1.90 %
Core powers 0.70 % 2.00 % 2.00 %
Energy per fission 0.60 % 0.50 % 0.50 %
Solid angle/Bary. displct. 0.07 % 0.08 % 0.08 %
Detector
Detection cross section 0.30 % 0.10 % 0.10 %
Target mass 0.30 % 0.20 % 0.20 % 0.20 % 0.20 % 0.02 %
Fiducial volume 0.20 %
Target free H fraction 0.80 % 0.50 % ? 0.20 % 0.10 %
Dead time (electronics) 0.25 %
Analysis (paticle id.)
e+ escape (D) 0.10 %
e+ capture (C)
e+ identification cut (E) 0.80 % 0.10 % 0.10 %
n escape (D) 0.10 %
n capture (% Gd) (C) 0.85 % 0.30 % 0.30 % 0.10 % 0.10 % 0.10 %
n identification cut (E) 0.40 % 0.20 % 0.20 % 0.20 % 0.20 % 0.10 %
νe time cut (T) 0.40 % 0.10 % 0.10 % 0.10 % 0.10 % 0.03 %
νe distance cut (D) 0.30 %
unicity (n multiplicity) 0.50 % 0.05 % 0.05 %
Total 2.72 % 2.88 % 0.44 % 2.82 % 0.39 % 0.20 %
Table 1: Breakdown of the systematic errors included in the computation of the sensitivity of Dou-
ble Chooz [24] and Daya Bay [25]. Since no breakdown of the RENO systematic errors has been pub-
lished we use the same systematic error budget as for Double Chooz. Double Chooz and Daya Bay relative
systematics are almost comparable, the only main difference coming from the determination of the gadolin-
ium concentration and the free proton fraction inside the target volume. The absolute determination of
the free proton fraction can have some impact in Daya Bay since multiple batches will be used to fill all
the 8 detectors (see section 7.2 for details). Nevertheless, there is no published value in the Daya Bay
proposal [25].
Through all the available publications [24, 25, 26, 28], the differences between the systematics are found
only for the relative normalization of the dectetor (σrel) and the subtraction uncertainties on background
rates (σBD
). From section 4 and Table 1, we thus group systematics in two categories to be used in our χ2
analysis eq. (6):
1. generic systematics common to all the experiments (Table 2):
– σabs, the theoretical uncertainty on reactor antineutrino spectrum prediction. We call it also the
absolute normalization of event rates (since common to all the detectors), extracted from Table 1
without power uncertainty contributions. σabs is at the level of 2 %;
– σshp, the theoretical reactor spectrum shape uncertainty, at the level of 2 %;
– σabs
, σrel
, the absolute and relative energy scale uncertainties, roughly assessed at the level of
0.5 % each;
– σpwr, the reactor thermal power uncertainty, at the level of 2.0 %;
– σcmp, the reactor core specific fuel composition uncertainty which is roughly at the level of the
power uncertainties (2 – 3 %) on each fuel element.
σabs σshp σ
σpwr σcmp
2.0 % 2.0 % 0.5 % 0.5 % 2.0 % 2 – 3 %
Table 2: Generic systematic uncertainties as included in the χ2 analysis. For more details about the
correlations between the systematics, we refer to the appendix, and more particularly to Table 15.
2. specific systematics:
– σrel, the relative normalization of event rates between all the detectors. This uncertainty is
uncorrelated between detectors;
– σBD
, the background subtraction unceratinties, described in section 6.3.
6.2 Impact of the scintillator composition
In this section we stress the impact of the scintillator composition on the sensitivity of reactor neutrino
experiments. All current projects will use a gadolinium doped liquid scintillator to enhance the neutron
capture. The long-term stability of this scintillator is among the most difficult experimental challenges,
since a degradation of the scintillator transparency would induce large systematic uncertainties. In the
following we consider a stable scintillator for all experiments. The choice of the scintillating base has
some importance since it defines the free proton number per unit volume, the νe rate and proton recoil
background rate. Similarly the 12C number per volume drives the long-lived muon induced isotopes in the
target scintillator.
Different bases can be used as neutrino target scintillator, mixture of dodecane (DOD), pseudocumene
(PC) or phenylxylylethane (PXE), or linear alkylbenzene (LAB), as described in details in Table 3. If we
consider the Double Chooz scintillator (80 % DOD + 20 % PXE) as our reference, a pure LAB scintillator
contains 4.9 % less free proton per volume, and 9.5 % more carbon atoms. In the following we will assume
the Daya Bay [25] and RENO [26] experiments will use pure LAB as the target scintillator, and we will
renormalize the neutrino and the backgound rates accordingly in section 7.2 and 7.3.
6.3 Estimation of the µ-induced backgrounds
Our estimates of the backgrounds induced by cosmic muons is based on the Double Chooz proposal [24]. A
modification of the MUSIC code [20] was used to compute the muon rates and energy spectra by propagating
Liquid Formula density 1028H/m3 1028C/m3
Dodecane (DOD) C12H26 0.753 6.93 3.20
pseudocumene (PC) C9H12 0.88 5.30 3.97
phenylxylylethane (PXE) C16H18 0.985 5.08 4.52
90 % DOD+10 % PC mixture in vol. 0.77 6.77 3.32
80 % DOD+20 % PXE mixture in vol. 0.80 6.56 3.46
linear alkylbenzene (LAB) C16H30 0.86 6.24 3.79
Table 3: Impact of the scintillator composition on the target free proton number driving the νe rate
as well as the recoil proton background, and on the carbon composition which drives the long-lived muon
induced isotopes produced in the detector. In the following we consider that Double Chooz is using modules
containing 8.26 tons of 80 % dodecane +20 % PXE (in volume) based target scintillator, and that Daya Bay
and RENO are both using 20 ton modules of a LAB based target scintillator.
surface muons through rock. The site topographies have been included, according to a digitized map of the
Chooz hill profile [22] in the case of the far site (300 m.w.e. overburden), and according to a flat topography
in the case of the near site (80 m.w.e. overburden). For the far site this full Monte-Carlo simulation predicts
a muon flux Φµ=0.612± 0.007 m−2 s−1, slightly higher than the approximate measured value quoted in [9].
The mean muon energy computed according to this method is 〈Eµ〉 = 61 GeV. For the near site, we get
Φµ = 5.9 m
−2 s−1, and 〈Eµ〉 = 22 GeV. A similar detailed computation was performed for the three sites
of the Daya Bay collaboration [25].
Thus, for both the cases of Double Chooz and Daya Bay we use only the values of the muon flux and mean
energy computed by the collaborations. However, we could not find any published data for the case of
RENO. We then use the underground muon fluxes and mean energies calculated analytically following [21].
In order to justify this approximation, Table 4 reports the muon flux and mean energy computed by the
Double Chooz and the Daya Bay collaborations, from 300 m.w.e. to 923 m.w.e., as well as the analytical
computations according to [21]. We found a reasonable agreement which bears out the use of the analytical
model [21] for the case of the RENO sites (depths of 255 m.w.e. and 675 m.w.e.). Nevertheless, note
that the analytical simulation assumes a flat topography. It is worth noting, however, that the mean muon
energy predicted by the analytical computation is systematically ∼ 25 % lower in the depth range of interest.
Therefore we arbitrarily renormalize the analytical calculation by 25 % to estimate the mean muon energy
at the RENO sites. We also note a large discrepancy between the detailed computation and the analytical
model of [21] for the Double Chooz near site, probably due to its very shallow depth.
Cross sections of muon induced isotope production on liquid scintillator targets (12C) have been measured
by the NA54 experiment at the CERN SPS muon beam at 100 GeV and 190 GeV muon energies [23]. The
energy dependence was found to scale as σtot(Eµ) ∝ 〈Eµ〉α with α = 0.73± 0.10 averaged over the various
isotopes produced. We consider in the following that both long-lived muon induced isotopes and muon
induced fast neutron backgrounds scale as Φµ ×〈Eµ〉α, our reference being taken at the Chooz far site (full
Monte-Carlo simulation). We define the depth scaling factor as
DSF = (Φµ 〈Eµ〉α)/(Φµ 〈Eµ〉α)Double Chooz far , (10)
which is illustrated in the last column of Table 4 for various detector sites. Daily background rates computed
for Daya Bay, Double Chooz, and RENO detectors at the different sites are then given in Table 5.
Two cases are considered and compared: the background rates taken from the literature when available,
and the background rates extrapolated from the background computed for the Double Chooz far detector,
scaled with the target mass, the scintillator free proton and carbon numbers, as well as the depth scaling
factor (DSF). We note here the good agreement between the Daya Bay cosmogenic induced backgrounds
(9Li/8He and fast neutrons) estimated from our Double Chooz extended model and the original estimates
of the Daya Bay collaboration. This bears out the use of our model for the RENO and Daya Bay mid
site configurations. For the case of the 9Li/8He background, we understand well this agreement since
the background rate mainly depends on the mass of the neutrino target region. The agreement is more
Site depth (m.w.e.), Detailed simulation Analytical model DSF
topography Φµ 〈Eµ〉 Φµ 〈Eµ〉
m−2 s−1 GeV m−2 s−1 GeV
DC near 80, flat 5.9 22 9.9 17 6.80
RENO near 230, hill — — 1.2 40 1.57
DB near 1 255, hill 1.2 55 0.9 44 1.32
DB near 2 291, hill 0.73 60 0.72 49 1.06
DC far 300, hill 0.61 61 0.67 50 1
DB mid 541, hill 0.17 97 0.15 71 0.32
RENO far 675, hill — — 0.084 94 0.20
DB far 923, hill 0.04 138 0.035 118 0.10
Table 4: Muon flux Φµ and mean energy 〈Eµ〉 for the underground site of the reactor neutrino experiments.
We compare the values obtained from a full Monte-Carlo simulation for Double Chooz and Daya Bay to the
analytical model of [21]. We use the latter model for RENO. The depth scaling factor (DSF) is defined by
the product (Φµ×〈Eµ〉α)/(Φµ×〈Eµ〉α)Double Chooz far, the Double Chooz far site is taken as the reference.
Backgrounds induced by cosmic muons are scaled according to this factor.
Detector Accidental (d−1) µ-induced fast-n (d−1) µ-induced 9Li/8He (d−1)
Site Original DC ext. Original DC ext. Original DC ext.
Double Chooz near 13.60 ± 1.36 1.36 ± 1.36 9.52 ± 4.76
RENO near — 7.10 ± 0.71 — 0.68 ± 0.68 — 5.40 ± 2.70
Daya Bay DB 1.86± 0.19 5.98 ± 0.60 0.50 ± 0.50 0.57 ± 0.57 3.7 ± 1.85 4.55 ± 2.27
Daya Bay LA 1.52± 0.15 4.76 ± 0.48 0.35 ± 0.35 0.45 ± 0.45 2.5 ± 1.25 3.63 ± 1.81
Double Chooz far 2.00± 0.20 — 0.20 ± 0.20 — 1.40 ± 0.70 —
Daya Bay mid — 1.45 ± 0.14 — 0.14 ± 0.14 — 1.10 ± 0.57
RENO far — 0.90 ± 0.09 — 0.09 ± 0.09 — 0.69 ± 0.35
Daya Bay far 0.12± 0.01 0.44 ± 0.04 0.03 ± 0.03 0.04 ± 0.04 0.26 ± 0.13 0.33 ± 0.17
Table 5: Daily background rates computed for Daya Bay, Double Chooz, and RENO detectors at the
different sites. We consider the three main background sources: accidental events, µ-induced fast neutrons,
and µ-induced 9Li/8He. The columns labelled “Original” quote the background rates taken from the
literature when available. The columns labelled “DC ext.” (for extended) quote the background value
extrapolated from the background computed for the Double Chooz far detector, scaled with the detector
target mass, the scintillator free proton and carbon numbers, as well as the depth scaling factor (DSF).
Background subtraction systematic errors (%)
Detector Accidental µ-induced fast-n µ-induced 9Li/8He
Site Original DC ext. Original DC ext. Original DC ext.
Double Chooz near 0.123 0.123 0.043
RENO near — 0.019 — 0.019 — 0.074
Daya Bay DB 0.020 0.064 0.054 0.061 0.199 0.245
Daya Bay LA 0.020 0.063 0.046 0.060 0.164 0.239
Double Chooz far 0.292 — 0.292 — 1.020 —
Daya Bay mid — 0.120 — 0.115 — 0.458
RENO far — 0.100 — 0.095 — 0.382
Daya Bay far 0.010 0.036 0.025 0.035 0.108 0.138
Table 6: Background subtraction systematic errors (in percent) computed for Daya Bay, Double Chooz, and
RENO detectors at the different sites. We consider the three main background sources: accidental events,
µ-induced fast neutrons, and µ-induced 9Li/8He. The columns labelled “Original” quote the systematic
errors taken from the literature when available. The columns labelled “DC ext.” (for extended) quote
the systematic errors extrapolated from the Double Chooz far detector, taking into account the estimated
detector signal to background ratio as well as the background rate uncertainty.
surprising, however, for the case of the fast neutron background, since the size of the liquid shielding around
the detector active area is rather different between the Double Chooz and Daya Bay detectors (the RENO
detector design is very close to the Double Chooz case). In addition, further detector differences such as
the thickness of the buffer oil shielding the inner target region, as well as the different mechanical structure
explain the discrepancy between the Daya Bay computation and the DC extended model for the case of
the accidental background. Nevertheless, we found out that these differences influence only weakly the
sensitivity computed for the three experiments since the accidental background energy spectrum is different
enough from the expected oscillation signal, and it is supposed to be known with a precision of 10 %.
In a similar way, Table 6 gives the background subtraction systematic errors (in percent) computed for
Daya Bay, Double Chooz, and RENO detectors at the different sites, taking into account the estimated
detector signal to noise ratios as well as the background rate uncertainties.
7 Reactor experiments baseline sensitivity
7.1 Double Chooz
The Double Chooz collaboration is composed of institutes from Brazil, France, Germany, Japan, Russia,
Spain, United Kingdom, and the United States. The experimental site is located close to the twin reactor
cores of the Chooz nuclear power station (two PWR3 producing 8.5 GWth), operated by the French company
Électricité de France (EDF). The two, almost identical, detectors will contain a 8.3 ton fiducial volume of
liquid scintillator (density of 0.8) doped with 0.1 g/l of gadolinium (Gd). The far detector will be installed
in the existing laboratory, 1.05 km from the cores barycenter, shielded by 300 m.w.e. of rock. This detector
should be operating alone for 1.5 – 2 years (DC Phase I), starting data taking by the end of 2008. The
second detector will be installed in the meantime about 280 m from the nuclear core barycenter, at the
bottom of a 40 m shaft (80 m.w.e.) to be excavated. Distances between detectors and nuclear cores as well
as site overburdens are given in Table 7. Since there are no more than two NPP cores, it is still possible to
install the near detector at a suitable position where the ratio of reactor νe fluxes from each core is the same
as for the far detector (the iso-ratio curve is plotted on figure 2). This allows reactor relative uncertainty
cancellations (NPP core compositions). This detector should be operational by 2010, and will take data
3Pressurized Water Reactor
Detector near far
Distance from West reactor (m) 290.7 1114.6± 0.1
Distance from East reactor (m) 260.3 997.9± 0.1
Detector Efficiency 80 % 80 %
Dead Time 25 % 2.5 %
Rate without efficiency (d−1) 977 66
Rate with detector efficiency (d−1) 782 53
Integrated rate (y−1) 1.67 105 1.48 104
Table 7: Double Chooz antineutrinos rate expected in the near and far detectors, with and without reactor
and detector efficiencies. The integrated rate in the last line includes detector efficiency, dead time, and
reactor off periods averaged over a year. The averaged reactor global load factor is estimated at 79 % [30].
Figure 2: Double Chooz experiment site configuration. We show also on this figure the far flux iso-ratio
line. Another detector located on this particular curve will receive the same reactor flux ratio as for the far
detector: 44.5 % from West and 55.5 % from East reactor. The near detector of Double Chooz is foreseen
to be placed on this line.
for three years (DC Phase II). Other details concerning the experiment may be found in the collaboration
proposals [24].
For the Double Chooz phase I (DC Phase I) analysis, we used systematics of Table 2, setting σrel and
to 0 since only one detector will be present. For a data taking period of 1.5 years, the sensitivity
is sin2(2θ13)lim = 0.0544. The second phase (DC Phase II) will then start and both detectors will take
data for 3 years as scheduled in the proposal. The full experiment will then achieve a final sensitivity
sin2(2θ13)lim = 0.0278, assuming systematics from Table 2 and σrel = 0.6 % [24]. The sensitivity worsens
for ∆m231 < 2.5 10
−3 eV2, due to the close distance of the far detector4. If we take the lower bound [12, 13]
on ∆m231 (2.0 10
−3 eV2), Double Chooz will lose 30 % in sensitivity whereas for the upper bound [12, 13]
on ∆m231 (3.0 10
−3 eV2), Double Chooz will gain 15 % in sensitivity.
7.2 Daya Bay
Daya Bay is an experiment proposed by institutes from China, the United States, and Russia. Daya Bay [25]
will be located in the Guang-Dong Province, on the site of the Daya Bay nuclear power station. The site is
made up of two pairs of twin reactors, Daya Bay (DB) and Ling Ao I (LA I). An additional pair of reactors,
Ling Ao II (LA II), is currently under construction and should be operational by 2010 – 2011 [25]. Each
core has a thermal power of 2.9 GW [30]. In the full installation setup 3.3 km of tunnel and 3 detector halls
have to be excavated, in order to accommodate 8 detector modules [25]. Each module contains an effective
volume of 20 tons of Gd-loaded LAB liquid scintillator (Table 3). Distances between detectors and nuclear
cores as well as site overburdens are given in Table 8. This site yields a rather complex signal composition
Detector near DB near LA mid far
Distance from DB 1 (m) 350 1,356 1,153 1,970
Distance from DB 2 (m) 381 1,331 1,161 2,000
Distance from LA I 1 (m) 942 492 783 1,619
Distance from LA I 2 (m) 1,030 475 818 1,623
Distance from LA II 1 (m) 1,378 500 968 1,602
Distance from LA II 2 (m) 1,463 555 1,029 1,624
Detector eff. 80 % 80 % 80 % 80 %
Dead Time 7.2 % 4.3 % 1 % 0.2 %
Rate without eff. (d−1) 1,938 1,813 494 430
Rate with detector eff. (d−1) 1,550 1,450 395 344
Integrated rate (y−1) 4.10 105 3.95 105 1.11 105 9.77 104
Table 8: Daya Bay antineutrino rates expected in the near and far detectors, with and without reactor and
detector efficiencies. The integrated rate in the last line includes detector efficiency, dead time, and reactor
off periods averaged over a year. We assumed that LA II NPP will be operating for the time the far site
will be fully installed, but for the Mid site installation we assumed that LA II will be off.
in each detector coming from up to 6 different NPP cores, as shown in Table 9. According to the Day Bay
proposal, our estimate of the sensitivity is sin2(2θ13) = 0.0085 very close to the Daya Bay quoted value
(sin2(2θ13) = 0.008). However, in the Daya Bay proposal, the uncertainties on the reactor fuel composition,
σcmp, as well as the energy scale associated uncertainties σ
and σrel
are neglected. Taking into account
these systematics (Table 2) and the quoted value of σrel = 0.39 % with no R&D [25], our estimate of the
Daya Bay final sensitivity is then sin2(2θ13) = 0.009, with the full installation (DB Phase II, Figure 3)
after 3 years of data taking. We draw the attention of the reader on the point that these computations are
based on the assumption that σrel = 0.39 % is fully uncorrelated between all the detectors, and in particular
4a bit too close to the NPP to get the maximum amount of information from first minimum of oscillation over the reactor
spectrum distortion
DB LA1 LA2
near 1 (DB) 83.1 % 11.4 % 5.5 %
near 2 (LA) 6.5 % 50.6 % 42.8 %
Mid (LA2 OFF) 32.3 % 67.7 % 0.0 %
Mid (LA2 ON) 22.5 % 47.1 % 30.4 %
far 24.9 % 37.4 % 37.7 %
Table 9: Daya Bay rate contributions from each NPP set (2 cores by set) while assuming, except if otherwise
noticed (3rd line), the new Ling Ao II NPP is operating at full power.
between detectors on a same site. Nevertheless this hypothesis is not guarenteed. We discuss this point as
well as the current filling scenario (multi-batches) just below.
Figure 3: Daya Bay installation phases and site configuration. On the left: phase I, with 2 × (2 × 20 t)
detectors, Daya Bay and Ling Ao I power plants are operating. On the right: phase II with 2× (2× 20 t)
near sites, and 4× 20 t at far site, all three power plants are operational.
A preliminary fast phase (DB Phase I) is proposed by the Daya Bay collaboration. This phase includes only
4 detectors, 2 of them located at the DB near site and the other 2 at the mid site (see Figure 3). Taking
systematics from Table 2 and σrel = 0.39 % fully uncorrelated between detectors, we get a sensitivity after
1 year of data taking of sin2(2θ13) = 0.040. if LA II NPP is off. If DB Phase I starts after 2010, with LA II
operational, we get a sensitivity of sin2(2θ13) = 0.038 still after 1 year of data taking. The reason for a
better sensitivity in the second scenario is that the mid detectors get 44 % more νe events (Table 8, 9 and
Figure 3), with a larger oscillation baseline with respect to LA I.
Daya Bay site correlation
The main concept of the Daya Bay experiment is based on the multi-inter-calibration of detectors. Since
many detectors are installed on a same site, the total uncorrelated uncertainty of a site is decreased by
a factor of 1/
NSd compared to the single detector uncorrelated uncertainty, where N
d is the number of
detectors on a given site. In the Daya Bay proposal, the full relative uncertainty (σrel = 0.39 %) is assumed
to be uncorrelated between all the detectors. However, the fraction of correlated and non-correlated error
between detectors of a same site is not trivial. It relies on many experimental assumptions on uncertainty
correlations. The absence of correlations between detectors on a same site implies there will be no detector-
to-detector correction applied. If detector responses happen to be different, any data correction from
detector to detector on a same site would yield correlations between detector uncertainties.
For DB Phase II, if we assume that σrel is fully uncorrelated between the detectors, we get a sensitivity of
sin2(2θ13) = 0.009. On the contrary, if we assume that σrel is fully uncorrelated between detectors in different
sites, but fully correlated between detectors on a same site, we get a sensitivity of sin2(2θ13) = 0.012. The
real sensitivity should lay between these two extremes.
For DB Phase I, if we assume σrel is fully correlated on a same site and fully uncorrelated on distant sites,
we get sin2(2θ13) = 0.041 if LA II is off, and sin
2(2θ13) = 0.038 if LA II is on. We conlude from these results
that DB Mid sensitivity does not strongly depend on the correlations in σrel. More generally, DB Mid setup
weakly depends on σrel. This latter point will be discussed in section 8, together with a full description of
the impact of each systematic on the forseen sensitivity.
Daya Bay and the filling procedure
A large amount of Gd-loaded liquid scintillator will have to be produced, stored and filled into the detectors
(8×20 tons, which is 10 times more than in Double Chooz). Due to the large number of detectors and
the large amount of liquid to manage, the Daya Bay collaboration plans to fill detectors with four different
Gd-doped liquid scintillator batches. A single batch will be used to fill detectors by pairs [25] (Figure 4).
The best installation scenario (which is the one chosen by the Daya Bay collaboration) is then to move
one of the filled detector to a near site, the other one to the far site (scheme 1 of Figure 4 and Table 10).
Another batch of Gd-loaded liquid scintillator will be used for the next pair of detectors and so on. With
the adopted filling procedure [25], extra systematic uncertainties on the hydrogen content between different
batches have to be included.
DB LA
Pair 1
Pair 2
Pair 3
Pair 4
Scheme 1 Scheme 2 Scheme 3
Scheme 4 Scheme 5 Scheme 6
Figure 4: Possible installation of detector pairs in the Daya Bay experiment according to the adopted filling
procedure [25]. Due to the large number of detectors, and the large amount of liquid to be managed,
the Daya Bay collaboration plans to fill detectors by pairs with four different Gd-doped liquid scintillator
batches. The forseen detector installation scenario [25] corresponds to scheme 1. We illustrate here other
installation possibilities (schemes 2 to 6).
Although the relative uncertainty on the free proton content within a same batch could be kept at a very
low level (0.2 % in the Daya Bay proposal [25], negligeable in the Double Chooz proposal [24]), it is not
necessarily true in the case of different batches, in which the chemical composition may slightly change.
The free proton content between different batches relies then on the measurement of this quantity. In the
CHOOZ experiment [9], the free proton fraction inside the Gd-loaded liquid scintillator was known to 0.8 %.
In Double Chooz, this uncertainty is assessed at the level of 0.5 %. Since there is no published value on the
absolute determination of this quantity in the Daya Bay proposal, we assume here, as in Table 1, a 0.5 %
uncertainty between different batches. The filling systematic coefficients are explained in Table 10 (refer to
the appendix and to Table 15 for full description). The uncertainty on the free proton fraction of a single
Scheme 1
Scheme 2
Scheme 3
Scheme 4
Scheme 5
Scheme 6
0.008 0.01 0.012 0.014 0.016
(2θ13)
Single batch
Four batches
Figure 5: Sensitivity on sin2(2θ13) at 90 % C.L. after 3 years of data taking for the 6 different installation
schemes illustrated on Figure 4, with σpair = 0.5 %. Left bounds are computed assuming uncorrelated errors
between all the detectors and right bounds are for the assumption of full correlation of σrel between detectors
of a same site. The real sensitivity should be somewhere in between these two bounds. For comparison,
we also show on this graph the computations for the single batch hypothesis where we take σrel = 0.39 %.
Note that obviously the first installation scheme provides the best sensitivity. In these results we do not
include any detector swapping scenario.
Error type k SD
Filling (Ns = 5Nd +Nb + 5Nr + 2)
of batch 1 Ns +1 σpair
αpair,1
of batch 2 Ns +2 σpair
αpair,2
of batch 3 Ns +3 σpair
αpair,3
of batch 4 Ns +4 σpair
αpair,4
Table 10: Daya Bay, phase II (8 detectors), specific filling systematic parameters table in addition to
standard one (see the appendix for details). Here we adopt a fully uncorrelated uncertainty of the different
batches, σpair = 0.5 %, but fully correlated in a same batch.
batch is taken to σpair = 0.5 %. This uncertainty is taken to be fully correlated when detectors are filled
with the same batch and fully uncorrelated otherwise.
According to this filling procedure, the final sensitivity of DB Phase II would be sin2(2θ13) = 0.0093
instead of 0.0089 with the initial installation scenario (scheme 1 of Figure 4). In all the other configuration
schemes (2 – 6), which allows comparing on a same site at least two detectors filled with the same batch,
the sensitivity is more largely weakened (Figure 5), to an extent depending on σpair.
Note that we did not include any detector swapping option in previous conclusions. In the Day Bay proposal,
the retained installation scenario is the first scheme of Figure 4. The baseline swapping option is then the
permutation of two detectors filled with the same batch, in 4 steps, 1 step per batch. On the one hand,
the drawback of such a swapping scenario is that two detectors filled with the same batch will never be
directly compared. On the other hand, configuration schemes 2 – 6 allow detector intercalibration within a
pair. However, it should be noticed that the time spent in any configuration different from scheme 1 may
decrease the combined final sin2(2θ13) sensitivity (Figure 5).
7.3 RENO
The RENO experiment [26] will be located close to the Yonggwang nuclear power plant in Korea, about
400 km south of Seoul. The power plant is a complex of six PWR reactors, each of them producing a thermal
power of 2.74 GW [30]. The Yonggwong power station is ranked number 4 in the world, with a total thermal
power of 16.4 GW. Its power rating is often cited as an advantage of the RENO experiment. These six
reactors are equally distributed on a straight segment spanning over 1.5 km. The average cumulative
operating factors for the reactors are all above 80 %. Figure 6 shows the foreseen layout of the experimental
site. The near and far detectors will be located 150 m and 1,500 m away from the center of the reactor
Figure 6: RENO experiment site configuration.
row (Table 11), and will be shielded by a 88 m hill (230 m.w.e.) and a 260 m “mountain” (675 m.w.e.)
respectively. Two neutrino laboratories have to be excavated and equipped in order to host the detectors.
They will be located at the bottom of two tunnels having a length of 100 m and 600 m for near and far
detector, respectively. In this configuration, the flux contribution from R1 to R6 ranges from 3 % to 39 %
for the near detector, and from 15 % to 18 % for the far detector (Table 12).
Assuming the sytematics of Table 1 and, lacking of published data, fixing σrel = 0.6 % as for Double Chooz,
we obtain a final sensitivity after 3 years of data taking of sin2(2θ13) = 0.021. This is calculated for
2× 20 t detectors. However, a recent talk [27], quotes a different detector size, with 15 t of Gd-doped liquid
scintillator. In that case, the final sensitivity after 3 years, would be sin2(2θ13) = 0.023.
As seen from Table 12, the near detector monitors mainly the two central NPP cores, and the experiment
sensitivity is quite affected by the reactor power uncertainties. If we compute the sensitivity with only the
2 central NPP cores, we get even better results compared to the full NPP configuration. This means that
four of the six cores are useless for the sin2(2θ13) measurement. This can be understood by the fact that the
Detector near far
Distance from R1 (m) 765 1677
Distance from R2 (m) 474 1566
Distance from R3 (m) 212 1507
Distance from R4 (m) 212 1507
Distance from R5 (m) 474 1566
Distance from R6 (m) 765 1677
Detector Efficiency 80 % 80 %
Dead Time 7.2 % 0.5 %
Rate without efficiency (d−1) 2859 121
Rate with detector efficiency (d−1) 2287 97
Integrated rate (y−1) 6.20 105 2.82 104
Table 11: RENO antineutrino rates expected in the near and far detectors, with and without reactor and
detector efficiencies. The integrated rate in the last line includes detector efficiency, dead time, and reactor
off periods averaged over a year.
R1 R2 R3 R4 R5 R6
near 3.0 % 7.8 % 39.2 % 39.2 % 7.8 % 3.0 %
far 14.8 % 16.9 % 18.3 % 18.3 % 16.9 % 14.8 %
Table 12: RENO rate contributions from each reactor core.
sensitivity gained by statistics is compensated by a loss of information on the νe rates and energy spectra.
Thus the appeal of this site is diminished. The sensitivity is equivalent to a 5.8 GWth NPP reactor neutrino
experiment for σpwr = 2.0 %.
The RENO collaboration considers using 3 small very near detectors (200 – 300 kg) to monitor sub-groups
of cores of the NPP. However, taking into account current knowledge on reactor spectra (σabs = 2.0 %,
σshp = 2.0 % [15]), even dedicated detectors with 10
5 νe events will not improve the thermal power knowledge
below ∼ 2 %. Thus, the overall sin2(2θ13) sensitivity will not improve.
8 Discussion
We develop here a two step comparison of the experiments described before: Double Chooz phase I (single
detector, DC I ), phase II (both detectors, DC II ), Daya Bay phase I (DB Mid) and phase II (DB Full) and,
RENO (RN ). The first elements of comparison are based on a single core equivalent approach. Although
purely hypothetical, this analysis provides a lot of information on the impact of the layout of the site
(locations of NPP reactor cores and detectors). The second approach, giving far more information on the
impact of systematics on each experiment, is based on the pulls-approach, presented in section 3 and detailed
in the Appendix. Note that in the following discussion we adopt the approximation that all the NPP cores
operate with the same average efficiency. However, this assumption is not guaranteed, and, especially for
NPP with many reactors such as RENO and Daya Bay experiments, running time and procedure of each
NPP core have to be taken into account in the final analysis. For the Double Chooz experiment, which
places the near detector on the flux iso-ratio line of the far detector, the full running operation time and
procedure of each core is not needed to perform the final analysis.
8.1 The single core equivalent approach
First of all we may simplify each experiment to its roughest single core equivalent (SCE) with total matching
power P =
r=1 P
r, with P r the power of the rth reactor and Nr the number of available reactors on site.
In this case, we compute the sin2(2θ13) sensitivity for each experiment (see Table 13) for their baseline
option [25, 24, 26] but also for a single core equivalent, and the averaged near and far detector locations
computed with
)−1/2
. (11)
This average distance, L, yields the same event rates associated to near and far detectors of each experiment
except for the Daya Bay Phase II experiment. For this particular case, we have to compute this average
distance in two steps for the equivalent near detector. In this special case, since there are two near sites,
we compute the L for the DB near site, LDB, and for the LA near site, LLA, and then compute the overall
single near detector equivalent distance as
)−1/2
. (12)
Following this SCE simplification, numerical values of sin2(2θ13) sensitivity are gathered in Table 13. As
DC DB Mid DB Full RN
LA II OFF LA II ON
L (in r.n.u.) 17 67 101 303 71
Lfar (in m) 1,051 931 951 1,716 1579
Lnear (in m) 274 484 576 441
⋆ 325
sin2(2θ13)lim 0.0278 0.0410 0.0381 0.0110 0.0213
sin2(2θ13)
lim 0.0274 0.0274 0.0289 0.0105 0.0176
Table 13: In this table we provide the luminosity (expressed in r.n.u., see eq. (3)), sin2(2θ13)lim at 90 % C.L.
of Double Chooz (DC II ), Daya Bay phase I (DB Mid) and phase II (DB Full), and RENO (RN ). Also
quoted in this table are the average distances, L, to a single equivalent core (SCE) with total power
r=1 P
r (see text for explanations, the star (⋆) indicates a particular treatement). The sensitivity in
the SCE case, sin2(2θ13)
lim , is then computed to highlight possible drawback on the site configuration by
comparison with the baseline sensitivity sin2(2θ13)lim.
a first remark, the biggest discrepancy between sin2(2θ13)lim and sin
2(2θ13)
is as large as 40 % for
the DB Mid experiment. With four to six times higher luminosity compared to DC, a farther near site
from the cores and a closer far site, the sensitivity for the hypothetical DB Mid SCE experiment is not
improved with respect to DC. The discrepancy between DB Mid and DB Mid SCE clearly comes from the
wide repartition of NPP. LA cores can not be properly monitored at the DB near site. We conclude that
the DB Mid experiment is half way between an experiment with a single far detector and an experiment
with two identical detectors, one near and one far. One may notice that DC is an experiment where the
reactor cores may be considered as a single equivalent core with double power since there is only a less
than 1 % difference between DC and DC SCE. This is not the case for the RN experiment where the
relative discrepancy between RN and RN SCE is at the level of 15 %. Daya Bay Phase II, thanks to its two
near sites, is only marginally affected by a ∼ 5 % difference between DB Full and DB Full SCE (more on
section 8.2).
8.2 The pulls analysis
In this discussion we are interested in assessing how much a given experiment sensitivity relies on the
knowldege of the systematics (e.g.the number of systematics and the impact on sensitivity). The pulls-
approach is perfectly adapted to this analysis. The idea is to break down the total ∆χ2
∆χ2(slim) = χ
2(slim)− χ2min (13)
= min
{α1,...,αK}
χ2(slim, α1, . . . , αK)− min
{s,α1,...,αK}
χ2(s, α1, . . . , αK) ,
(where s is shorthand for sin2(2θ13)) (14)
into sub-parts δχ2i which represent their relative contribution to the overall ∆χ
2 of eq. (13). Since the
sensitivity limit on sin2(2θ13) is computed at 90 % C.L., ∆χ
2 has a common value for every experiment
and is equal to 2.71. Thus, δχ2i is defined as
δχ2i =
ith pull term
with the trivial induced normalization:
i = 1.
Table 14 shows the results of our computation for the baseline option of each experimental setup. We report,
together with the final sensitivities discussed earlier, the relative contributions δχ2i where δχ
N1,N2,F
are the
observables (the contribution from the first term in eq. (6) for the respective detector) and the other δχ2i
are the pulls (the weight term contributions in eq. (6)). Since the role of the far detector is to determine
δχ2i in % DC I DC II DB Mid DB Full RN
δχ2N1 — 3.0 % 4.3 % 1.1 % 1.5 %
δχ2N2 — — — 3.3 % —
δχ2F 29.5 % 38.0 % 23.4 % 31.2 % 34.4 %
29.1 % 1.5 % 9.0 % 1.0 % 7.9 %
18.4 % 1.3 % 8.4 % 0.5 % 1.0 %
δχ2rel — 48.3 % 6.6 % 56.8 % 28.5 %
δχ2scl,abs 6.5 % 1.2 % 6.1 % 0.1 % 0.1 %
δχ2scl,rel — 5.0 % 11.8 % 1.6 % 0.2 %
1.0 % 0.8 % 0.4 % 0.1 % 0.5 %
δχ2pwr 14.7 % 0.8 % 27.3 % 3.9 % 16.9 %
δχ2cmp 0.1 % 0.0 % 0.6 % 0.1 % 9.1 %
δχ2ε 0.6 % 0.0 % 2.2 % 0.3 % 0.0 %
sin2(2θ13)lim 0.054 0.028 0.041 0.011 0.021
Table 14: Relative contributions, δχ2i , to the global ∆χ
2. The higher is the δχ2i contribution, the more
the sin2(2θ13) sensitivity depends on the considered parameter. In red we highlight the main contributions
(20 – 60 %), in orange other significant terms (5 – 20 %). All the values are calculated for the base case of
each experimental setup. For the DB Full setup, where correlations between detectors on a same site are
possible, we take σrel half correlated and half uncorrelated between detectors of a same site, and completely
uncorrelated between detectors of different sites (see section 7.2 for details). Note that for Daya Bay we do
not include here batch-to-batch uncertainties.
sin2(2θ13), it is obvious that the associated residual should significantly contribute to the sensitivity. How-
ever what we see is that all computed sensitivities mainly depend on systematics, which contribute from 60 %
to 70 % of the overall ∆χ2. In the concept of identical detectors, correlated uncertainties between detectors
should weakly impact the sensitivity (at the level of near detector “precision”). This is automatically the
case if the near detector successfully monitors the NPP cores. Two of the quoted experimental setups reach
this goal: DC II and DB Full. Double Chooz, with its final two detector installation, has one dominant
systematic: the relative normalization uncertainty. The second most important contribution comes from
the relative energy scale uncertainty.
Daya Bay full installation is mostly limited by the relative normalization uncertainty. The weaker impact
of the relative energy scale uncertainties comes from the better far site distance to the NPP Cores. The
uncertainty on the energy scale matches less the oscillation induced distortion. On the other hand, three
of the described experimental setups still rely on theoretical knowledge of the spectrum and NPP cores
associated uncertainties: DC I, DB Mid and RN. In particular, the DB Mid installation is sensitive to
several systematics, especially the NPP power uncertainties. Taking data on a longer time scale (3 years,
for instance) with such a detector configuration will not improve the sin2(2θ13) sensitivity as much. Single
core power uncertainties do not weaken the sensitivity in two particular cases:
– if the near and far detectors have the same NPP core flux ratio contributions (this is the case of
DC II);
– if the far detector distance to each NPP core is the same, even if the spectra ratios are not the same in
near/far detectors. In this particular case, the oscillation pattern is not entangled with power uncer-
tainties in the far detector, since the νe travelling distances are the same. Power uncertainties would
only contribute, weakly, through the absolute normalization and correlations with other systematics
in the near detector.
The DB site configuration does not meet any of the above conditions. Moreover, for DB Mid, no near site
monitors the LA I NPP. This makes the DB Mid setup an intermediate between a two identical near/far
detector experiment and a single far detector configuration. Since the near site is farther away from the
NPP cores (Table 13), theoretical uncertainties on the spectrum have a larger impact than in DC II. Also,
since the average distance of DB Mid far site is closer, the oscillation pattern matches slightly better with
the energy scale associated distortion (bigger contribution than in DC II).
The RENO far site location is the best among the quoted setups in canceling the impact of the relative
and absolute energy scale uncertainties. However, because the site configuration does not fill any of the two
conditions for the cancellation of the NPP core power uncertainties, this experiment relies on the precision
with which each core power can be determined. Moreover, the near detector is a bit farther away than in
the DC II case, which explains why the global reactor νe rate is less effectively determined and have a larger
contribution than in DC II to the final sin2(2θ13) sensitivity.
8.3 Touching the “right systematic chord”
In the previous section we have determined the dominant systematics of each setup. In this section we
focus on the comparison of all the reactor experiments under the assumption that systematics are known
at the same level. Moreover, we want to illustrate the impact of the determination of the most significant
systematics on the sensitivity of each experimental setup:
• the single core power uncertainties;
• the relative normalization between detectors;
• the energy scale uncertainties (absolute and relative, between detectors).
In the CHOOZ experiment, the power uncertainties were assessed at 0.6 % [9]. However, this estimate
was uniquely based on the heat balance of the steam generators. Even if quite precise, this method could
be inaccurate. Other methods, such as the external neutron flux measurements, more directly linked to
the fission rates inside the cores, lead to a power evaluation less effectively determined with an assessed
error around 1.5 %. This latter method allows continuous tracking of the NPP core power variations. The
Double Chooz and Daya Bay proposals set their baseline estimates of these uncertainties at a conservative
value of 2 %. We studied the impact of this knowledge on the sensitivity by assuming two extreme scenarios:
in the worst case, a 3 % error, and the best case of 0.6 % precision. As a standard, we set central value
σpwr = 2.0 % for all the experiments.
The relative normalization between detectors is the most significant systematic in two identical detector
setups, with a near detector successfully monitoring the whole NPP (DC II and DB Full setups). The
Total
∆m231
0.4 0.6 0.8 1 1.2 1.4 1.6
Double Chooz Phase I
 sin2(2θ13)lim = 0.0539 (90 % C.L.)
Total
∆m231
0.4 0.6 0.8 1 1.2 1.4 1.6
Double Chooz Phase II
 sin2(2θ13)lim = 0.0235 (90 % C.L.)
Total
∆m231
0.4 0.6 0.8 1 1.2 1.4 1.6
Daya Bay Phase I
 sin2(2θ13)lim = 0.0402 (90 % C.L.)
Total
∆m231
0.4 0.6 0.8 1 1.2 1.4 1.6
Daya Bay Phase II
 sin2(2θ13)lim = 0.0106 (90 % C.L.)
Total
∆m231
0.4 0.6 0.8 1 1.2 1.4 1.6
 sin2(2θ13)lim = 0.0180 (90 % C.L.)
Common systematic framework
σabs 2.0 %
σshp 2.0 %
σrel 0.4 %
σpwr 2.0 %
0.5 %
(eV2) 2.5 10−3
Best Worst
σpwr 0.6 % 3.0 %
σrel 0.2 % 0.6 %
0.0 % 1.0 %
(eV2) 3 10−3 2 10−3
Figure 7: Double Chooz, Daya Bay and RENO sensitivities as a function of the size of the main systematics.
The common systematic framework is what experimentalists believe to be achievable, without any further
R&D. It is worth noting that the main difference between the common and the baseline cases comes from
Double Chooz, which takes a conservative value of the relative normalization at 0.6 %. The common
framework is used to compute the reference sin2(2θ13) sensitivity of each setup (value on top of each graph).
Then each systematic (σpwr, σrel, σscl) impact on sensitivity is separately computed and illustrated as
ratio R = sin2(2θ13)best or worst/ sin
2(2θ13)baseline on each graph. The overall impact changing all three
systematics together is also illustrated with the “Total” label. Moreover we also provide a quick guess on
sin2(2θ13) sensitivity behaviour as a function of ∆m
31 best fit value provided by other experiments. For the
Daya Bay Phase II experiment, where possible correlation between detectors on a same site may happen, we
take σrel half correlated and half uncorrelated between detectors of a same site, and completely uncorrelated
between detectors of different sites (see section 7.2 for details).
two available detailed quantifications of this uncertainty are the Double Chooz [24] and Daya Bay [25]
proposals. Each detector is estimated to measure the νe rate to a relative accuracy with respect to each
other of 0.39 % (DB Full) and 0.44 % (DC II). In the Double Chooz proposal, however, a conservative
value has been preferred for the baseline sensitivity calculation: σrel = 0.6 %. We will take this number
as the worst case. The Daya Bay collaboration plans, after some R&D, to reach a relative uncertainty of
0.2 %. This value has been taken as the best case. We set as a standard central value σrel = 0.4 % for all
experiments.
Even if we did not implement detector response in this simulations, we included energy scale uncertainties.
The Double Chooz proposal quotes σabs
= 0.5 % and σrel
= 0.5 %. This is taken as the common central
values for all the experiments. However, in the CHOOZ experiment [9], the energy scale uncertainty was
estimated at the level of 1.1 %. We thus take a 1.0 % uncertainty on both relative and absolute energy scale
determination as the worst case. As a best case, we switched off the impact of energy scale systematics on
the sensitivity.
Although the impact of the ∆m231 uncertainty on the sensitivity to sin
2(2θ13) is negligible with the current
knowledge, the central best fit value on this parameter from other experiments such as MINOS [8], K2K [7]
and SuperK [4], may have some influence on the reactor experiment sensitivities. We thus include the current
∆m231 bounds on the sensitivity computations: the “worst case” is taken to be ∆m
31 = 2.0 10
−3 eV2 and the
“best” one ∆m231 = 3.0 10
−3 eV2 (2 σ bounds from [13]). The standard central value for all the experiments
has been taken to be ∆m231 = 2.5 10
−3 eV2.
We illustrate in Figure 7 these three systematic scenarii: best, central and worst cases. Each contribution
is assessed separately, but we also show on this graph the total impact by summing the effect of the
three discussed systematics (σpwr, σrel and σscl) to their respective best, central and worst values. We also
illustrate the impact of the true central value of ∆m231 on the sensitivity. In this representation, we show the
ratio of the computed sensitivity sin2(2θ13)b,w for the best (resp. worst) case over the sensitivity sin
2(2θ13)c
for standard central systematic values. The “Total” bar shows that in Daya Bay and RENO the sensitivity
can vary from 0.6 to 1.2 – 1.3 of the baseline case, for experimental systematics ranging from a “best” to
a “worst” scenario. In the case of Double Chooz, the impact of systematics is less significant, at the level
of 20 % on both sides. In the Double Chooz and DB Mid cases, the sensitivity could be worsened for best
fit values of ∆m231 below 2.5 10
−3 eV2. In DB Full, the sensitivity is quite stable over the current allowed
range for ∆m231 with only a 5 % effect on sensitivity.
Double Chooz is an optimized experiment in the sense of robustness with respect to systematics for a goal
sensitivity in the 0.02 – 0.03 range. Daya Bay phase II is adequate to reach a sensitivity at the level of 0.01.
However, a simpler experiment for this class of sensitivity would be a scaled-up variant of Double Chooz,
with a very close near site at 150 m and a 1.5 km baseline for the far site. At the Diablo Canyon power
plant [19], where two 3.19 GWth cores are operational and modest civil engineering works would be required,
four 20 t detectors (2 near, 2 far) would give a sensitivity of 0.013 after 3 years of data taking.
9 Conclusion
In this work we have presented a detailed comparative analysis of the sensitivities to sin2(2θ13) of upcoming
and proposed reactor experiments.
We have first calculated the sensitivities using all available data published by the respective collaborations
for the baseline of both the systematical uncertainties and the experimental setups. Our results are generally
in good agreement with the sensitivities quoted by the collaborations: 0.054 for Double Chooz Phase I; 0.028
for Double Chooz Phase II; 0.041 for Daya Bay “mid”; 0.0089 for Daya Bay “full”; and 0.021 for RENO.
In the case of Daya Bay, we have additionally evaluated the impact of the proposed filling procedure,
with pairs of near-far detectors filled with the same scintillator batch and 4 different scintillator batches.
If the hydrogen mass fraction is controlled to 0.5 % between different batches, the sensitivity worsens
slightly to 0.0093. We also examined, still for Day Bay, the until-now implicit assumption that the errors
of the relative normalizations between the 8 detectors are fully uncorrelated. In reality this is the most
optimistic scenario, since a part of these uncertainties may come from site-dependent systematics. In the
most pessimistic scenario (all relative normalizations fully correlated for the same site), the Daya Bay
sensitivity would be 0.012.
An important result of this work is that the total thermal power available for an experiment, a figure of
merit that has been often used as a strong argument to “rank” different projects, has a modest impact on
the success of an experiment. Large powers are only available in multi-core sites, which are very difficult to
monitor. The associated systematics can be overwhelming with respect to the benefit from the statistics.
This is very nicely exemplified by the case of RENO, which would reach the same sensitivity with just 2 of
its 6 reactors on, and by Daya Bay “mid”, which results to be just half way between Double Chooz Phase I
and Double Chooz Phase II. We have illustrated how optimal is the use of the available thermal power in
each site through a comparison of the real experiments with ideal “single core equivalent” setups: Double
Chooz and Daya Bay “full” are nearly optimal, Daya Bay “mid” and RENO do not make full advantage of
their huge power. Daya Bay pays for the complexity of its nuclear power plant by the inevitable construction
of two near sites.
We have carried out a detailed and unified χ2−pull analysis for all the experiments, under common assump-
tions for all systematic uncertainties. This study allowed us to compare all projects on an equal footing and
evaluating the impact of each single systematic uncertainty on the sensitivity of each experiment. In this
calculation the Double Chooz baseline sensitivity is 0.0235 and a single systematic dominates, which is the
error of the relative normalization between near and far detector. This shows that taking into consideration
its small mass, Double Chooz is an optimized experiment. With respect to the other projects, the Double
Chooz sensitivity has a more pronounced dependence on the best fit ∆m213, with sin
2(2θ13)lim ranging from
0.020 to 0.031 for the currently 2 σ−allowed ∆m213 interval.
Daya Bay “full” proves to be robust with respect to the size of the systematical errors and to variations of
∆m213 and is the only partly approved project with an achievable sensitivity potential below 0.01. The Daya
Bay sensitivity is dominated by the accuracy of the relative normalization between detectors and the degree
of correlation existing on a same site between the latter parameters. With the knowledge of the systematics
we have today, the Daya Bay sensitivity would be on average between 0.0094 and 0.0123, depending on the
degree of correlation of the systematics between detectors on the same site.
Contrary to Double Chooz and Daya Bay, the sensitivity of RENO is largely degraded by the uncertainties
of the reactor powers and fuel composition. This, again, shows that the site is not optimal. Nevertheless,
due to the large target mass and optimal baseline, a very competitive sensitivity, around 0.02, is achievable.
This pull analysis also shows that the impact of the backgrounds on the χ2 is minor with respect to other
systematics. Backgrounds, at least in our simulation, are therefore not critical in any of the analyzed
experiments.
Taken into consideration all the above results, we come to a conclusion about the features of the optimal
experiment to approach a sin2(2θ13) sensitivity of 0.01. Where by “optimal” we mean a robust sensitivity,
the simplest configuration, the minimal amount of civil works and the smallest mass. Such an optimal
experiment would have a nuclear power plant layout as simple and powerful as Double Chooz; a favorable
topography for sufficiently deep underground laboratories, a very close, single near site, a ∼ 1.5 km baseline
for the far site and a total target mass of about the half of Daya Bay. Diablo Canyon, California, is a good
example of an suitable site for such an experiment.
Acknowledgement
We are greatful to A. Milsztajn for the careful proofreading of this article and his useful comments. We
wish also to acknowledge M. Lindner for fruitful discussions on the comparison of the θ13 experiments. It
is also a pleasure to thank M. Cribier and H. de Kerret for continuous helpful exchanges.
Appendix
In this section we first describe the way we computed event rates, and then the χ2 analysis implementation
with detailed systematic inclusions.
Event rates
The visible energy inside the detector has a simple expression as a function of the positron energy or neutrino
energy of the inverse β-decay reaction:
Evis = Ee+ +me ≃ Eν − Ethrν + 2me , (16)
where Ethrν = Mn−Mp+me is the νe threshold energy of the reaction. The event rates produced in reactor
R and recorded in detector D per visible energy bin [Ei;Ei+1] may be written as
i (θ13,∆m
31) =
∫ Ei+1−me
Ei−me
(Ee+ , Eν) (17)
(Ee+ , Eν) =
4πL2R,D
h(LR,D, L)σ(Eν)φ
R,D(Eν) ǫ(Ee+) (18)
×R(Ee+ , Eν)Pee(Eν , L, θ13,∆m231) ,
where h(LR,D, L), σ(Eν ), ǫ(Ee+), φ
R,D(Eν), R(Ee+ , Eν) stand for the finite size effect function the νe
inverse β-decay reaction cross section, the e+ detection efficiency, the νe flux from reactor R in detector D
and the energy response of the detector respectively. The generic normalization factor NR,D is the product
of the experiment life time by the number of available free protons inside the target volume, the global load
factor of reactor R and the dead time of detector D. The νe flux from reactor R in detector D is described
in term of the isotope composition as:
φR,D(Eν) = P
Efisℓ
ℓ (Eν) (19)
where ℓ = 235U, 238U, 239Pu, 241Pu labels the most important isotopes contributing to the νe flux, C
is the relative contribution of the isotope ℓ to the total reactor power (CRℓ = N
R, and Nfisℓ is the
number of fissions per second of isotope ℓ), Efisℓ is the energy release per fission for isotope ℓ and P
R is the
thermal power of reactor R. In eq. (19), φ
ℓ (Eν) is the energy differential number of neutrinos emitted
per fission by the isotope ℓ, and we adopt the parameterization for the φ
ℓ (Eν) from ref. [16]. For the C
we take a typical isotope composition in a nuclear reactor given in eq. (2).
We take for Pee the oscillation probability expressed in eq. (4). We assume in this article a constant efficiency
of ǫ(Ee+) = 80 % and a Gaussian energy response function
R(Ee+ , Eν) =
2πρ(Ee+)
Ee+ − Eν +Mn −Mp
2ρ(Ee+)
. (20)
with an energy resolution of ρ(Ee+) = 8 %/
Ee+ [MeV ]. The finite size effect function h(LR,D, L) is
assumed to be a Dirac distribution (pointlike sources and detectors) in this paper. The total event rates in
ith bin of detector D is then simply expressed as
NDi (θ13,∆m
31) =
R=R1,...,RNr
i (θ13,∆m
31) . (21)
χ2 analysis and systematics inclusion
The computed event rates, N
i , are then included in a χ
2 pull-approach analysis [14], where correlations
between the systematic uncertainties are properly included:
χ2 = min
i=1,...,Nb
D=D1,...,DN
∆Di −
k,k′=1
k,k′αk′ . (22)
with,
∆Di =
i −NDi
/UDi (23)
and UDi are given by eq. (9). The αk and S
i,k coefficients are described in Table 15.
The SDi,k coefficient represents the shift of the i
th bin of detector D spectrum due to a 1 σ variation in the
kth systematic uncertainty parameter αk. Most of the systematics are expressed as function of N
i of B
quantities already described previously. The energy scale systematic coefficients in SDi,k are defined through
MDi which follows the relation
MDi =
R=R1,...,RNr
i , (24)
where
∫ Ei+1−me
Ei−me
(Ee+ , Eν) . (25)
It is often assumed in the pull-approach that Wk,k′ = δk,k′ . If we keep this definition of Wk,k′ then we
are faced with the problem that the reactor spectrum shape uncertainties may contribute to the absolute
normalization error and the fuel composition uncertainties may contribute to the reactor core power errors.
If we want to get rid of these free contributions we could use two methods:
1. the first one consists to infer that
ℓ αcmp,ℓC
ℓ = 0
2. the second one is to introduce additional weight terms in the χ2 definition (22):
ℓ αcmp,ℓC
ℓ /εcmp
The first method allows disentangling fuel composition from power uncertainties. However, this assumption
is a bit too restrictive since in practice the sum
ℓ αcmp,ℓC
R = 0 is only constrained at the knowledge
level of the power of reactor R. The second method has the advantage of allowing an estimate of the level
of contribution of this systematic to the power uncertainties. Moreover this simply leads to redefining the
Wk,k′ matrix as
W−1k,k′ = δk,k′ +
ℓ,ℓ′,R
cmp,R
ℓ,ℓ′,k,k′
CRℓ C
ε2cmp
, (26)
cmp,R
ℓ,ℓ′,k,k′ =
δℓ,k−kR
δℓ′,k′−kR
if k, k′ ∈ {kR0 + 1, . . . , kR0 + 5},
kR0 = 5Nd +Nb +Nr + 2 + 4(R− 1),
0 otherwise.
With these definitions, εcmp determines at which level the fuel composition uncertainties are allowed to
contribute to the core power errors. One wants typically that fuel composition uncertainties contribute
within the allowed region of power uncertainty. Thus,
εcmp = σpwr/P
R . (28)
Regarding the fuel composition uncertainties, σcmp may be assessed roughly at the level of σpwr uncertainties:
σ2cmp = 2 − 3 % . (29)
Error type k SD
i,k ×UDi αDi,k
Absolute normalization 1 σabsN
i αabs
Relative normalization (Ns = 1)
in D1 Ns + 1 σrelN
in DNd Ns +Nd σrelN
Absolute Energy scale Nd + 2 σsclN
i αscl
Relative Energy scale (Ns = Nd + 2)
in D1 Ns + 1 σ
MD1i α
in DNd Ns +Nd σ
Backgrounds (Ns = 2Nd + 2)
accidentals in D1 Ns + 1 σ
BD11,i α
accidentals in DNd Ns +Nd σ
1,i α
cosmogenics in D1 Ns +Nd + 1 σ
BD12,i α
cosmogenics in DNd Ns + 2Nd σ
2,i α
proton recoils in D1 Ns + 2Nd + 1 σ
BD13,i α
proton recoils in DNd Ns + 3Nd σ
3,i α
Reactor spectrum shape (Ns = 5Nd + 2)
in bin 1 Ns + 1 σshpN
1 αshp,1
in bin Nb Ns +Nb σshpN
αshp,Nb
Reactor power (Ns = 5Nd +Nb + 2)
from R1 Ns + 1 σ
from RNr Ns +Nr σ
pwr N
RNr ,D
Reactor R composition (Ns = 5Nd +Nb +Nr + 2 + 4(R− 1))
from 235U Ns + 1 σcmpN
cmp,R
from 239Pu Ns + 2 σcmpN
cmp,R
from 238U Ns + 3 σcmpN
cmp,R
from 241Pu Ns + 4 σcmpN
cmp,R
Table 15: Systematic parameters table. We used the following definitions: Nb is the number of bins in the
reactor spectra, Nd is the number of detectors in the experiment, Nr is the number of reactor cores in the
NPP, Ns is short for the number of previously defined systematic parameters. For specific values of σabs,
σrel, σshp, σBD
, σpwr, σcmp, we refer to the experiment comparison sections 6 – 8.
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http://arxiv.org/abs/hep-ex/0402041
[24] F. Ardellier et al., hep-ex/0405032; S. Berridge et al., hep-ex/0410081; M. Goodman, Th. Lasserre et
al., hep-ex/0606025.
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hep-ex/0610024. Seminar of D. Jaffe at CEA/Saclay on 0ctober 23 2006,
www-dapnia.cea.fr/Phocea/file.php?class=std&file=Seminaires/1425/1425.pdf
[26] http://neutrino.snu.ac.kr/RENO/
[27] http://www.ba.infn.it/~now/now2006/Program/program.html
[28] M. Aoki et al., hep-ex/0607013.
[29] J.C. Anjos et al., hep-ex/0511059.
[30] CEA, Nuclear power plants in the world (2005).
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[31] Achkar B. et al., Phys. Lett. B374, 243(1996).
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[34] G. Mention, PhD. Thesis, http://doublechooz.in2p3.fr/
[35] M. Apollonio, et al., Eur. Phys. J. C27, (2003) 331, hep-ex/0301017.
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http://arxiv.org/abs/hep-ex/0405032
http://arxiv.org/abs/hep-ex/0410081
http://arxiv.org/abs/hep-ex/0606025
http://arxiv.org/abs/hep-ex/0701029
http://arxiv.org/abs/hep-ex/0610024
http://arxiv.org/abs/hep-ex/0607013
http://arxiv.org/abs/hep-ex/0511059
http://arxiv.org/abs/hep-ph/0211111
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http://doublechooz.in2p3.fr/
http://arxiv.org/abs/hep-ex/0301017
	Experimental context
	Neutrino oscillation at reactor and 13
	Generic analysis of 13 sensitivity
	Generic overview of systematic error inputs
	Backgrounds: description and modelization
	Comparison of the current proposals
	Detailed systematics review
	Impact of the scintillator composition
	Estimation of the -induced backgrounds
	Reactor experiments baseline sensitivity
	Double Chooz
	Daya Bay
	RENO
	Discussion
	The single core equivalent approach
	The pulls analysis
	Touching the ``right systematic chord''
	Conclusion

  We present in this article a detailed quantitative discussion of the
measurement of the leptonic mixing angle theta_13 through currently scheduled
reactor neutrino oscillation experiments. We thus focus on Double Chooz (Phase
I & II), Daya Bay (Phase I & II) and RENO experiments. We perform a unified
analysis, including systematics, backgrounds and accurate experimental setup in
each case. Each identified systematic error and background impact has been
assessed on experimental setups following published data when available and
extrapolating from Double Chooz acquired knowledge otherwise. After reviewing
the experiments, we present a new analysis of their sensitivities to sin^2(2
theta_13) and study the impact of the different systematics based on the pulls
approach. Through this generic statistical analysis we discuss the advantages
and drawbacks of each experimental setup.

RN.eps
A unified analysis of the reactor neutrino program
towards the measurement of the θ13 mixing angle
G. Mention
(a), Th. Lasserre (a,b), D. Motta (a)
(a)DAPNIA/SPP, CEA Saclay, 91191 Gif sur Yvette, France
(b) Laboratoire Astroparticule et Cosmologie (APC), Paris, France
November 9, 2018
Abstract
We present in this article a detailed quantitative discussion of the measurement of the leptonic
mixing angle θ13 through currently scheduled reactor neutrino oscillation experiments. We thus focus
on Double Chooz (Phase I & II), Daya Bay (Phase I & II) and RENO experiments. We perform a
unified analysis, including systematics, backgrounds and accurate experimental setup in each case. Each
identified systematic error and background impact has been assessed on experimental setups following
published data when available and extrapolating from Double Chooz acquired knowledge otherwise.
After reviewing the experiments, we present a new analysis of their sensitivities to sin2(2θ13) and study
the impact of the different systematics based on the pulls approach. Through this generic statistical
analysis we discuss the advantages and drawbacks of each experimental setup.
1 Experimental context
Over the last years the phenomenon of neutrino flavor conversion induced by nonzero neutrino masses
has been demonstrated by experiments with solar [1, 2, 3], atmospheric [4], reactor [5, 6] and accelerator
neutrinos [7, 8]. Neutrino oscillation, that can be described by the Pontecorvo–Maki–Nakagawa–Sakata
(PMNS) mixing matrix [11], is the current best mechanism to explain the data. Considering only the three
known families, the neutrino mixing matrix is parameterized by the three mixing angles (θ12, θ23, θ13) and a
possible δ CP violation phase. The angle θ12 has been measured to be large (sin
2(2θ12) ≃ 0.8), the angle θ23
has been measured to be close to maximum (sin2(2θ23) & 0.9); but the last angle θ13 has only been upper
bounded sin2(2θ13) . 0.15 at 90 % C.L., by the CHOOZ reactor experiment [9, 12]. These achievements
have now shifted the field of neutrino oscillation physics into a new era of precision measurements. Next
generation experiments are underway all around the world to further pin down the values of the oscillation
parameters of both solar and atmosheric driven oscillations. Currently the most important task, for the
experimentalists, is the determination of the last oscillation through the measurement of the unknown
mixing angle θ13. An improved sensitivity on θ13 is not only important for the understanding of neutrino
oscillations, but also to open up the possibility of observing CP-violation in the lepton sector if the θ13 driven
oscillation is discovered by the forthcoming experiments.
In order to improve the CHOOZ constraint on θ13 at least two identical unsegmented liquid scintillator
neutrino detectors close to a nuclear power plant (NPP) are required. The near detector(s) located a few
hundred meters away from the reactor cores monitor the unoscillated νe flux. The far detector(s) is(are)
located at a distance between 1 and 2 km, searching for a departure from the 1/L2 behavior induced by
oscillations. Experimental errors are being partially cancelled when using identical detectors. The goal is
to achieve an overall effective systematic error of less than 1 % [19, 34].
Three experiments have received partial or full approval to perform such a measurement in a near future:
Double Chooz in France [24], Daya Bay in China [25] and RENO in Korea [26]. In addition, a project is
http://arxiv.org/abs/0704.0498v2
under study at the Angra power plant in Brazil to further improve the sensitivity of the measurement on a
longer time scale [29]. Furthermore the Japanese KASKA collaboration is promoting the reactor neutrino
oscillation physics [28].
2 Neutrino oscillation at reactor and θ13
Fission reactors are prodigious sources of electron antineutrinos which have a continuous energy spectrum
up to about 10 MeV. For Eνe > Ethr = 1.806 MeV they can be detected though the νe+p → e++n reaction
using the delayed coincidence technique, where an electron antineutrino interacts with a free proton in a
tank containing a target volume filled with Gd loaded liquid scintillator. The positron and the resultant
annihilation gamma-rays are detected as a prompt signal while the neutron slows down and then thermalizes
in the liquid scintillator before being captured by a hydrogen or gadolinium nucleus. The excited nucleus
then emits gamma rays which are detected as the delayed signal. Electron antineutrinos energy is derived
from the measured visible energy from positron energy loss and annihilation,
Evis = Ee+ +me ≃ Eν − Ethrν + 2me . (1)
The νe spectrum is calculated from measurements of the beta decay spectra of
235U, 239Pu and 241Pu [15]
after fissioning by thermal neutrons and theoretical 238U spectrum, since no data are available for 238U 1.
As a nuclear reactor operates, the fission element proportions evolve in time (the so-called burn-up). Since
we are interested here on long term interpretation of the data for oscillation search, we will use an average
fuel composition for a reactor cycle corresponding to
235U (55.6 %), 239Pu (32.6 %), 238U (7.1 %) and 241Pu (4.7 %) . (2)
The mean energy release per fission, 〈Ef 〉, is then 205 MeV and the energy weighted cross section for
νep → e+n amounts to 〈σf 〉 = 6 10−43 cm2 per fission. Let us introduce a new luminosity unit, called the
r.n.u. (for reactor neutrino unit) and defined as 1 r.n.u. = 0.197 1060 MeV. With this unit, an experiment
taking data for T years with a total NPP (nuclear power plant) thermal power of P GW and with N 1030 free
protons inside the target has a luminosity L = T P N r.n.u.. The event number, N(L), at a distance L from
the source, assuming no - oscillation, can be quickly assessed with
N(L) =
〈σf 〉
4π 〈Ef 〉
≃ 4.6 109
1 GWth
For the full antineutrino reactor energy spectra simulation, we follow Vogel’s analytical parameteriza-
tion [16], based on second order Eν polynomials. Higher order parameterizations [18] give very comparable
results and do not require a specific attention for our aim in this article. The antineutrino event rates
per energy range is then computed according to the mean reactor core composition (2) and experimental
site specifications (reactor and detector locations, average efficiencies and running time as described in
section 6).
Reactor neutrino experiments measure the survival probability Pee which does not depend on the Dirac
δCP phase. In addition, the oscillation of MeV’s reactor neutrinos studied over a distance of a few kilome-
ters is not affected by the modification of the coherent forward scattering from matter electrons [32, 33].
Expanding the full three flavors νe oscillation probability as a function of (∆m
21/∆m
2 ≃ 1/302 ratio
and sin2(2θ13), Pee measurements from reactor experiments on the kilometer scale may be described by the
simplest two flavors oscillation formula:
Pee ≃ 1− sin2(2θ13) sin2
∆m231L
. (4)
as long as sin2(2θ13) & 10
−3. We assume that in eq. (4), ∆m231 is measured by other experiments (MINOS [8],
K2K [7] and super-K [4]). With a determination of ∆m231 better than 10 %, the impact on sin
2(2θ13)
1238U fissions only with fast neutrons. Theoretical predictions are computed by summing all known beta decay processes
contributing.
determination can be neglected [34]. All results within this study are, unless otherwise stated, computed
for a representative value of ∆m231 [13]:
∆m231 = 2.5
+0.25
−0.25 10
−3 eV2 at 68 % C.L.. (5)
3 Generic analysis of θ13 sensitivity
The calculation of event rates is a convolution of the νe flux spectrum, the cross section, the oscillation
probability, the detector efficiency with the energy response function.
The detector energy response simulation, as well as its correction through detector callibrations are specific
to each experiment. The details of the corrections are thus beyond the scope of this article. We therefore
assume in the following that the reconstructed energy is identical to the true deposited energy. We will
implement, anyway, a simple energy scale systematic uncertainty (section 6.1).
We based our event rates computations on an extended version of the numerical code developed for Dou-
ble Chooz [34, 24]. These computations take into account the characteristics of each experimental setup as
the number of reactors, detectors, locations, overburdens, efficiencies, operating time, and so on which will
be described in section 6.
The resulting event rates, then, form the basis for a χ2 analysis, where systematic uncertainties are properly
included. Since event rates in the disappearance channel of reactor experiments are quite large, we can use
a Gaussian χ2, which has the advantage of allowing a natural inclusion of systematic errors through the
so-called “pull-approach” [14]:
χ2 = min
i=1,...,Nb
D=D1,...,DN
∆Di −
k,k′=1
k,k′αk′
. (6)
This generic χ2 definition encompasses all the spectral information (i index) from each detector (D index)
and systematics parameterization through αk and S
i,k. For S
i,k = 0, we recover the classical χ
2 definition,
χ2no syst =
, through
∆Di =
i −NDi
/UDi (7)
where we assume that the simulated data event numbers, N
i , are uncorrelated between bins and detectors.
In the absence of real data, they are computed for fixed given values of ∆m231
⋆ and sin2(2θ13)
⋆. On the
other hand NDi , the theoretical model, relies on the searched sin
2(2θ13) value. We assume an uncorrelated
weight error UDi which, in the absence of systematic uncertainty, is simply expressed as the statistical error:
UDi =
NDi .
Systematic uncertainties are included in the χ2 definition (6) through αk and S
i,k coefficients. The S
coefficient represents the shift of the ith bin of detector D spectrum due to a 1 σ variation in the kth
systematic uncertainty parameter αk. Following this definition, we introduce bin, detector and reactor
correlations in the systematic errors through SDi,k definitions whereas systematic parameter correlations are
gathered in Wk,k′ (we refer to the appendix for details). Eventually, some fully uncorrelated systematic
uncertainties may be included through the UDi definition, by adding quadratically all their effects together
with the statistical uncertainty. We will use this property to include background shape uncertainties in
our analysis as described in section 5. We refer to the appendix for the proper inclusion and definition of
systematic coefficients SDi,k and αk inside the χ
2 definition (6).
We define the sensitivity or sensitivity limit sin2(2θ13)lim as the largest value of sin
2(2θ13) which fits the
true value sin2(2θ13)
⋆ = 0 at the chosen confidence level. We therefore determine the sin2(2θ13) sensitivity
at 90 % C.L. of an experiment as the value of sin2(2θ13) for which
∆χ2 = χ2(sin2(2θ13))− χ2min = 2.71 . (8)
4 Generic overview of systematic error inputs
Systematic errors can be classified into three main categories: reactor, detector and data analysis induced
uncertainties. In this section we provide a brief and generic description of the systematic uncertainties
included in our modelization. Details concerning specific experimental cases are given in sections 6, 7.
The dominant reactor induced systematic error comes from our limited knowledge of the physical processes
which produce electron antineutrinos in nuclear reactors. This leads to an overall normalization error on
the production rate of 1.9 % [9]. Similarily we include a 2.0 % uncertainty on the antineutrino spectral
shape [15], with the conservative hypothesis that the energy bins are not correlated among themselves.
Furthermore, even at a perfectly defined thermal power and with an absolute knowledge of the number of
antineutrinos emitted for each fission, an underlying uncertainty remains since the nuclear energy released
per fission is known to about 0.5 % [9]. In our model the last three uncertainties are taken to be fully
correlated between the nuclear cores.
We included another group of reactor induced systematics, taken to be uncorrelated between the reactor
cores: the uncertainty on the determination of the thermal power of each nuclear core, within 0.6 – 3 % and
the uncertainty on the isotopic composition of the nuclear core fuel elements, within 2 – 3 %. Also, finite
size and solid angle effects, distances bias between reactors and detectors, as well as displacements of the
neutrino production barycenter might affect the fluxes at the near detector(s) if they are close to the power
plants (below 200 m) up to a level of 0.1 %.
We did not implemented the uncertainty coming from neutrinos produced in the spent fuel pools, often
located within tens of meters from the nuclear cores since we could not gather all the relevant information
for the different sites. We thus neglect this effect in our simulation, whithout any justification except in
the case of Double Chooz, since a detailed evaluation has shown that this uncertainty does not affect its
sensitivity [24]. We point out that in particular cases this additional neutrino source slightly affects the
antineutrino spectrum, and is thus relevant for experiments aiming at high sensitivities, e.g. sin2(2θ13) ∼
0.01. We could also have introduced a specific error on the inverse-beta decay neutrino cross section of
0.1 % [9, 36]. However, being fully correlated between the detectors, the latter can be gathered into a global
uncertainty, adding up to the overall neutrino rate knowledge.
The basic principle of the multi-detector concept is the cancellation of the reactor induced systematics;
additional contributions would not modify significantly the sensitivities of the forthcoming experiments.
Let us now focus on the uncorrelated errors between detectors that could affect strongly the experimental
results.
The uncorrelated errors between detectors directly contribute to the relative normalization of the mea-
sured antineutrino energy spectrum of each detector. One of the major improvement with respect to the
CHOOZ experiment relies on the precise measurement of the number of free protons inside target volumes,
proportional to the antineutrino rates. Experimentally the target mass will be determined at 0.2 %. An
uncertainty on the fraction of free hydrogen per unit volume remains, at the level of 0.2 – 0.8 %, if different
batches of liquid scintillator are used to fill the detectors of a given experiment. This complex case diserve a
special treatment as described in section 7.2. We did not include any error associated with the measurement
of the live time of the experiments.
The last set of systematics concerns the selection cuts applied to extract the antineutrino signal and reject
the backgrounds. Neutrino events are identified as positrons followed in time by a single neutron captured on
a gadolinium nucleus. New detector designs have been proposed in order to simplify the analysis, reducing
the systematic errors while keeping high statistics and high detection efficiency. We accounted for three
uncertainties for both positron and neutron associated to a candidate event: the possibility of missing the
particle as it escapes the target (escape), the uncertainty related to the particle interactions2 (capture) and
2Note that it affects essentially the neutrons, since the Gd concentration might differ between the detectors if they are not
the identification cut based on the energy deposited in the detector active region (identification). Finally
we take into account the uncertainty on the efficiency of the delay cut and an error on the neutron unicity
of the event selections, whereas we do not consider any position vertex reconstruction. We provide in
section 6.1 (Table 1) the detailed systematic inputs necessary for our simulations. The uncertainty on these
efficiencies have been treated, otherwise stated, as uncorrelated between detectors. Uncertainties induced
by the background subtractions are discussed in sections 5 and 6.3.
5 Backgrounds: description and modelization
In this section we briefly review the three main kinds of background for the next generation of reactor
neutrino experiments: accidental coincidences, fast neutrons and the long-lived muon induced isotopes
9Li/8He. We then describe our simplified background modelization.
Naturally occurring radioactivity mostly creates accidental background, defined as a coincidence of a prompt
energy deposition between 0.5 and 10 MeV, followed by a delayed neutron-like event in the fiducial volume
of the detector within a few hundredths of a millisecond. Selection of high purity materials for detector
construction (scintillator, mineral oil, PMT’s, steel, etc.) and passive shielding provide an efficient handle
against this type of background. We assume that the accidental background rate can be measured in situ
with a precision of 10 %.
Cosmic ray muons will be the dominating trigger rate at the depth of all near detector sites. Even though the
energy deposition corresponds to about 2 MeV per centimeter path length (providing a strong discrimination
tool) they induce the main source of background.
Muon induced production of the radioactive isotopes 8He, 9Li and 11Li can not be correlated to the primary
muon interaction since their lifetimes are much longer than the characteristic time between two subsequent
muon interactions. The characteristic signature of this last class of events consists in a four-fold coincidence
(µ → n → β → n). The initial muon interaction is followed by the capture of spallation neutrons within
about 1 ms. The time scale of the decay of the considered isotopes is on the order of a few 100 ms, again
followed by a neutron capture. This background mimics the νe signal and is considered among the most
serious difficulty to overcome for the next generation reactor neutrino experiments. In our simulation we
will assume that it can be estimated to within 50 %.
A further source of background are neutrons that are produced in the surrounding rocks by radioactivity
and in cosmic ray muon induced hadronic cascades. In the latter case, which is dominant at shallow depth,
the primary cosmic ray muon may not penetrate the detector, being thus invisible. Fast neutrons may
then enter the detector and create recoil protons and be captured by hydrogen or gadolinium nuclei after
thermalization. Such a sequence can mimick a νe event. In the case of Double Chooz far detector (depth of
300 m.w.e.), muon induced neutron production can be fairly well estimated from the results of the CHOOZ
experiment, since it was the dominating backgroundmonitored during reactor off periods [9]. We will assume
that this background rate can be estimated within a factor of two. Figure 1 illustrates the background
spectra that we implemented in our modelization. We used the CHOOZ reactor off data [9] to estimate the
fast neutron background spectral shape, measured to be flat. We used a simple approximate exponential
shape for accidental backgrounds. Finally we implemented the spectra of 8He and 9Li based on nuclear data
information; we weighted them in the ratio 0.2/0.8, respectively. We checked that slight modifications of
the background shapes do not change the results of our simulations for sin2(2θ13) sensitivities above 0.01.
Background rates are adjusted to match to the predictions at each detector location. Afterward they are
subtracted from the total Evis spectrum in each detector. These three backgrounds, Bn, have rates and
shapes known at σBD
and σshp,BD
, respectively. We take the conservative assumption that these shape
uncertainties are fully uncorrelated between bins. Thus, the σshp,BD
contributions may be directly included
inside UDi (eq. (7)). These generic uncorrelated errors will then take into account the statistical and the
background shape subtraction uncertainties:
filled with a single batch of liquid scintillator.
0 1 2 3 4 5 6 7 8 9 10
Evis (MeV)
Proton recoils
Accidentals
Cosmogenics
Figure 1: Energy spectrum of the backgrounds from spallation neutrons, accidentals, and cosmogenic
20 % 8He and 80 % 9Li. Each curve is normalized to unity.
UDi =
NDi +
BDn,i + σ
shp,BD
BDn,i
As the background rate uncertainties are correlated between bins, we treat them with additional pull terms,
, in eq. (6), with weights σBD
included in SDi,k (see the appendix).
6 Comparison of the current proposals
Several sites are currently being considered for new reactor experiments to search for θ13: Angra dos
Reis (Angra, Brazil), Chooz (Double Chooz, France, and possibly Triple Chooz), Daya Bay (Daya Bay,
China), Kashiwazaki (KASKA, Japan) and Yonggwang (RENO, Korea). All these experiments may be
classified in two generations. The first aims to probe the value of sin2(2θ13) till 0.02 – 03, and the second to
track sin2(2θ13) down to 0.01 (90 % C.L.). The first phase concerns Double Chooz, RENO, and possibly
Daya Bay (with its phase I). This phase should end by 2013. Angra, Daya Bay (nominal setup with
8 detectors), KASKA and possibly Triple Chooz are focusing on the second phase. For these second
generation experiments, a significant R&D effort is required since the effective Gd-scintillator mass will be
increased by, at least, one order of magnitude, and systematics, as well as backgrounds uncertainties, have
to be further reduced with respect to the first phase experiments. In the following comparisons we will not
include Angra, KASKA and Triple Chooz. We will only focus on Double Chooz, Daya Bay and RENO.
In the next sections we first introduce a generic discussion on systematics, scintillator composition and
backgrounds (sections 6.1 to 6.3). We will then shortly describe each setup and compute the associated
baseline sensitivity (sections 7.1 to 7.3). We then perform a comparative analysis of the setups in section 8
to highlight advantages and drawbacks of each setup.
6.1 Detailed systematics review
The two Double Chooz [24] and Daya Bay [25] proposals take a careful inventory of systematics, compiled
in Table 1 for comparison. Double Chooz and Daya Bay estimates for the case of no additional R&D are
at hand. We decided to strictly use the systematic errors (Table 1) and background values quoted by the
collaborations [24, 25, 26]. However, we could not find any detailed background estimate for the RENO and
Daya Bay Mid site setups. In the latter cases we use a simple model to estimate the background subtraction
uncertainties from the scaling of the Double Chooz far detector (see section 6.3).
Error Description CHOOZ Double Chooz Daya Bay
No R&D R&D
Absolute Absolute Relative Absolute Relative Relative
Reactor
Production cross section 1.90 % 1.90 % 1.90 %
Core powers 0.70 % 2.00 % 2.00 %
Energy per fission 0.60 % 0.50 % 0.50 %
Solid angle/Bary. displct. 0.07 % 0.08 % 0.08 %
Detector
Detection cross section 0.30 % 0.10 % 0.10 %
Target mass 0.30 % 0.20 % 0.20 % 0.20 % 0.20 % 0.02 %
Fiducial volume 0.20 %
Target free H fraction 0.80 % 0.50 % ? 0.20 % 0.10 %
Dead time (electronics) 0.25 %
Analysis (paticle id.)
e+ escape (D) 0.10 %
e+ capture (C)
e+ identification cut (E) 0.80 % 0.10 % 0.10 %
n escape (D) 0.10 %
n capture (% Gd) (C) 0.85 % 0.30 % 0.30 % 0.10 % 0.10 % 0.10 %
n identification cut (E) 0.40 % 0.20 % 0.20 % 0.20 % 0.20 % 0.10 %
νe time cut (T) 0.40 % 0.10 % 0.10 % 0.10 % 0.10 % 0.03 %
νe distance cut (D) 0.30 %
unicity (n multiplicity) 0.50 % 0.05 % 0.05 %
Total 2.72 % 2.88 % 0.44 % 2.82 % 0.39 % 0.20 %
Table 1: Breakdown of the systematic errors included in the computation of the sensitivity of Dou-
ble Chooz [24] and Daya Bay [25]. Since no breakdown of the RENO systematic errors has been pub-
lished we use the same systematic error budget as for Double Chooz. Double Chooz and Daya Bay relative
systematics are almost comparable, the only main difference coming from the determination of the gadolin-
ium concentration and the free proton fraction inside the target volume. The absolute determination of
the free proton fraction can have some impact in Daya Bay since multiple batches will be used to fill all
the 8 detectors (see section 7.2 for details). Nevertheless, there is no published value in the Daya Bay
proposal [25].
Through all the available publications [24, 25, 26, 28], the differences between the systematics are found
only for the relative normalization of the dectetor (σrel) and the subtraction uncertainties on background
rates (σBD
). From section 4 and Table 1, we thus group systematics in two categories to be used in our χ2
analysis eq. (6):
1. generic systematics common to all the experiments (Table 2):
– σabs, the theoretical uncertainty on reactor antineutrino spectrum prediction. We call it also the
absolute normalization of event rates (since common to all the detectors), extracted from Table 1
without power uncertainty contributions. σabs is at the level of 2 %;
– σshp, the theoretical reactor spectrum shape uncertainty, at the level of 2 %;
– σabs
, σrel
, the absolute and relative energy scale uncertainties, roughly assessed at the level of
0.5 % each;
– σpwr, the reactor thermal power uncertainty, at the level of 2.0 %;
– σcmp, the reactor core specific fuel composition uncertainty which is roughly at the level of the
power uncertainties (2 – 3 %) on each fuel element.
σabs σshp σ
σpwr σcmp
2.0 % 2.0 % 0.5 % 0.5 % 2.0 % 2 – 3 %
Table 2: Generic systematic uncertainties as included in the χ2 analysis. For more details about the
correlations between the systematics, we refer to the appendix, and more particularly to Table 15.
2. specific systematics:
– σrel, the relative normalization of event rates between all the detectors. This uncertainty is
uncorrelated between detectors;
– σBD
, the background subtraction unceratinties, described in section 6.3.
6.2 Impact of the scintillator composition
In this section we stress the impact of the scintillator composition on the sensitivity of reactor neutrino
experiments. All current projects will use a gadolinium doped liquid scintillator to enhance the neutron
capture. The long-term stability of this scintillator is among the most difficult experimental challenges,
since a degradation of the scintillator transparency would induce large systematic uncertainties. In the
following we consider a stable scintillator for all experiments. The choice of the scintillating base has
some importance since it defines the free proton number per unit volume, the νe rate and proton recoil
background rate. Similarly the 12C number per volume drives the long-lived muon induced isotopes in the
target scintillator.
Different bases can be used as neutrino target scintillator, mixture of dodecane (DOD), pseudocumene
(PC) or phenylxylylethane (PXE), or linear alkylbenzene (LAB), as described in details in Table 3. If we
consider the Double Chooz scintillator (80 % DOD + 20 % PXE) as our reference, a pure LAB scintillator
contains 4.9 % less free proton per volume, and 9.5 % more carbon atoms. In the following we will assume
the Daya Bay [25] and RENO [26] experiments will use pure LAB as the target scintillator, and we will
renormalize the neutrino and the backgound rates accordingly in section 7.2 and 7.3.
6.3 Estimation of the µ-induced backgrounds
Our estimates of the backgrounds induced by cosmic muons is based on the Double Chooz proposal [24]. A
modification of the MUSIC code [20] was used to compute the muon rates and energy spectra by propagating
Liquid Formula density 1028H/m3 1028C/m3
Dodecane (DOD) C12H26 0.753 6.93 3.20
pseudocumene (PC) C9H12 0.88 5.30 3.97
phenylxylylethane (PXE) C16H18 0.985 5.08 4.52
90 % DOD+10 % PC mixture in vol. 0.77 6.77 3.32
80 % DOD+20 % PXE mixture in vol. 0.80 6.56 3.46
linear alkylbenzene (LAB) C16H30 0.86 6.24 3.79
Table 3: Impact of the scintillator composition on the target free proton number driving the νe rate
as well as the recoil proton background, and on the carbon composition which drives the long-lived muon
induced isotopes produced in the detector. In the following we consider that Double Chooz is using modules
containing 8.26 tons of 80 % dodecane +20 % PXE (in volume) based target scintillator, and that Daya Bay
and RENO are both using 20 ton modules of a LAB based target scintillator.
surface muons through rock. The site topographies have been included, according to a digitized map of the
Chooz hill profile [22] in the case of the far site (300 m.w.e. overburden), and according to a flat topography
in the case of the near site (80 m.w.e. overburden). For the far site this full Monte-Carlo simulation predicts
a muon flux Φµ=0.612± 0.007 m−2 s−1, slightly higher than the approximate measured value quoted in [9].
The mean muon energy computed according to this method is 〈Eµ〉 = 61 GeV. For the near site, we get
Φµ = 5.9 m
−2 s−1, and 〈Eµ〉 = 22 GeV. A similar detailed computation was performed for the three sites
of the Daya Bay collaboration [25].
Thus, for both the cases of Double Chooz and Daya Bay we use only the values of the muon flux and mean
energy computed by the collaborations. However, we could not find any published data for the case of
RENO. We then use the underground muon fluxes and mean energies calculated analytically following [21].
In order to justify this approximation, Table 4 reports the muon flux and mean energy computed by the
Double Chooz and the Daya Bay collaborations, from 300 m.w.e. to 923 m.w.e., as well as the analytical
computations according to [21]. We found a reasonable agreement which bears out the use of the analytical
model [21] for the case of the RENO sites (depths of 255 m.w.e. and 675 m.w.e.). Nevertheless, note
that the analytical simulation assumes a flat topography. It is worth noting, however, that the mean muon
energy predicted by the analytical computation is systematically ∼ 25 % lower in the depth range of interest.
Therefore we arbitrarily renormalize the analytical calculation by 25 % to estimate the mean muon energy
at the RENO sites. We also note a large discrepancy between the detailed computation and the analytical
model of [21] for the Double Chooz near site, probably due to its very shallow depth.
Cross sections of muon induced isotope production on liquid scintillator targets (12C) have been measured
by the NA54 experiment at the CERN SPS muon beam at 100 GeV and 190 GeV muon energies [23]. The
energy dependence was found to scale as σtot(Eµ) ∝ 〈Eµ〉α with α = 0.73± 0.10 averaged over the various
isotopes produced. We consider in the following that both long-lived muon induced isotopes and muon
induced fast neutron backgrounds scale as Φµ ×〈Eµ〉α, our reference being taken at the Chooz far site (full
Monte-Carlo simulation). We define the depth scaling factor as
DSF = (Φµ 〈Eµ〉α)/(Φµ 〈Eµ〉α)Double Chooz far , (10)
which is illustrated in the last column of Table 4 for various detector sites. Daily background rates computed
for Daya Bay, Double Chooz, and RENO detectors at the different sites are then given in Table 5.
Two cases are considered and compared: the background rates taken from the literature when available,
and the background rates extrapolated from the background computed for the Double Chooz far detector,
scaled with the target mass, the scintillator free proton and carbon numbers, as well as the depth scaling
factor (DSF). We note here the good agreement between the Daya Bay cosmogenic induced backgrounds
(9Li/8He and fast neutrons) estimated from our Double Chooz extended model and the original estimates
of the Daya Bay collaboration. This bears out the use of our model for the RENO and Daya Bay mid
site configurations. For the case of the 9Li/8He background, we understand well this agreement since
the background rate mainly depends on the mass of the neutrino target region. The agreement is more
Site depth (m.w.e.), Detailed simulation Analytical model DSF
topography Φµ 〈Eµ〉 Φµ 〈Eµ〉
m−2 s−1 GeV m−2 s−1 GeV
DC near 80, flat 5.9 22 9.9 17 6.80
RENO near 230, hill — — 1.2 40 1.57
DB near 1 255, hill 1.2 55 0.9 44 1.32
DB near 2 291, hill 0.73 60 0.72 49 1.06
DC far 300, hill 0.61 61 0.67 50 1
DB mid 541, hill 0.17 97 0.15 71 0.32
RENO far 675, hill — — 0.084 94 0.20
DB far 923, hill 0.04 138 0.035 118 0.10
Table 4: Muon flux Φµ and mean energy 〈Eµ〉 for the underground site of the reactor neutrino experiments.
We compare the values obtained from a full Monte-Carlo simulation for Double Chooz and Daya Bay to the
analytical model of [21]. We use the latter model for RENO. The depth scaling factor (DSF) is defined by
the product (Φµ×〈Eµ〉α)/(Φµ×〈Eµ〉α)Double Chooz far, the Double Chooz far site is taken as the reference.
Backgrounds induced by cosmic muons are scaled according to this factor.
Detector Accidental (d−1) µ-induced fast-n (d−1) µ-induced 9Li/8He (d−1)
Site Original DC ext. Original DC ext. Original DC ext.
Double Chooz near 13.60 ± 1.36 1.36 ± 1.36 9.52 ± 4.76
RENO near — 7.10 ± 0.71 — 0.68 ± 0.68 — 5.40 ± 2.70
Daya Bay DB 1.86± 0.19 5.98 ± 0.60 0.50 ± 0.50 0.57 ± 0.57 3.7 ± 1.85 4.55 ± 2.27
Daya Bay LA 1.52± 0.15 4.76 ± 0.48 0.35 ± 0.35 0.45 ± 0.45 2.5 ± 1.25 3.63 ± 1.81
Double Chooz far 2.00± 0.20 — 0.20 ± 0.20 — 1.40 ± 0.70 —
Daya Bay mid — 1.45 ± 0.14 — 0.14 ± 0.14 — 1.10 ± 0.57
RENO far — 0.90 ± 0.09 — 0.09 ± 0.09 — 0.69 ± 0.35
Daya Bay far 0.12± 0.01 0.44 ± 0.04 0.03 ± 0.03 0.04 ± 0.04 0.26 ± 0.13 0.33 ± 0.17
Table 5: Daily background rates computed for Daya Bay, Double Chooz, and RENO detectors at the
different sites. We consider the three main background sources: accidental events, µ-induced fast neutrons,
and µ-induced 9Li/8He. The columns labelled “Original” quote the background rates taken from the
literature when available. The columns labelled “DC ext.” (for extended) quote the background value
extrapolated from the background computed for the Double Chooz far detector, scaled with the detector
target mass, the scintillator free proton and carbon numbers, as well as the depth scaling factor (DSF).
Background subtraction systematic errors (%)
Detector Accidental µ-induced fast-n µ-induced 9Li/8He
Site Original DC ext. Original DC ext. Original DC ext.
Double Chooz near 0.123 0.123 0.043
RENO near — 0.019 — 0.019 — 0.074
Daya Bay DB 0.020 0.064 0.054 0.061 0.199 0.245
Daya Bay LA 0.020 0.063 0.046 0.060 0.164 0.239
Double Chooz far 0.292 — 0.292 — 1.020 —
Daya Bay mid — 0.120 — 0.115 — 0.458
RENO far — 0.100 — 0.095 — 0.382
Daya Bay far 0.010 0.036 0.025 0.035 0.108 0.138
Table 6: Background subtraction systematic errors (in percent) computed for Daya Bay, Double Chooz, and
RENO detectors at the different sites. We consider the three main background sources: accidental events,
µ-induced fast neutrons, and µ-induced 9Li/8He. The columns labelled “Original” quote the systematic
errors taken from the literature when available. The columns labelled “DC ext.” (for extended) quote
the systematic errors extrapolated from the Double Chooz far detector, taking into account the estimated
detector signal to background ratio as well as the background rate uncertainty.
surprising, however, for the case of the fast neutron background, since the size of the liquid shielding around
the detector active area is rather different between the Double Chooz and Daya Bay detectors (the RENO
detector design is very close to the Double Chooz case). In addition, further detector differences such as
the thickness of the buffer oil shielding the inner target region, as well as the different mechanical structure
explain the discrepancy between the Daya Bay computation and the DC extended model for the case of
the accidental background. Nevertheless, we found out that these differences influence only weakly the
sensitivity computed for the three experiments since the accidental background energy spectrum is different
enough from the expected oscillation signal, and it is supposed to be known with a precision of 10 %.
In a similar way, Table 6 gives the background subtraction systematic errors (in percent) computed for
Daya Bay, Double Chooz, and RENO detectors at the different sites, taking into account the estimated
detector signal to noise ratios as well as the background rate uncertainties.
7 Reactor experiments baseline sensitivity
7.1 Double Chooz
The Double Chooz collaboration is composed of institutes from Brazil, France, Germany, Japan, Russia,
Spain, United Kingdom, and the United States. The experimental site is located close to the twin reactor
cores of the Chooz nuclear power station (two PWR3 producing 8.5 GWth), operated by the French company
Électricité de France (EDF). The two, almost identical, detectors will contain a 8.3 ton fiducial volume of
liquid scintillator (density of 0.8) doped with 0.1 g/l of gadolinium (Gd). The far detector will be installed
in the existing laboratory, 1.05 km from the cores barycenter, shielded by 300 m.w.e. of rock. This detector
should be operating alone for 1.5 – 2 years (DC Phase I), starting data taking by the end of 2008. The
second detector will be installed in the meantime about 280 m from the nuclear core barycenter, at the
bottom of a 40 m shaft (80 m.w.e.) to be excavated. Distances between detectors and nuclear cores as well
as site overburdens are given in Table 7. Since there are no more than two NPP cores, it is still possible to
install the near detector at a suitable position where the ratio of reactor νe fluxes from each core is the same
as for the far detector (the iso-ratio curve is plotted on figure 2). This allows reactor relative uncertainty
cancellations (NPP core compositions). This detector should be operational by 2010, and will take data
3Pressurized Water Reactor
Detector near far
Distance from West reactor (m) 290.7 1114.6± 0.1
Distance from East reactor (m) 260.3 997.9± 0.1
Detector Efficiency 80 % 80 %
Dead Time 25 % 2.5 %
Rate without efficiency (d−1) 977 66
Rate with detector efficiency (d−1) 782 53
Integrated rate (y−1) 1.67 105 1.48 104
Table 7: Double Chooz antineutrinos rate expected in the near and far detectors, with and without reactor
and detector efficiencies. The integrated rate in the last line includes detector efficiency, dead time, and
reactor off periods averaged over a year. The averaged reactor global load factor is estimated at 79 % [30].
Figure 2: Double Chooz experiment site configuration. We show also on this figure the far flux iso-ratio
line. Another detector located on this particular curve will receive the same reactor flux ratio as for the far
detector: 44.5 % from West and 55.5 % from East reactor. The near detector of Double Chooz is foreseen
to be placed on this line.
for three years (DC Phase II). Other details concerning the experiment may be found in the collaboration
proposals [24].
For the Double Chooz phase I (DC Phase I) analysis, we used systematics of Table 2, setting σrel and
to 0 since only one detector will be present. For a data taking period of 1.5 years, the sensitivity
is sin2(2θ13)lim = 0.0544. The second phase (DC Phase II) will then start and both detectors will take
data for 3 years as scheduled in the proposal. The full experiment will then achieve a final sensitivity
sin2(2θ13)lim = 0.0278, assuming systematics from Table 2 and σrel = 0.6 % [24]. The sensitivity worsens
for ∆m231 < 2.5 10
−3 eV2, due to the close distance of the far detector4. If we take the lower bound [12, 13]
on ∆m231 (2.0 10
−3 eV2), Double Chooz will lose 30 % in sensitivity whereas for the upper bound [12, 13]
on ∆m231 (3.0 10
−3 eV2), Double Chooz will gain 15 % in sensitivity.
7.2 Daya Bay
Daya Bay is an experiment proposed by institutes from China, the United States, and Russia. Daya Bay [25]
will be located in the Guang-Dong Province, on the site of the Daya Bay nuclear power station. The site is
made up of two pairs of twin reactors, Daya Bay (DB) and Ling Ao I (LA I). An additional pair of reactors,
Ling Ao II (LA II), is currently under construction and should be operational by 2010 – 2011 [25]. Each
core has a thermal power of 2.9 GW [30]. In the full installation setup 3.3 km of tunnel and 3 detector halls
have to be excavated, in order to accommodate 8 detector modules [25]. Each module contains an effective
volume of 20 tons of Gd-loaded LAB liquid scintillator (Table 3). Distances between detectors and nuclear
cores as well as site overburdens are given in Table 8. This site yields a rather complex signal composition
Detector near DB near LA mid far
Distance from DB 1 (m) 350 1,356 1,153 1,970
Distance from DB 2 (m) 381 1,331 1,161 2,000
Distance from LA I 1 (m) 942 492 783 1,619
Distance from LA I 2 (m) 1,030 475 818 1,623
Distance from LA II 1 (m) 1,378 500 968 1,602
Distance from LA II 2 (m) 1,463 555 1,029 1,624
Detector eff. 80 % 80 % 80 % 80 %
Dead Time 7.2 % 4.3 % 1 % 0.2 %
Rate without eff. (d−1) 1,938 1,813 494 430
Rate with detector eff. (d−1) 1,550 1,450 395 344
Integrated rate (y−1) 4.10 105 3.95 105 1.11 105 9.77 104
Table 8: Daya Bay antineutrino rates expected in the near and far detectors, with and without reactor and
detector efficiencies. The integrated rate in the last line includes detector efficiency, dead time, and reactor
off periods averaged over a year. We assumed that LA II NPP will be operating for the time the far site
will be fully installed, but for the Mid site installation we assumed that LA II will be off.
in each detector coming from up to 6 different NPP cores, as shown in Table 9. According to the Day Bay
proposal, our estimate of the sensitivity is sin2(2θ13) = 0.0085 very close to the Daya Bay quoted value
(sin2(2θ13) = 0.008). However, in the Daya Bay proposal, the uncertainties on the reactor fuel composition,
σcmp, as well as the energy scale associated uncertainties σ
and σrel
are neglected. Taking into account
these systematics (Table 2) and the quoted value of σrel = 0.39 % with no R&D [25], our estimate of the
Daya Bay final sensitivity is then sin2(2θ13) = 0.009, with the full installation (DB Phase II, Figure 3)
after 3 years of data taking. We draw the attention of the reader on the point that these computations are
based on the assumption that σrel = 0.39 % is fully uncorrelated between all the detectors, and in particular
4a bit too close to the NPP to get the maximum amount of information from first minimum of oscillation over the reactor
spectrum distortion
DB LA1 LA2
near 1 (DB) 83.1 % 11.4 % 5.5 %
near 2 (LA) 6.5 % 50.6 % 42.8 %
Mid (LA2 OFF) 32.3 % 67.7 % 0.0 %
Mid (LA2 ON) 22.5 % 47.1 % 30.4 %
far 24.9 % 37.4 % 37.7 %
Table 9: Daya Bay rate contributions from each NPP set (2 cores by set) while assuming, except if otherwise
noticed (3rd line), the new Ling Ao II NPP is operating at full power.
between detectors on a same site. Nevertheless this hypothesis is not guarenteed. We discuss this point as
well as the current filling scenario (multi-batches) just below.
Figure 3: Daya Bay installation phases and site configuration. On the left: phase I, with 2 × (2 × 20 t)
detectors, Daya Bay and Ling Ao I power plants are operating. On the right: phase II with 2× (2× 20 t)
near sites, and 4× 20 t at far site, all three power plants are operational.
A preliminary fast phase (DB Phase I) is proposed by the Daya Bay collaboration. This phase includes only
4 detectors, 2 of them located at the DB near site and the other 2 at the mid site (see Figure 3). Taking
systematics from Table 2 and σrel = 0.39 % fully uncorrelated between detectors, we get a sensitivity after
1 year of data taking of sin2(2θ13) = 0.040. if LA II NPP is off. If DB Phase I starts after 2010, with LA II
operational, we get a sensitivity of sin2(2θ13) = 0.038 still after 1 year of data taking. The reason for a
better sensitivity in the second scenario is that the mid detectors get 44 % more νe events (Table 8, 9 and
Figure 3), with a larger oscillation baseline with respect to LA I.
Daya Bay site correlation
The main concept of the Daya Bay experiment is based on the multi-inter-calibration of detectors. Since
many detectors are installed on a same site, the total uncorrelated uncertainty of a site is decreased by
a factor of 1/
NSd compared to the single detector uncorrelated uncertainty, where N
d is the number of
detectors on a given site. In the Daya Bay proposal, the full relative uncertainty (σrel = 0.39 %) is assumed
to be uncorrelated between all the detectors. However, the fraction of correlated and non-correlated error
between detectors of a same site is not trivial. It relies on many experimental assumptions on uncertainty
correlations. The absence of correlations between detectors on a same site implies there will be no detector-
to-detector correction applied. If detector responses happen to be different, any data correction from
detector to detector on a same site would yield correlations between detector uncertainties.
For DB Phase II, if we assume that σrel is fully uncorrelated between the detectors, we get a sensitivity of
sin2(2θ13) = 0.009. On the contrary, if we assume that σrel is fully uncorrelated between detectors in different
sites, but fully correlated between detectors on a same site, we get a sensitivity of sin2(2θ13) = 0.012. The
real sensitivity should lay between these two extremes.
For DB Phase I, if we assume σrel is fully correlated on a same site and fully uncorrelated on distant sites,
we get sin2(2θ13) = 0.041 if LA II is off, and sin
2(2θ13) = 0.038 if LA II is on. We conlude from these results
that DB Mid sensitivity does not strongly depend on the correlations in σrel. More generally, DB Mid setup
weakly depends on σrel. This latter point will be discussed in section 8, together with a full description of
the impact of each systematic on the forseen sensitivity.
Daya Bay and the filling procedure
A large amount of Gd-loaded liquid scintillator will have to be produced, stored and filled into the detectors
(8×20 tons, which is 10 times more than in Double Chooz). Due to the large number of detectors and
the large amount of liquid to manage, the Daya Bay collaboration plans to fill detectors with four different
Gd-doped liquid scintillator batches. A single batch will be used to fill detectors by pairs [25] (Figure 4).
The best installation scenario (which is the one chosen by the Daya Bay collaboration) is then to move
one of the filled detector to a near site, the other one to the far site (scheme 1 of Figure 4 and Table 10).
Another batch of Gd-loaded liquid scintillator will be used for the next pair of detectors and so on. With
the adopted filling procedure [25], extra systematic uncertainties on the hydrogen content between different
batches have to be included.
DB LA
Pair 1
Pair 2
Pair 3
Pair 4
Scheme 1 Scheme 2 Scheme 3
Scheme 4 Scheme 5 Scheme 6
Figure 4: Possible installation of detector pairs in the Daya Bay experiment according to the adopted filling
procedure [25]. Due to the large number of detectors, and the large amount of liquid to be managed,
the Daya Bay collaboration plans to fill detectors by pairs with four different Gd-doped liquid scintillator
batches. The forseen detector installation scenario [25] corresponds to scheme 1. We illustrate here other
installation possibilities (schemes 2 to 6).
Although the relative uncertainty on the free proton content within a same batch could be kept at a very
low level (0.2 % in the Daya Bay proposal [25], negligeable in the Double Chooz proposal [24]), it is not
necessarily true in the case of different batches, in which the chemical composition may slightly change.
The free proton content between different batches relies then on the measurement of this quantity. In the
CHOOZ experiment [9], the free proton fraction inside the Gd-loaded liquid scintillator was known to 0.8 %.
In Double Chooz, this uncertainty is assessed at the level of 0.5 %. Since there is no published value on the
absolute determination of this quantity in the Daya Bay proposal, we assume here, as in Table 1, a 0.5 %
uncertainty between different batches. The filling systematic coefficients are explained in Table 10 (refer to
the appendix and to Table 15 for full description). The uncertainty on the free proton fraction of a single
Scheme 1
Scheme 2
Scheme 3
Scheme 4
Scheme 5
Scheme 6
0.008 0.01 0.012 0.014 0.016
(2θ13)
Single batch
Four batches
Figure 5: Sensitivity on sin2(2θ13) at 90 % C.L. after 3 years of data taking for the 6 different installation
schemes illustrated on Figure 4, with σpair = 0.5 %. Left bounds are computed assuming uncorrelated errors
between all the detectors and right bounds are for the assumption of full correlation of σrel between detectors
of a same site. The real sensitivity should be somewhere in between these two bounds. For comparison,
we also show on this graph the computations for the single batch hypothesis where we take σrel = 0.39 %.
Note that obviously the first installation scheme provides the best sensitivity. In these results we do not
include any detector swapping scenario.
Error type k SD
Filling (Ns = 5Nd +Nb + 5Nr + 2)
of batch 1 Ns +1 σpair
αpair,1
of batch 2 Ns +2 σpair
αpair,2
of batch 3 Ns +3 σpair
αpair,3
of batch 4 Ns +4 σpair
αpair,4
Table 10: Daya Bay, phase II (8 detectors), specific filling systematic parameters table in addition to
standard one (see the appendix for details). Here we adopt a fully uncorrelated uncertainty of the different
batches, σpair = 0.5 %, but fully correlated in a same batch.
batch is taken to σpair = 0.5 %. This uncertainty is taken to be fully correlated when detectors are filled
with the same batch and fully uncorrelated otherwise.
According to this filling procedure, the final sensitivity of DB Phase II would be sin2(2θ13) = 0.0093
instead of 0.0089 with the initial installation scenario (scheme 1 of Figure 4). In all the other configuration
schemes (2 – 6), which allows comparing on a same site at least two detectors filled with the same batch,
the sensitivity is more largely weakened (Figure 5), to an extent depending on σpair.
Note that we did not include any detector swapping option in previous conclusions. In the Day Bay proposal,
the retained installation scenario is the first scheme of Figure 4. The baseline swapping option is then the
permutation of two detectors filled with the same batch, in 4 steps, 1 step per batch. On the one hand,
the drawback of such a swapping scenario is that two detectors filled with the same batch will never be
directly compared. On the other hand, configuration schemes 2 – 6 allow detector intercalibration within a
pair. However, it should be noticed that the time spent in any configuration different from scheme 1 may
decrease the combined final sin2(2θ13) sensitivity (Figure 5).
7.3 RENO
The RENO experiment [26] will be located close to the Yonggwang nuclear power plant in Korea, about
400 km south of Seoul. The power plant is a complex of six PWR reactors, each of them producing a thermal
power of 2.74 GW [30]. The Yonggwong power station is ranked number 4 in the world, with a total thermal
power of 16.4 GW. Its power rating is often cited as an advantage of the RENO experiment. These six
reactors are equally distributed on a straight segment spanning over 1.5 km. The average cumulative
operating factors for the reactors are all above 80 %. Figure 6 shows the foreseen layout of the experimental
site. The near and far detectors will be located 150 m and 1,500 m away from the center of the reactor
Figure 6: RENO experiment site configuration.
row (Table 11), and will be shielded by a 88 m hill (230 m.w.e.) and a 260 m “mountain” (675 m.w.e.)
respectively. Two neutrino laboratories have to be excavated and equipped in order to host the detectors.
They will be located at the bottom of two tunnels having a length of 100 m and 600 m for near and far
detector, respectively. In this configuration, the flux contribution from R1 to R6 ranges from 3 % to 39 %
for the near detector, and from 15 % to 18 % for the far detector (Table 12).
Assuming the sytematics of Table 1 and, lacking of published data, fixing σrel = 0.6 % as for Double Chooz,
we obtain a final sensitivity after 3 years of data taking of sin2(2θ13) = 0.021. This is calculated for
2× 20 t detectors. However, a recent talk [27], quotes a different detector size, with 15 t of Gd-doped liquid
scintillator. In that case, the final sensitivity after 3 years, would be sin2(2θ13) = 0.023.
As seen from Table 12, the near detector monitors mainly the two central NPP cores, and the experiment
sensitivity is quite affected by the reactor power uncertainties. If we compute the sensitivity with only the
2 central NPP cores, we get even better results compared to the full NPP configuration. This means that
four of the six cores are useless for the sin2(2θ13) measurement. This can be understood by the fact that the
Detector near far
Distance from R1 (m) 765 1677
Distance from R2 (m) 474 1566
Distance from R3 (m) 212 1507
Distance from R4 (m) 212 1507
Distance from R5 (m) 474 1566
Distance from R6 (m) 765 1677
Detector Efficiency 80 % 80 %
Dead Time 7.2 % 0.5 %
Rate without efficiency (d−1) 2859 121
Rate with detector efficiency (d−1) 2287 97
Integrated rate (y−1) 6.20 105 2.82 104
Table 11: RENO antineutrino rates expected in the near and far detectors, with and without reactor and
detector efficiencies. The integrated rate in the last line includes detector efficiency, dead time, and reactor
off periods averaged over a year.
R1 R2 R3 R4 R5 R6
near 3.0 % 7.8 % 39.2 % 39.2 % 7.8 % 3.0 %
far 14.8 % 16.9 % 18.3 % 18.3 % 16.9 % 14.8 %
Table 12: RENO rate contributions from each reactor core.
sensitivity gained by statistics is compensated by a loss of information on the νe rates and energy spectra.
Thus the appeal of this site is diminished. The sensitivity is equivalent to a 5.8 GWth NPP reactor neutrino
experiment for σpwr = 2.0 %.
The RENO collaboration considers using 3 small very near detectors (200 – 300 kg) to monitor sub-groups
of cores of the NPP. However, taking into account current knowledge on reactor spectra (σabs = 2.0 %,
σshp = 2.0 % [15]), even dedicated detectors with 10
5 νe events will not improve the thermal power knowledge
below ∼ 2 %. Thus, the overall sin2(2θ13) sensitivity will not improve.
8 Discussion
We develop here a two step comparison of the experiments described before: Double Chooz phase I (single
detector, DC I ), phase II (both detectors, DC II ), Daya Bay phase I (DB Mid) and phase II (DB Full) and,
RENO (RN ). The first elements of comparison are based on a single core equivalent approach. Although
purely hypothetical, this analysis provides a lot of information on the impact of the layout of the site
(locations of NPP reactor cores and detectors). The second approach, giving far more information on the
impact of systematics on each experiment, is based on the pulls-approach, presented in section 3 and detailed
in the Appendix. Note that in the following discussion we adopt the approximation that all the NPP cores
operate with the same average efficiency. However, this assumption is not guaranteed, and, especially for
NPP with many reactors such as RENO and Daya Bay experiments, running time and procedure of each
NPP core have to be taken into account in the final analysis. For the Double Chooz experiment, which
places the near detector on the flux iso-ratio line of the far detector, the full running operation time and
procedure of each core is not needed to perform the final analysis.
8.1 The single core equivalent approach
First of all we may simplify each experiment to its roughest single core equivalent (SCE) with total matching
power P =
r=1 P
r, with P r the power of the rth reactor and Nr the number of available reactors on site.
In this case, we compute the sin2(2θ13) sensitivity for each experiment (see Table 13) for their baseline
option [25, 24, 26] but also for a single core equivalent, and the averaged near and far detector locations
computed with
)−1/2
. (11)
This average distance, L, yields the same event rates associated to near and far detectors of each experiment
except for the Daya Bay Phase II experiment. For this particular case, we have to compute this average
distance in two steps for the equivalent near detector. In this special case, since there are two near sites,
we compute the L for the DB near site, LDB, and for the LA near site, LLA, and then compute the overall
single near detector equivalent distance as
)−1/2
. (12)
Following this SCE simplification, numerical values of sin2(2θ13) sensitivity are gathered in Table 13. As
DC DB Mid DB Full RN
LA II OFF LA II ON
L (in r.n.u.) 17 67 101 303 71
Lfar (in m) 1,051 931 951 1,716 1579
Lnear (in m) 274 484 576 441
⋆ 325
sin2(2θ13)lim 0.0278 0.0410 0.0381 0.0110 0.0213
sin2(2θ13)
lim 0.0274 0.0274 0.0289 0.0105 0.0176
Table 13: In this table we provide the luminosity (expressed in r.n.u., see eq. (3)), sin2(2θ13)lim at 90 % C.L.
of Double Chooz (DC II ), Daya Bay phase I (DB Mid) and phase II (DB Full), and RENO (RN ). Also
quoted in this table are the average distances, L, to a single equivalent core (SCE) with total power
r=1 P
r (see text for explanations, the star (⋆) indicates a particular treatement). The sensitivity in
the SCE case, sin2(2θ13)
lim , is then computed to highlight possible drawback on the site configuration by
comparison with the baseline sensitivity sin2(2θ13)lim.
a first remark, the biggest discrepancy between sin2(2θ13)lim and sin
2(2θ13)
is as large as 40 % for
the DB Mid experiment. With four to six times higher luminosity compared to DC, a farther near site
from the cores and a closer far site, the sensitivity for the hypothetical DB Mid SCE experiment is not
improved with respect to DC. The discrepancy between DB Mid and DB Mid SCE clearly comes from the
wide repartition of NPP. LA cores can not be properly monitored at the DB near site. We conclude that
the DB Mid experiment is half way between an experiment with a single far detector and an experiment
with two identical detectors, one near and one far. One may notice that DC is an experiment where the
reactor cores may be considered as a single equivalent core with double power since there is only a less
than 1 % difference between DC and DC SCE. This is not the case for the RN experiment where the
relative discrepancy between RN and RN SCE is at the level of 15 %. Daya Bay Phase II, thanks to its two
near sites, is only marginally affected by a ∼ 5 % difference between DB Full and DB Full SCE (more on
section 8.2).
8.2 The pulls analysis
In this discussion we are interested in assessing how much a given experiment sensitivity relies on the
knowldege of the systematics (e.g.the number of systematics and the impact on sensitivity). The pulls-
approach is perfectly adapted to this analysis. The idea is to break down the total ∆χ2
∆χ2(slim) = χ
2(slim)− χ2min (13)
= min
{α1,...,αK}
χ2(slim, α1, . . . , αK)− min
{s,α1,...,αK}
χ2(s, α1, . . . , αK) ,
(where s is shorthand for sin2(2θ13)) (14)
into sub-parts δχ2i which represent their relative contribution to the overall ∆χ
2 of eq. (13). Since the
sensitivity limit on sin2(2θ13) is computed at 90 % C.L., ∆χ
2 has a common value for every experiment
and is equal to 2.71. Thus, δχ2i is defined as
δχ2i =
ith pull term
with the trivial induced normalization:
i = 1.
Table 14 shows the results of our computation for the baseline option of each experimental setup. We report,
together with the final sensitivities discussed earlier, the relative contributions δχ2i where δχ
N1,N2,F
are the
observables (the contribution from the first term in eq. (6) for the respective detector) and the other δχ2i
are the pulls (the weight term contributions in eq. (6)). Since the role of the far detector is to determine
δχ2i in % DC I DC II DB Mid DB Full RN
δχ2N1 — 3.0 % 4.3 % 1.1 % 1.5 %
δχ2N2 — — — 3.3 % —
δχ2F 29.5 % 38.0 % 23.4 % 31.2 % 34.4 %
29.1 % 1.5 % 9.0 % 1.0 % 7.9 %
18.4 % 1.3 % 8.4 % 0.5 % 1.0 %
δχ2rel — 48.3 % 6.6 % 56.8 % 28.5 %
δχ2scl,abs 6.5 % 1.2 % 6.1 % 0.1 % 0.1 %
δχ2scl,rel — 5.0 % 11.8 % 1.6 % 0.2 %
1.0 % 0.8 % 0.4 % 0.1 % 0.5 %
δχ2pwr 14.7 % 0.8 % 27.3 % 3.9 % 16.9 %
δχ2cmp 0.1 % 0.0 % 0.6 % 0.1 % 9.1 %
δχ2ε 0.6 % 0.0 % 2.2 % 0.3 % 0.0 %
sin2(2θ13)lim 0.054 0.028 0.041 0.011 0.021
Table 14: Relative contributions, δχ2i , to the global ∆χ
2. The higher is the δχ2i contribution, the more
the sin2(2θ13) sensitivity depends on the considered parameter. In red we highlight the main contributions
(20 – 60 %), in orange other significant terms (5 – 20 %). All the values are calculated for the base case of
each experimental setup. For the DB Full setup, where correlations between detectors on a same site are
possible, we take σrel half correlated and half uncorrelated between detectors of a same site, and completely
uncorrelated between detectors of different sites (see section 7.2 for details). Note that for Daya Bay we do
not include here batch-to-batch uncertainties.
sin2(2θ13), it is obvious that the associated residual should significantly contribute to the sensitivity. How-
ever what we see is that all computed sensitivities mainly depend on systematics, which contribute from 60 %
to 70 % of the overall ∆χ2. In the concept of identical detectors, correlated uncertainties between detectors
should weakly impact the sensitivity (at the level of near detector “precision”). This is automatically the
case if the near detector successfully monitors the NPP cores. Two of the quoted experimental setups reach
this goal: DC II and DB Full. Double Chooz, with its final two detector installation, has one dominant
systematic: the relative normalization uncertainty. The second most important contribution comes from
the relative energy scale uncertainty.
Daya Bay full installation is mostly limited by the relative normalization uncertainty. The weaker impact
of the relative energy scale uncertainties comes from the better far site distance to the NPP Cores. The
uncertainty on the energy scale matches less the oscillation induced distortion. On the other hand, three
of the described experimental setups still rely on theoretical knowledge of the spectrum and NPP cores
associated uncertainties: DC I, DB Mid and RN. In particular, the DB Mid installation is sensitive to
several systematics, especially the NPP power uncertainties. Taking data on a longer time scale (3 years,
for instance) with such a detector configuration will not improve the sin2(2θ13) sensitivity as much. Single
core power uncertainties do not weaken the sensitivity in two particular cases:
– if the near and far detectors have the same NPP core flux ratio contributions (this is the case of
DC II);
– if the far detector distance to each NPP core is the same, even if the spectra ratios are not the same in
near/far detectors. In this particular case, the oscillation pattern is not entangled with power uncer-
tainties in the far detector, since the νe travelling distances are the same. Power uncertainties would
only contribute, weakly, through the absolute normalization and correlations with other systematics
in the near detector.
The DB site configuration does not meet any of the above conditions. Moreover, for DB Mid, no near site
monitors the LA I NPP. This makes the DB Mid setup an intermediate between a two identical near/far
detector experiment and a single far detector configuration. Since the near site is farther away from the
NPP cores (Table 13), theoretical uncertainties on the spectrum have a larger impact than in DC II. Also,
since the average distance of DB Mid far site is closer, the oscillation pattern matches slightly better with
the energy scale associated distortion (bigger contribution than in DC II).
The RENO far site location is the best among the quoted setups in canceling the impact of the relative
and absolute energy scale uncertainties. However, because the site configuration does not fill any of the two
conditions for the cancellation of the NPP core power uncertainties, this experiment relies on the precision
with which each core power can be determined. Moreover, the near detector is a bit farther away than in
the DC II case, which explains why the global reactor νe rate is less effectively determined and have a larger
contribution than in DC II to the final sin2(2θ13) sensitivity.
8.3 Touching the “right systematic chord”
In the previous section we have determined the dominant systematics of each setup. In this section we
focus on the comparison of all the reactor experiments under the assumption that systematics are known
at the same level. Moreover, we want to illustrate the impact of the determination of the most significant
systematics on the sensitivity of each experimental setup:
• the single core power uncertainties;
• the relative normalization between detectors;
• the energy scale uncertainties (absolute and relative, between detectors).
In the CHOOZ experiment, the power uncertainties were assessed at 0.6 % [9]. However, this estimate
was uniquely based on the heat balance of the steam generators. Even if quite precise, this method could
be inaccurate. Other methods, such as the external neutron flux measurements, more directly linked to
the fission rates inside the cores, lead to a power evaluation less effectively determined with an assessed
error around 1.5 %. This latter method allows continuous tracking of the NPP core power variations. The
Double Chooz and Daya Bay proposals set their baseline estimates of these uncertainties at a conservative
value of 2 %. We studied the impact of this knowledge on the sensitivity by assuming two extreme scenarios:
in the worst case, a 3 % error, and the best case of 0.6 % precision. As a standard, we set central value
σpwr = 2.0 % for all the experiments.
The relative normalization between detectors is the most significant systematic in two identical detector
setups, with a near detector successfully monitoring the whole NPP (DC II and DB Full setups). The
Total
∆m231
0.4 0.6 0.8 1 1.2 1.4 1.6
Double Chooz Phase I
 sin2(2θ13)lim = 0.0539 (90 % C.L.)
Total
∆m231
0.4 0.6 0.8 1 1.2 1.4 1.6
Double Chooz Phase II
 sin2(2θ13)lim = 0.0235 (90 % C.L.)
Total
∆m231
0.4 0.6 0.8 1 1.2 1.4 1.6
Daya Bay Phase I
 sin2(2θ13)lim = 0.0402 (90 % C.L.)
Total
∆m231
0.4 0.6 0.8 1 1.2 1.4 1.6
Daya Bay Phase II
 sin2(2θ13)lim = 0.0106 (90 % C.L.)
Total
∆m231
0.4 0.6 0.8 1 1.2 1.4 1.6
 sin2(2θ13)lim = 0.0180 (90 % C.L.)
Common systematic framework
σabs 2.0 %
σshp 2.0 %
σrel 0.4 %
σpwr 2.0 %
0.5 %
(eV2) 2.5 10−3
Best Worst
σpwr 0.6 % 3.0 %
σrel 0.2 % 0.6 %
0.0 % 1.0 %
(eV2) 3 10−3 2 10−3
Figure 7: Double Chooz, Daya Bay and RENO sensitivities as a function of the size of the main systematics.
The common systematic framework is what experimentalists believe to be achievable, without any further
R&D. It is worth noting that the main difference between the common and the baseline cases comes from
Double Chooz, which takes a conservative value of the relative normalization at 0.6 %. The common
framework is used to compute the reference sin2(2θ13) sensitivity of each setup (value on top of each graph).
Then each systematic (σpwr, σrel, σscl) impact on sensitivity is separately computed and illustrated as
ratio R = sin2(2θ13)best or worst/ sin
2(2θ13)baseline on each graph. The overall impact changing all three
systematics together is also illustrated with the “Total” label. Moreover we also provide a quick guess on
sin2(2θ13) sensitivity behaviour as a function of ∆m
31 best fit value provided by other experiments. For the
Daya Bay Phase II experiment, where possible correlation between detectors on a same site may happen, we
take σrel half correlated and half uncorrelated between detectors of a same site, and completely uncorrelated
between detectors of different sites (see section 7.2 for details).
two available detailed quantifications of this uncertainty are the Double Chooz [24] and Daya Bay [25]
proposals. Each detector is estimated to measure the νe rate to a relative accuracy with respect to each
other of 0.39 % (DB Full) and 0.44 % (DC II). In the Double Chooz proposal, however, a conservative
value has been preferred for the baseline sensitivity calculation: σrel = 0.6 %. We will take this number
as the worst case. The Daya Bay collaboration plans, after some R&D, to reach a relative uncertainty of
0.2 %. This value has been taken as the best case. We set as a standard central value σrel = 0.4 % for all
experiments.
Even if we did not implement detector response in this simulations, we included energy scale uncertainties.
The Double Chooz proposal quotes σabs
= 0.5 % and σrel
= 0.5 %. This is taken as the common central
values for all the experiments. However, in the CHOOZ experiment [9], the energy scale uncertainty was
estimated at the level of 1.1 %. We thus take a 1.0 % uncertainty on both relative and absolute energy scale
determination as the worst case. As a best case, we switched off the impact of energy scale systematics on
the sensitivity.
Although the impact of the ∆m231 uncertainty on the sensitivity to sin
2(2θ13) is negligible with the current
knowledge, the central best fit value on this parameter from other experiments such as MINOS [8], K2K [7]
and SuperK [4], may have some influence on the reactor experiment sensitivities. We thus include the current
∆m231 bounds on the sensitivity computations: the “worst case” is taken to be ∆m
31 = 2.0 10
−3 eV2 and the
“best” one ∆m231 = 3.0 10
−3 eV2 (2 σ bounds from [13]). The standard central value for all the experiments
has been taken to be ∆m231 = 2.5 10
−3 eV2.
We illustrate in Figure 7 these three systematic scenarii: best, central and worst cases. Each contribution
is assessed separately, but we also show on this graph the total impact by summing the effect of the
three discussed systematics (σpwr, σrel and σscl) to their respective best, central and worst values. We also
illustrate the impact of the true central value of ∆m231 on the sensitivity. In this representation, we show the
ratio of the computed sensitivity sin2(2θ13)b,w for the best (resp. worst) case over the sensitivity sin
2(2θ13)c
for standard central systematic values. The “Total” bar shows that in Daya Bay and RENO the sensitivity
can vary from 0.6 to 1.2 – 1.3 of the baseline case, for experimental systematics ranging from a “best” to
a “worst” scenario. In the case of Double Chooz, the impact of systematics is less significant, at the level
of 20 % on both sides. In the Double Chooz and DB Mid cases, the sensitivity could be worsened for best
fit values of ∆m231 below 2.5 10
−3 eV2. In DB Full, the sensitivity is quite stable over the current allowed
range for ∆m231 with only a 5 % effect on sensitivity.
Double Chooz is an optimized experiment in the sense of robustness with respect to systematics for a goal
sensitivity in the 0.02 – 0.03 range. Daya Bay phase II is adequate to reach a sensitivity at the level of 0.01.
However, a simpler experiment for this class of sensitivity would be a scaled-up variant of Double Chooz,
with a very close near site at 150 m and a 1.5 km baseline for the far site. At the Diablo Canyon power
plant [19], where two 3.19 GWth cores are operational and modest civil engineering works would be required,
four 20 t detectors (2 near, 2 far) would give a sensitivity of 0.013 after 3 years of data taking.
9 Conclusion
In this work we have presented a detailed comparative analysis of the sensitivities to sin2(2θ13) of upcoming
and proposed reactor experiments.
We have first calculated the sensitivities using all available data published by the respective collaborations
for the baseline of both the systematical uncertainties and the experimental setups. Our results are generally
in good agreement with the sensitivities quoted by the collaborations: 0.054 for Double Chooz Phase I; 0.028
for Double Chooz Phase II; 0.041 for Daya Bay “mid”; 0.0089 for Daya Bay “full”; and 0.021 for RENO.
In the case of Daya Bay, we have additionally evaluated the impact of the proposed filling procedure,
with pairs of near-far detectors filled with the same scintillator batch and 4 different scintillator batches.
If the hydrogen mass fraction is controlled to 0.5 % between different batches, the sensitivity worsens
slightly to 0.0093. We also examined, still for Day Bay, the until-now implicit assumption that the errors
of the relative normalizations between the 8 detectors are fully uncorrelated. In reality this is the most
optimistic scenario, since a part of these uncertainties may come from site-dependent systematics. In the
most pessimistic scenario (all relative normalizations fully correlated for the same site), the Daya Bay
sensitivity would be 0.012.
An important result of this work is that the total thermal power available for an experiment, a figure of
merit that has been often used as a strong argument to “rank” different projects, has a modest impact on
the success of an experiment. Large powers are only available in multi-core sites, which are very difficult to
monitor. The associated systematics can be overwhelming with respect to the benefit from the statistics.
This is very nicely exemplified by the case of RENO, which would reach the same sensitivity with just 2 of
its 6 reactors on, and by Daya Bay “mid”, which results to be just half way between Double Chooz Phase I
and Double Chooz Phase II. We have illustrated how optimal is the use of the available thermal power in
each site through a comparison of the real experiments with ideal “single core equivalent” setups: Double
Chooz and Daya Bay “full” are nearly optimal, Daya Bay “mid” and RENO do not make full advantage of
their huge power. Daya Bay pays for the complexity of its nuclear power plant by the inevitable construction
of two near sites.
We have carried out a detailed and unified χ2−pull analysis for all the experiments, under common assump-
tions for all systematic uncertainties. This study allowed us to compare all projects on an equal footing and
evaluating the impact of each single systematic uncertainty on the sensitivity of each experiment. In this
calculation the Double Chooz baseline sensitivity is 0.0235 and a single systematic dominates, which is the
error of the relative normalization between near and far detector. This shows that taking into consideration
its small mass, Double Chooz is an optimized experiment. With respect to the other projects, the Double
Chooz sensitivity has a more pronounced dependence on the best fit ∆m213, with sin
2(2θ13)lim ranging from
0.020 to 0.031 for the currently 2 σ−allowed ∆m213 interval.
Daya Bay “full” proves to be robust with respect to the size of the systematical errors and to variations of
∆m213 and is the only partly approved project with an achievable sensitivity potential below 0.01. The Daya
Bay sensitivity is dominated by the accuracy of the relative normalization between detectors and the degree
of correlation existing on a same site between the latter parameters. With the knowledge of the systematics
we have today, the Daya Bay sensitivity would be on average between 0.0094 and 0.0123, depending on the
degree of correlation of the systematics between detectors on the same site.
Contrary to Double Chooz and Daya Bay, the sensitivity of RENO is largely degraded by the uncertainties
of the reactor powers and fuel composition. This, again, shows that the site is not optimal. Nevertheless,
due to the large target mass and optimal baseline, a very competitive sensitivity, around 0.02, is achievable.
This pull analysis also shows that the impact of the backgrounds on the χ2 is minor with respect to other
systematics. Backgrounds, at least in our simulation, are therefore not critical in any of the analyzed
experiments.
Taken into consideration all the above results, we come to a conclusion about the features of the optimal
experiment to approach a sin2(2θ13) sensitivity of 0.01. Where by “optimal” we mean a robust sensitivity,
the simplest configuration, the minimal amount of civil works and the smallest mass. Such an optimal
experiment would have a nuclear power plant layout as simple and powerful as Double Chooz; a favorable
topography for sufficiently deep underground laboratories, a very close, single near site, a ∼ 1.5 km baseline
for the far site and a total target mass of about the half of Daya Bay. Diablo Canyon, California, is a good
example of an suitable site for such an experiment.
Acknowledgement
We are greatful to A. Milsztajn for the careful proofreading of this article and his useful comments. We
wish also to acknowledge M. Lindner for fruitful discussions on the comparison of the θ13 experiments. It
is also a pleasure to thank M. Cribier and H. de Kerret for continuous helpful exchanges.
Appendix
In this section we first describe the way we computed event rates, and then the χ2 analysis implementation
with detailed systematic inclusions.
Event rates
The visible energy inside the detector has a simple expression as a function of the positron energy or neutrino
energy of the inverse β-decay reaction:
Evis = Ee+ +me ≃ Eν − Ethrν + 2me , (16)
where Ethrν = Mn−Mp+me is the νe threshold energy of the reaction. The event rates produced in reactor
R and recorded in detector D per visible energy bin [Ei;Ei+1] may be written as
i (θ13,∆m
31) =
∫ Ei+1−me
Ei−me
(Ee+ , Eν) (17)
(Ee+ , Eν) =
4πL2R,D
h(LR,D, L)σ(Eν)φ
R,D(Eν) ǫ(Ee+) (18)
×R(Ee+ , Eν)Pee(Eν , L, θ13,∆m231) ,
where h(LR,D, L), σ(Eν ), ǫ(Ee+), φ
R,D(Eν), R(Ee+ , Eν) stand for the finite size effect function the νe
inverse β-decay reaction cross section, the e+ detection efficiency, the νe flux from reactor R in detector D
and the energy response of the detector respectively. The generic normalization factor NR,D is the product
of the experiment life time by the number of available free protons inside the target volume, the global load
factor of reactor R and the dead time of detector D. The νe flux from reactor R in detector D is described
in term of the isotope composition as:
φR,D(Eν) = P
Efisℓ
ℓ (Eν) (19)
where ℓ = 235U, 238U, 239Pu, 241Pu labels the most important isotopes contributing to the νe flux, C
is the relative contribution of the isotope ℓ to the total reactor power (CRℓ = N
R, and Nfisℓ is the
number of fissions per second of isotope ℓ), Efisℓ is the energy release per fission for isotope ℓ and P
R is the
thermal power of reactor R. In eq. (19), φ
ℓ (Eν) is the energy differential number of neutrinos emitted
per fission by the isotope ℓ, and we adopt the parameterization for the φ
ℓ (Eν) from ref. [16]. For the C
we take a typical isotope composition in a nuclear reactor given in eq. (2).
We take for Pee the oscillation probability expressed in eq. (4). We assume in this article a constant efficiency
of ǫ(Ee+) = 80 % and a Gaussian energy response function
R(Ee+ , Eν) =
2πρ(Ee+)
Ee+ − Eν +Mn −Mp
2ρ(Ee+)
. (20)
with an energy resolution of ρ(Ee+) = 8 %/
Ee+ [MeV ]. The finite size effect function h(LR,D, L) is
assumed to be a Dirac distribution (pointlike sources and detectors) in this paper. The total event rates in
ith bin of detector D is then simply expressed as
NDi (θ13,∆m
31) =
R=R1,...,RNr
i (θ13,∆m
31) . (21)
χ2 analysis and systematics inclusion
The computed event rates, N
i , are then included in a χ
2 pull-approach analysis [14], where correlations
between the systematic uncertainties are properly included:
χ2 = min
i=1,...,Nb
D=D1,...,DN
∆Di −
k,k′=1
k,k′αk′ . (22)
with,
∆Di =
i −NDi
/UDi (23)
and UDi are given by eq. (9). The αk and S
i,k coefficients are described in Table 15.
The SDi,k coefficient represents the shift of the i
th bin of detector D spectrum due to a 1 σ variation in the
kth systematic uncertainty parameter αk. Most of the systematics are expressed as function of N
i of B
quantities already described previously. The energy scale systematic coefficients in SDi,k are defined through
MDi which follows the relation
MDi =
R=R1,...,RNr
i , (24)
where
∫ Ei+1−me
Ei−me
(Ee+ , Eν) . (25)
It is often assumed in the pull-approach that Wk,k′ = δk,k′ . If we keep this definition of Wk,k′ then we
are faced with the problem that the reactor spectrum shape uncertainties may contribute to the absolute
normalization error and the fuel composition uncertainties may contribute to the reactor core power errors.
If we want to get rid of these free contributions we could use two methods:
1. the first one consists to infer that
ℓ αcmp,ℓC
ℓ = 0
2. the second one is to introduce additional weight terms in the χ2 definition (22):
ℓ αcmp,ℓC
ℓ /εcmp
The first method allows disentangling fuel composition from power uncertainties. However, this assumption
is a bit too restrictive since in practice the sum
ℓ αcmp,ℓC
R = 0 is only constrained at the knowledge
level of the power of reactor R. The second method has the advantage of allowing an estimate of the level
of contribution of this systematic to the power uncertainties. Moreover this simply leads to redefining the
Wk,k′ matrix as
W−1k,k′ = δk,k′ +
ℓ,ℓ′,R
cmp,R
ℓ,ℓ′,k,k′
CRℓ C
ε2cmp
, (26)
cmp,R
ℓ,ℓ′,k,k′ =
δℓ,k−kR
δℓ′,k′−kR
if k, k′ ∈ {kR0 + 1, . . . , kR0 + 5},
kR0 = 5Nd +Nb +Nr + 2 + 4(R− 1),
0 otherwise.
With these definitions, εcmp determines at which level the fuel composition uncertainties are allowed to
contribute to the core power errors. One wants typically that fuel composition uncertainties contribute
within the allowed region of power uncertainty. Thus,
εcmp = σpwr/P
R . (28)
Regarding the fuel composition uncertainties, σcmp may be assessed roughly at the level of σpwr uncertainties:
σ2cmp = 2 − 3 % . (29)
Error type k SD
i,k ×UDi αDi,k
Absolute normalization 1 σabsN
i αabs
Relative normalization (Ns = 1)
in D1 Ns + 1 σrelN
in DNd Ns +Nd σrelN
Absolute Energy scale Nd + 2 σsclN
i αscl
Relative Energy scale (Ns = Nd + 2)
in D1 Ns + 1 σ
MD1i α
in DNd Ns +Nd σ
Backgrounds (Ns = 2Nd + 2)
accidentals in D1 Ns + 1 σ
BD11,i α
accidentals in DNd Ns +Nd σ
1,i α
cosmogenics in D1 Ns +Nd + 1 σ
BD12,i α
cosmogenics in DNd Ns + 2Nd σ
2,i α
proton recoils in D1 Ns + 2Nd + 1 σ
BD13,i α
proton recoils in DNd Ns + 3Nd σ
3,i α
Reactor spectrum shape (Ns = 5Nd + 2)
in bin 1 Ns + 1 σshpN
1 αshp,1
in bin Nb Ns +Nb σshpN
αshp,Nb
Reactor power (Ns = 5Nd +Nb + 2)
from R1 Ns + 1 σ
from RNr Ns +Nr σ
pwr N
RNr ,D
Reactor R composition (Ns = 5Nd +Nb +Nr + 2 + 4(R− 1))
from 235U Ns + 1 σcmpN
cmp,R
from 239Pu Ns + 2 σcmpN
cmp,R
from 238U Ns + 3 σcmpN
cmp,R
from 241Pu Ns + 4 σcmpN
cmp,R
Table 15: Systematic parameters table. We used the following definitions: Nb is the number of bins in the
reactor spectra, Nd is the number of detectors in the experiment, Nr is the number of reactor cores in the
NPP, Ns is short for the number of previously defined systematic parameters. For specific values of σabs,
σrel, σshp, σBD
, σpwr, σcmp, we refer to the experiment comparison sections 6 – 8.
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	Experimental context
	Neutrino oscillation at reactor and 13
	Generic analysis of 13 sensitivity
	Generic overview of systematic error inputs
	Backgrounds: description and modelization
	Comparison of the current proposals
	Detailed systematics review
	Impact of the scintillator composition
	Estimation of the -induced backgrounds
	Reactor experiments baseline sensitivity
	Double Chooz
	Daya Bay
	RENO
	Discussion
	The single core equivalent approach
	The pulls analysis
	Touching the ``right systematic chord''
	Conclusion
