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MPP-2004-28

Prosp ects of accelerator and reactor neutrino oscillation exp eriments for the coming ten years

P. Hubera , M. Lindnerb , M. Rolinecc, T. Schwetzd , and W. Wintere

arXiv:hep-ph/0403068 v2 13 Oct 2004

a,b,c,d,e

Physik-Department, Technische Universit?t Munchen, a ? James-Franck-Strasse, D-85748 Garching, Germany

a

Max-Planck-Institut fur Physik, Postfach 401212, D-80805 Munchen, Germany ? ?

Abstract We analyze the physics p otential of long baseline neutrino oscillation exp eriments planned for the coming ten years, where the main focus is the sensitivity limit to the small mixing angle 13 . The discussed exp eriments include the conventional b eam exp eriments MINOS, ICARUS, and OPERA, which are under construction, the planned sup erb eam exp eriments J-PARC to Sup er-Kamiokande and NuMI off-axis, as well as new reactor exp eriments with near and far detectors, represented by the Double-Chooz pro ject. We p erform a complete numerical simulation including systematics, correlations, and degeneracies on an equal footing for all exp eriments using the GLoBES software. After discussing the improvement of our knowledge on the atmospheric parameters 23 and m21 by these exp eriments, we investigate the p otential to determine 3 13 within the next ten years in detail. Furthermore, we show that under optimistic assumptions and for 13 close to the current b ound, even the next generation of exp eriments might provide some information on the Dirac CP phase and the typ e of the neutrino mass hierarchy.

a b c d e

E E E E E

ma ma ma ma ma

il: il: il: il: il:

phuber@ph.tum.de lindner@ph.tum.de rolinec@ph.tum.de schwetz@ph.tum.de wwinter@ph.tum.de

1

Intro duction

Within the last ten years a huge progress has been achieved in neutrino oscillation physics. In particular, the results of the atmospheric neutrino experiments [1-3] and the K2K accelerator neutrino experiment [4] have demonstrated that atmospheric muon neutrinos oscillate predominately into tau neutrinos with a mixing angle close to maximal mixing. Furthermore, solar neutrino experiments [5, 6] and the KamLAND reactor neutrino experiment [7] have established that the reduced flux of solar electron neutrinos is consistently understo o d by the so-called LMA-MSW solution [8]. Lo oking back at these exciting developments, it is tempting to extrapolate where we could stand in ten years from now with the experiments being under construction or planned. Certainly, neutrino physics will turn from the discovery era to the precision age, which however, will make this field by no means less exciting. The next ma jor challenge will be the determination of the third, unknown mixing angle 13 , which at present is only known to be small [9, 10]. Further important issues will be the determination of the neutrino mass hierarchy and, if 13 turns out to be large enough, the Dirac CP phase. Three different classes of experiments are under discussion for the next generation of long-baseline oscillation experiments, which are able to address at least some of these topics: Conventional beam experiments, first-generation superbeams, and new reactor experiments with near and far detectors. In this study, we consider specific proposals for such experiments, which are under construction or in active preparation, and could deliver physics results within the next ten years. An already existing conventional beam experiment is the K2K experiment [4], which is sending a neutrino beam from the KEK accelerator to the Super-Kamiokande detector. This experiment has already confirmed the disappearance of Е as predicted by atmospheric neutrino data, and with more statistics it will slightly reduce the allowed range of the atmospheric mass splitting m21 . In this study, we consider in detail the next generation of 3 such conventional beam experiments, which are the MINOS experiment [11] in US, and the CERN to Gran Sasso (CNGS) experiments ICARUS [12] and OPERA [13]. These experiments are currently under construction and should easily obtain physics results within the next ten years, including five years of data taking. Moreover, we consider the subsequent generation of beam experiments, the so-called superbeam experiments. They use the same technology as conventional beams with several improvements. The most advanced superbeam proposals are the J-PARC to SuperKamiokande experiment (JPARC-SK) [14] in Japan, and the NuMI off-axis experiment [15], using a neutrino beam pro duced at Fermilab in US. For these two experiments specific Letters of Intent exist and we use the setups discussed in there. JPARC-SK and NuMI could deliver important new results towards the end of the timescale considered in this work. Recently, there has been a lot of activity to investigate the potential of new reactor neutrino experiments [16]. It has been realized that the performance of previous experiments, such as CHOOZ [9, 10] or Palo Verde [17], can be significantly improved if a near detector is used to control systematics and if the statistics is increased [18-20]. A number of possible sites are discussed, including reactors in Brasil, China, France, Japan, Russia, Taiwan, and the US (see Ref. [16] for an extensive review). Among the discussed options are the KASKA pro ject in Japan [19] at the Kashiwazaki-Kariwa power plant, several power plants in USA [21, 1

22] (e.g., Diablo Canyon in California or Braidwo o d in Illinois), and the Double-Cho oz pro ject [23] (D-Cho oz), which is planned at the original CHOOZ site [10] in France. The particular selection of experiments considered in this study is determined by the requirement that results should be available within about ten years from now. This either requires that the experiments are already under construction (such as MINOS, ICARUS, and OPERA), or that specific proposals (Letters of Intent) including feasibility studies exist. From the current perspective, the only superbeam experiments fulfilling this requirement are the JPARC-SK and NuMI pro jects. Concerning reactors, we consider in this study the Double-Cho oz pro ject [23], since this proposal has the advantage that a lot of infrastructure from the first CHOOZ experiment can be re-used. In particular, the existence of the detector hall drastically reduces the required amount of civil engineering, which is considered to be time-critical for a future reactor experiment. Therefore, it seems rather likely that a medium size experiment can be built at the CHOOZ site within a few years and deliver physics results during the timescale considered here. We would like to stress that other reactor experiments of similar size, such as the KASKA pro ject in Japan [19], would lead to results similar to Double-Cho oz. To fully explore the potential of neutrino oscillation experiments at nuclear reactors, we furthermore consider an even larger reactor neutrino experiment (Reactor-I I). This could be especially interesting if a large value of 13 was found. Reactor-I I is the only exception for which we use an abstract setup, which could, in principle, be built at one of the sites mentioned above. For example, some pro jects discussed in the US, such as Diablo Canyon or Braidwo o d [22, 24], are similar to our Reactor-I I setup. Such an experiment could be feasible within a timescale similar to the superbeam experiments, and could provide results at the end of the perio d considered in this work. Note that in this study, we do not consider oscillation experiments using a natural neutrino source, such as solar, atmospheric, or supernova neutrinos. The outline of the paper is as follows: After a brief description of the considered experiments in Section 2, we discuss the analysis metho ds and some analytical qualitative features of our results in Section 3. The main results of this study are given in Sections 4, 5, 6, and 7. First, in Section 4, we investigate the improvement of the atmospheric parameters 23 and m21 from long-baseline experiments within ten years. Then we move to the discussion of 3 the sin2 213 sensitivity limit if no finite value of sin2 213 can be established. We consider in Section 5 the conventional beam experiments MINOS, ICARUS, and OPERA. In Section 6, we discuss the potential of reactor neutrino experiments to constrain sin2 213 , and we compare the final sin2 213 bounds from the conventional beams, Double-Cho oz, JPARC-SK, and NuMI. In Section 7, we investigate the assumption that sin2 213 is large, and discuss what we could learn from the next generation of experiments on the Dirac CP phase and the type of the neutrino mass hierarchy. In this section, the Reactor-I I setup will become important. A summary of our results is given in Section 8. In Appendix A, we describe in detail our simulation of MINOS, ICARUS, and OPERA. Furthermore, in Appendix B, technical details of the reactor experiment analysis are given. Eventually, we present a thorough discussion of our definition of the sin2 213 limit in Appendix C.

2

2

Description of the considered exp eriments

In this section, we discuss in detail the individual experiments considered in this work. The main characteristics of the used setups are summarized in Table 1. 2.1 Conventional beam experiments

Conventional beam experiments use an accelerator for neutrino pro duction: A proton beam hits a target and pro duces a pion beam (with a contribution of kaons). The resulting pions mainly decay into muon neutrinos with some electron neutrino contamination. The far detector is usually lo cated in the center of the beam. The primary goal of these beams is the improvement of the precision of the atmospheric oscillation parameters. In addition, an improvement of the CHOOZ limit for sin2 213 is expected. For more details, see Ref. [11] for the MINOS experiment and Refs. [12, 13] for the CNGS experiments. In addition, we describe our simulation in more detail in Appendix A. The neutrino beam for the MINOS experiment is pro duced at Fermilab. Protons with an energy of about 120 GeV hit a graphite target with an intended exposure of 3.7 З 1020 protons on target (pot) per year. A two-horn fo cusing system allows to direct the pions towards the Soudan mine where the magnetized iron far detector is lo cated, which results in a baseline of 735 km. The flavor content of the beam is, because of the decay characteristics of the pions, almost only Е with a contamination of approximately 1% e . The mean neutrino energy is at E 3 GeV, which is small compared to the -pro duction threshold. The main purpose is to observe Е Е disappearance with high statistics, and thus to determine the "atmospheric" oscillation parameters. In addition, the Е e appearance channel will provide some information on sin2 213 . The CNGS beam is pro duced at CERN and directed towards the Gran Sasso Laboratory, where the ICARUS and OPERA detectors are lo cated at a baseline of 732 km. The primary protons are accelerated in the SPS to 400 GeV, and the luminosity is planned to be 4.5 З 1019 pot y-1 . Again the beam mainly contains Е with a small contamination of e at the level of 1%. The main difference to the NuMI beam is the higher neutrino energy. The mean energy is 17 GeV, well above the -pro duction threshold. Therefore, the CNGS experiments will be able to study the -appearance in the Е channel. Two far detectors with very different technologies designed for detection will be used for the CNGS experiment. The OPERA detector is an emulsion cloud chamber, whereas ICARUS is based on a liquid Argon TPC. In addition to the detection, it is possible to identify electrons and muons in the OPERA and ICARUS detectors. This in addition allows to study the Е e appearance channel providing the main information on sin2 213 , and the Е disappearance channel, which contributes significantly to the determination of the atmospheric oscillation parameters. 2.2 The first-generation superbeams JPARC-SK and NuMI

Superbeams are based upon the technology of conventional beam experiments with some technical improvements. All superbeams use a near detector for a better control of the sys3

Label L E Conventional beam experiments: MINOS 735 km 3 GeV 3.7 З 1 ICARUS 732 km 17 GeV 4.5 З 1 OPERA 732 km 17 GeV 4.5 З 1 Superbeams: JPARC-SK 295 km 0.76 GeV 1.0 З 1 NuMI 812 km 2.22 GeV 4.0 З 1 Reactor experiments: D-Cho oz 1.05 km 4 MeV 2з Reactor-I I 1.70 km 4 MeV

P

Source

Detector technology Magn. iron calorim. Liquid Argon TPC Emul. cloud chamb. Water Cherenkov Low-Z-calorimeter Liquid Scintillator Liquid Scintillator

mD

et

tr

un

020 pot/y 019 pot/y 019 pot/y 021 pot/y 020 pot/y 4.25 GW 8 GW

5.4 kt 5 yr 2.35 kt 5 yr 1.65 kt 5 yr 22.5 kt 5 yr 50 kt 5 yr 11.3 t 3 yr 200 t 5 yr

Table 1: The different classes of experiments and the considered setups. The table shows the label of
the experiment, the baseline L, the mean neutrino energy E , the source power PSource (for beams: in protons on target per year, for reactors: in gigawatts of thermal reactor power), the detector technology, the fiducial detector mass mDet , and the running time trun . Note that most results are, to a first approximation, a function of the product of running time, detector mass, and source power.

tematics and are aiming for higher target powers than the conventional beam experiments. In addition, the detectors are better optimized for the considered purpose. Since the primary goal of superbeams is the sin2 213 sensitivity, the Е e appearance channel is expected to provide the most interesting results. In order to reduce the irreducible fraction of e from the meson decays (which is also called "background") and the unwanted highenergy tail in the neutrino energy spectrum, one uses the off-axis-technology [25] to pro duce a narrow-band beam, i.e., a neutrino beam with a sharply peaking energy spectrum. For this technology, the far detector is situated slightly off the beam axis. The simulation of the superbeams is performed as described in Ref. [26]; here we give only a short summary. The J-PARC to Super-Kamiokande superbeam, which we further on call JPARC-SK,1 is supposed to have a target power of 0.77 MW with 1021 pot per year [14]. It uses the SuperKamiokande detector, a water Cherenkov detector with a fiducial mass of 22.5 kt at a baseline of L = 295 km and an off-axis angle of 2 . The Super-Kamiokande detector has excellent electron-muon separation and neutral current rejection capabilities. Since the mean neutrino energy is 0.76 GeV, quasi-elastic scattering is the dominant detection pro cess. For the NuMI off-axis experiment [15], which we further on call NuMI, a low-Z-calorimeter with a fiducial mass of 50 kt is planned [28]. Because of the higher average neutrino energy of about 2.2 GeV, deep inelastic scattering is the dominant detection pro cess. Thus, the hadronic fraction of the energy deposition is larger at these energies, which makes the low-Zcalorimeter the more efficient detector technology. For the baseline and off-axis angle, many configurations are under discussion. As it has been demonstrated in Refs. [26, 29, 30], a NuMI baseline significantly longer than 712 km increases the overall physics potential because of the larger contribution of matter effects. In this study, we use a baseline of 812 km and
The JPARC-SK setup considered in this work is the same as the setup labeled JHF-SK in previous publications [20, 26, 27].
1

4

an off-axis angle of 0.72 , which corresponds to a lo cation close to the proposed Ash River site, and to the longest possible baseline within the United States. The beam is supposed to have a target power of about 0.43 MW with 4.0 З 1020 pot per year. 2.3 The reactor experiments Double-Cho oz and Reactor-I I

The key idea of the new proposed reactor experiments is the use of a near detector at a distance of few hundred meters away from the reactor core. If near and far detectors are built as identical as possible, systematic uncertainties related to the neutrino flux will cancel. In addition, detectors considerably larger than the CHOOZ detector are anticipated, which has, for example, been demonstrated to be feasible by KamLAND [7]. Except from these improvements, such a reactor experiment would be very similar to previous experiments, such as CHOOZ [10] or Palo Verde [17]. The basic principle is the detection of antineutrinos by the inverse -decay pro cess, which are pro duced by -decay in a nuclear fission reactor. For details of our simulation of reactor neutrino experiments, see Ref. [20] and Appendix B. For the Double-Cho oz experiment, we assume a total number of 60 000 un-oscillated events in the far detector [23], which corresponds (for 100% detection efficiency) to the integrated luminosity of 288 t З GW З yr, compared to the original CHOOZ experiment with 12.25 t З GW З yr leading to about 2 500 un-oscillated events [9]. The integrated luminosity is given as the pro duct of thermal reactor power, running time, and detector mass. Note that, at least for a background-free measurement, one can scale the individual factors such that their pro duct remains constant. The possibility to re-use the cavity of the original CHOOZ experiment is a striking feature of the Double-Cho oz proposal, although it confines the far detector to a baseline of 1.05 km, which is slightly to o short for the current best-fit value m21 2 З 10-3 eV2 . 3

If a positive signal for sin2 213 is found so on, i.e., sin2 213 turns out to be large, it will be the primary ob jective to push the knowledge on sin2 213 and CP with the next generations of experiments. From the initial measurements of superbeams, sin2 213 and CP will be highly correlated (see Section 7). In order to disentangle these parameters, some complementary information is needed. For this purpose, one can either use extensive antineutrino running at a beam experiment, or use an additional large reactor experiment to measure sin2 213 precisely [20, 31]. Because the antineutrino cross sections are much smaller than the neutrino cross sections, a superbeam experiment would have to run about three times longer in the antineutrino mo de than in the neutrino mo de in order to obtain comparable statistical information. Thus, a superbeam could not supply the necessary information within the anticipated timescale. We therefore suggest the large reactor experiment Reactor-I I from Ref. [20] at the optimal baseline of L = 1.7 km in order to demonstrate the combined potential of all experiments. It has 636 200 un-oscillated events, which corresponds to an integrated luminosity of 8 000 t З GW З yr. Such a reactor experiment could, for example, be built at the Diablo Canyon or Braidwo o d power plants [22, 24].

5

3

Qualitative discussion and analysis metho ds

In general, our calculations are done in the three flavor framework, where we use the standard parameterization U of the leptonic mixing matrix described by three mixing angles and one CP phase [32]. Our results are based on a full numerical simulation of the exact transition probabilities, and we also include Earth matter effects [8] because of the long baselines used for the NuMI beam. We take into account matter density uncertainties by imposing an error of 5% on the average matter density [33]. The probabilities are convoluted with the neutrino fluxes, detection cross sections, energy resolutions, and experimental efficiencies to calculate the event rates, which are the basis of the full statistical 2 -analysis. We use all the information available, i.e., the appearance and disappearance channels, as well as the energy information. The simulation metho ds are described in the Appendices of Ref. [27]; for details of the conventional beam experiments, see also Appendix A, for the superbeam experiments Ref. [26], and for the the reactor experiments Ref. [20] and Appendix B. All of the calculations are performed with the GLoBES software [34]. In order to obtain a qualitative analytical understanding of the effects, it is sufficient to use simplified expressions for the transition probabilities, which are obtained by expanding the probabilities in vacuum simultaneously in the mass hierarchy parameter m21 /m21 2 3 and the small mixing angle sin 213 . The expression for the Е e appearance probability up to second order in and sin 213 is given by [35, 36] P (Е e ) sin2 213 sin2 23 sin2

sin 213 sin CP sin 212 sin 223 sin2 + sin 213 cos CP sin 212 sin 223 cos sin + 2 cos2 23 sin2 212 2 (1 )

with m21 L/(4E ). The sign of the second term is negative for neutrinos and positive 3 for antineutrinos. The relative weight of each of the individual terms in Eq. (1) is determined by the values of and sin 213 , which means that the superbeam performance is highly affected by the true values m21 and m21 given by nature. Reactor experiments can be 2 3 described by the corresponding expansion of the disappearance probability up to second order in sin 213 and [19, 20, 36] 1-P
ee ??

sin2 213 sin2 + 2 2 cos4 13 sin2 212 .

(2 )

The second term on the right-hand side of this equation is for sin2 213 10-3 and close to the first atmospheric oscillation maximum relatively small compared to the first one, and can therefore be neglected in the relevant parameter space region. In principle, there are also terms of the order sin2 213 and higher orders in Eq. (2). Though some of these terms could be of the order of the 2 -term for large values of sin2 213 , they are, close to the atmospheric oscillation maximum, always suppressed compared to the sin2 213 -term by at least one order of . Thus, the sin2 213 -term carries the main information. From Eq. (2), it is obvious that a reactor experiment cannot access 23 , the mass hierarchy, or CP . In addition, the measurements of m21 would only be possible for large values 3 6

of sin2 213 [20]. These parameters can be only measured by the Е Е , Е e , and Е channels in beam experiments. However, comparing Eqs. (1) and (2), one can easily see that reactor experiments should allow a "clean" and degenerate-free measurement of sin2 213 [19]. In contrast, the determination of sin2 213 using the appearance channel in Eq. (1) is strongly affected by the more complicated parameter dependence of the oscillation probability, which leads to multi-parameter correlations [27] and to the (, 13 ) [37], sgn(m21 ) [38], and (23 , /2 - 23 ) [39] degeneracies, i.e., an overall "eight-fold" degener3 acy [40]. In the analysis, we take into account all of these degeneracies. Note however, that the (23 , /2 - 23 ) degeneracy is not present, since we always adopt for the true value of 23 the current atmospheric best-fit value 23 = /4. The proper treatment of correlations and degeneracies is of particular importance for the calculation of a sensitivity limit on sin2 213 . This issue is discussed in detail in Appendix C, where we give also a precise definition of the sin2 213 sensitivity limit. In some cases we compare the actual sin2 213 sensitivity limit to the so-called (sin2 213 )eff sensitivity limit, which includes only statistical and systematical errors (but no correlations and degeneracies). This limit corresponds roughly to the potential of a given experiment to observe a positive signal, which is "parameterized" by some (unphysical) mixing parameter (sin2 213 )eff (see also Appendix C for a precise definition). If not otherwise stated, we use in the following for the "solar" and "atmospheric" parameters the current best-fit values with their 3 -allowed ranges: |m21 | = 2.0 3 m21 = 7.0 2
+1.2 -0.9 +2.5 -1.6

З 10 З 10

-3 -5

eV2 , eV2 ,

sin2 223 = 1

+0 -0.15

, . (3 )

sin2 212 = 0.8

+0.15 -0.1

The numbers are taken from Refs. [41, 42], which include the latest SNO salt solar neutrino data [6] and the results of the re-analysis of the Super-Kamiokande atmospheric neutrino data [2]. The interesting dependencies on the true parameter values are usually shown within the 3 -allowed ranges. For the upper bound on sin2 213 at 90% CL (3 ) we use sin2 213 0.14 (0.25) , (4 )

obtained from the CHOOZ data [9] combined with global solar neutrino and KamLAND data at the best fit value m21 = 2 З 10-3 eV2 [42]. In order to take into account relevant 3 information from experiments not considered explicitly, we impose external input given by the 1 error on the respective parameters. This is mainly relevant for the "solar parameters", where we assume that the ongoing KamLAND experiment will improve the errors down to 2 a level of about 10% on each m21 and sin 212 [43]. For the "atmospheric parameters" we assume as external input roughly the current error of 20% for |m21 | and 5% for sin2 223 , 3 which however, becomes irrelevant after about one year of data taking of the conventional beams, since then these parameters (especially |m21 |) will be determined to a better 3 precision from the experiments themselves. Furthermore, we assume a precision of 5% for |m21 | for the separate analysis of the reactor experiments, since the conventional beams 3 should supply results until then. However, it can be shown that the results would only marginally change for an error of 20% for |m21 |. 3

In general our results presented in the following depend on the assumed true values of the oscillation parameters. In particular they show a strong dependence on the true value of 7

m21 , and therefore this dependence will be depicted in figures where appropriate. The 3 13 sensitivity limit obtained from PeЕ moreover also depends strongly on the true value of m21 (see Figure 4 below). In principle also the variation of 12 plays a role. However, PeЕ 2 depends only on the pro duct of З sin 212 up to second order in as shown in Eq. (1). Therefore a variation of the true value of 12 is equivalent to a rescaling of the true value of m21 . The variation of the true value of 23 within the range given in Eq. (3) pro duces 2 only slight changes in the results. In particular, those changes are much smaller than the ones caused by the variation of m21 . Thus, in order to keep the presentation of our results 3 concise, we do not explicitly discuss the dependence of the results on 23 , and we always adopt the current best fit value 23 = /4 for the true value.

4

The measurements of m21 and 2 3

3

In this section, we investigate the ability of the conventional beam experiments and superbeams to measure the leading atmospheric parameters m21 and 23 . We do not include 3 the reactor experiments in this discussion, since they are rather insensitive to m21 , and 3 cannot access 23 at all. The measurement of these parameters is dominated by the Е Е disappearance channel in the beam experiments. In Figure 1, we compare the predicted allowed regions for m21 and sin2 23 from the 3 combined conventional beams (MINOS, ICARUS, OPERA), JPARC-SK, NuMI, and all beam experiments combined to the current allowed region from Super-Kamiokande atmospheric neutrino data. We show the fit-manifold section in the sin2 23 -m21 -plane (upper row), as 3 well as the pro jection onto this plane (lower row). For a section, all oscillation parameters which are not shown are fixed at their true values, whereas for a pro jection the 2 -function is minimized over these parameters. Therefore, the pro jection corresponds to the final result, since it includes the fact that the other fit parameters are not exactly known. In general, the 2 -value becomes smaller by the minimization over the not shown fit parameters, which means that the allowed regions become larger. In Figure 1 the sgn(m21 )-degeneracy is 3 not included, since it usually do es not pro duce large effects in the disappearance channels. In addition, we use the true values sin2 213 = 0.1 and CP = 0 in Figure 1. Although the fit-manifold sections shown in the upper row of Figure 1 depend to some extent on this choice, the effect for the final results of the disappearance channels is very small, i.e., the lower row of Figure 1 is hardly changed for sin2 213 = 0. The first thing to learn from Figure 1 is that the precision on m21 will drastically improve 3 during the next ten years, whereas our knowledge on 23 will be increased rather mo destly. The combination of all the beam experiments will improve the current precision from the Super-Kamiokande atmospheric neutrino data [2] on sin2 23 roughly by a factor of two, while the precision on m21 will be improved by an order of magnitude. Neither the three 3 conventional beams combined nor NuMI will obtain a precision on 23 better than current Super-Kamiokande data, only JPARC-SK might improve the precision slightly. We note however, that the 23 accuracy of the long-baseline experiments strongly depends on the true value of m21 , and it will be improved if m21 turns out to be larger than the current 3 3 best-fit point.

8

Conv. beams: Section
2.8 2.6 eV2 eV2 2.4 2.2 2.0 1.8 1.6 1.4 0.3 0.4 0.5 0.6 sin2 23 0.7
3 3

J PARC SK: Section
2.8 2.6 eV2 2.4 2.2 2.0 1.8 1.6 1.4 0.3 0.4 0.5 0.6 sin2 23 0.7
3

NuMI: Section
2.8 2.6 2.4 2.2 2.0 1.8 1.6 1.4 0.3 0.4 0.5 0.6 sin2 23 0.7 eV2
3

Combined: Section
2.8 2.6 2.4 2.2 2.0 1.8 1.6 1.4 0.3 0.4 0.5 0.6 sin2 23 0.7

m2 10 31

m2 10 31

m2 10 31

Conv. beams: Projection
2.8 2.6 eV2 eV2 2.4 2.2 2.0 1.8 1.6 1.4 0.3 0.4 0.5 0.6 sin2 23 0.7
3 3

J PARC SK: Projection
2.8 2.6 eV2 2.4 2.2 2.0 1.8 1.6 1.4 0.3 0.4 0.5 0.6 sin2 23 0.7
3

NuMI: Projection
2.8 2.6 2.4 2.2 2.0 1.8 1.6 1.4 0.3 0.4 0.5 0.6 sin2 23 0.7 eV2
3

m2 10 31

Combined: Projection
2.8 2.6 2.4 2.2 2.0 1.8 1.6 1.4 0.3 0.4 0.5 0.6 sin2 23 0.7

m2 10 31

m2 10 31

m2 10 31

Figure 1: The 90% CL (solid curves) and 3 (dashed curves) allowed regions (2 d.o.f.) in the sin2 23 m21 -plane for the combined conventional beams (MINOS, ICARUS, OPERA), JPARC-SK, NuMI, and all 3 beam experiments combined. For the true values of the oscillation parameters, we choose the current best-fit values from Eq. (3), a normal mass hierarchy, sin2 213 = 0.1 and CP = 0. The upper row shows a section of the fit manifold (with the un-displayed oscillation parameters fixed at their true values), and the lower row shows the pro jection onto the sin2 23 -m21 -plane as the final result. The shaded regions correspond 3 to the 90% CL allowed region from current atmospheric neutrino data [2].

In most cases, the correlations with the un-displayed oscillation parameters do not cause significant differences between the sections and pro jections in the upper and lower rows of Figure 1. Only for NuMI, the pro jection is affected by the multi-parameter correlation with sin2 213 and CP . Since we do not assume additional knowledge about sin2 213 for the individual experiments other than from their own appearance channels, the appearance 2 channels can indirectly affect the m31 or 23 measurement results. This can be understo o d in terms of the disappearance probability, which to leading order is given by [35, 36] P
ЕЕ

= 1 - sin2 223 sin

2

m21 L 3 + ... 4E

m2 10 31

(5 )

where the dots refer to higher order terms in = m21 /m21 and 13 , as well as pro ducts of 2 3 these. Thus, the sin2 213 -precision, which comes from the appearance channels, is necessary to constrain the amplitude of the higher order terms in this equation which are proportional to 13 . Since, however, 13 is strongly correlated with CP in the appearance channels, this two-parameter correlation can lead to multi-parameter correlations with 23 or m21 in 3 the disappearance channel through the higher order terms in Eq. (5). This explains the small differences between the section and pro jection plots in Figure 1. In addition, the measurement of sin2 213 at NuMI is affected by matter effects, and hence, is somewhat different for the opposite sign of m21 . Therefore, one can also expect a slightly different 3 shape of the fit manifold for the sgn(m21 )-degeneracy. Note that the initial asymmetry 3 between sin2 23 < 0.5 and sin2 23 > 0.5 for NuMI is caused by its large matter effects. 9

Experiment/Combination MINOS + OPERA + ICARUS JPARC-SK NuMI All beam experiments combined 2 2 2 2

+0.34 -0.18

|m21 | 3 З 10 З 10 З 10 З 10

23 eV eV eV eV
2 2 2 2

sin2 23
0.22 0.19 0.13 0.10 0.24 0.21 0.13 0.10

-3 -3 -3 -3

( /4)+ - ( /4)+ - ( /4)+ - ( /4)+ -

0.5 0.5 0.5 0.5

+0.21 -0.18 +0.13 -0.10 +0.23 -0.20 +0.12 -0.09

+0.15 -0.09 +0.43 -0.07 +0.12 -0.06

Table 2: The expected allowed ranges (3, 1 d.o.f.) for the atmospheric oscillation parameters. For the
true values of the oscillation parameters, we choose the current best-fit values, a normal mass hierarchy, sin2 213 = 0.1, and CP = 0 . The impact of an inverted mass hierarchy, and different values for sin2 213 or CP on these final results is rather small.

Eventually, one obtains the precision of the the lower row plots in Figure 1 (for one degr we show our prediction for the 3 -allowed from the conventional beam experiments one degree of freedom.

individual parameter m21 or 23 as pro jection of 3 ee of freedom) onto the respective axis. In Table 2 ranges of the atmospheric oscillation parameters and first generation superbeam experiments for

5

Improved sin2 213 b ounds from conventional b eams

Let us now come to the crucial next step in neutrino oscillation physics: the determination of the small mixing angle 13 . We start this discussion by investigating the potential of the conventional beam experiments MINOS, ICARUS, and OPERA to improve the current bound on sin2 213 . In Table 3, we show the signal and background event rates after one year of nominal operation for each experiment (computed for sin2 213 = 0.1 and = 0). Based on these numbers, one would expect that MINOS performs significantly better than ICARUS. However, Table 3 only shows integrated event rates and do es not include the energy dependence of signal versus background event numbers. In the CNGS beam, the energy distribution of the intrinsic e -contamination is rather different from the energy distribution of the signal events. Thus, in a full analysis including energy information, the impact of the background is reduced. On the other hand, for the NuMI neutrino beam, the intrinsic e -contamination has an energy distribution which is much closer to the one of the signal events. Therefore, the impact of the background is relatively high. An important issue for the sin2 213 sensitivity limit from the conventional beams is the finally achieved integrated luminosity, which might differ significantly from the nominal value due to some unforeseen experimental circumstances. Therefore, we discuss the sin2 213 sensitivity as a function of the integrated number of protons on target. In Figure 2, the sensitivity limits for MINOS, ICARUS, and OPERA are shown as a function of the luminosity. Note that since the CNGS experiments will be running simultaneously, we also show the combined ICARUS and OPERA sensitivity limit. In order to compare the achievable limits as a function of the running time, the dashed lines refer to the results after one, two, and 10

Signal Background S/B

MINOS ICARUS OPERA 7.1 4.4 1.6 21.6 12.2 5.4 0.33 0.36 0.30

Table 3: The number of signal and background events after one year of nominal operation of MINOS,
ICARUS, and OPERA. For the oscillation parameters, we use the current best-fit values with sin2 2 CP = 0, and a normal mass hierarchy.
13

= 0.1,

five years of data taking with the nominal beam fluxes given in Refs. [12, 44, 45]. The lowest curves are obtained for the statistics limits only, whereas the highest curves are obtained after successively switching on systematics, correlations, and degeneracies. Thus, the actual sin2 213 sensitivity limit in Figure 2 is given by the highest curves. The figure indicates that the CNGS experiments together can improve the CHOOZ bound after about one and a half years of running time, and MINOS after about two years. We note that the impact of systematics increases for MINOS with increasing luminosity, illustrating the typical background problem mentioned above. In Figure 3, we eventually summarize the sin2 213 sensitivity after a total running time of five years for each experiment, assuming the true value of m21 = 2 З 10-3 eV2 . One can directly read off this figure that the sin2 213 3 sensitivity limits of ICARUS and MINOS are very similar, and ICARUS and OPERA combined are slightly better than MINOS. Let us briefly compare our results to sin2 213 sensitivity limit calculations for MINOS, ICARUS, and OPERA existing in the literature. In the analysis of Ref. [46], the correlation 2 with CP and the sign(m31 )-degeneracy are included, and hence these results should be compared with our final sensitivity limits, although we also include correlations with respect to all the other oscillation parameters. However, for the comparison, one has to take into account the different considered running times for MINOS (2 years vs. 5 years), as well as the difference in the chosen true value of |m21 | (3.0 З 10-3 eV2 vs. 2.0 З 10-3 eV2 ). In the 3 analysis performed in Ref. [47], the correlation with CP and the sign(m21 )-degeneracy 3 were not considered, while correlations with |m21 | were taken into account. Therefore, 3 the results from that study should roughly be compared to our (sin2 213 )eff limits. Again one has to take into account different assumptions about the running times and the true value for m21 (5.0 З 10-5 eV2 vs. 7.0 З 10-5 eV2 ). Finally, in Appendix A.2 we demonstrate 2 explicitly that our results are in excellent agreement with the ones obtained by the MINOS, ICARUS, and OPERA collaborations [12, 44, 45] if we use the same assumptions. A very interesting issue for the conventional beam experiments is the impact of the true value of m21 on the sin2 213 sensitivity. (The impact of the true value of m21 is dis3 2 cussed in Section 6.) One can easily see from Eq. (1) that the effect of CP increases with 2 increasing m21 /m31 , which determines the amplitude of the second and third terms 2 in this equation. Since the main contribution to the correlation part of the discussed figures comes from the correlation with CP (with some contribution of the uncertainty of the solar 2 parameters), a larger m21 causes a larger correlation bar. This can clearly by seen from Figure 4, which shows the combined potential of the conventional beams after five years of

11

Figure 2: The sin2 213 sensitivity limit as function of the total number of protons on target at the 90%
confidence level for MINOS, ICARUS, OPERA, and ICARUS and OPERA combined (5% flux uncertainty assumed). The dashed curves refer to the sensitivity limits after one, two, and five years of running. The lowest curves are obtained for the statistics limits only, whereas the highest curves are obtained after successively switching on systematics, correlations, and degeneracies, i.e., they correspond to the final sensitivity limits. The gray-shaded area shows the current sin2 213 excluded region sin2 213 0.14 at the 90% CL [42]. For the true values of the oscillation parameters we use the current best-fit values Eq. (3) and a normal mass hierarchy.
2 running time (for each experiment) as a function of m21 . In this figure the right edge of the blue band corresponds to the limit based only on statistical and systematical errors, i.e., the (sin2 213 )eff sensitivity limit. We find that the larger m21 is, the better becomes the 2 systematics-based (sin2 213 )eff sensitivity limit, and the worse becomes the final sensitivity limit on sin2 213 . Since the LMA-II region is now disfavored by the latest solar neutrino and KamLAND data, Figure 4 demonstrates that the conventional beam experiments can definitively improve the current sin2 213 -bound. One may expect an improvement down to sin2 213 0.05 - 0.07 within the LMA-I allowed region, where the sin2 213 sensitivity limit at the current best-fit value is about sin2 213 0.06.

Since the sin2 213 sensitivity limit is expected to be sin2 213 0.06 for MINOS, ICARUS, and OPERA combined (with five years running time for each experiment), a further improvement from the conventional beams seems to be unlikely. In addition, the systematics limitation, which can be clearly seen in Figure 2, demonstrates that a further increase of the luminosity would not lead to significantly better bounds on sin2 213 . Therefore, one has to pro ceed to 12

Systematics Correlation Degeneracy

OPERA

ICARUS ICARUS& OPERA MINOS
5% flux uncertainty 0.02 0.03 0.04 0.05 0.08 0.1
Chooz & Solar excluded at 90% CL

0.2

sin2 213 sensitivity limit
13 sensitivity limit at the 90% confidence level after a running time of five years for the different experiments. The left edges of the bars are obtained for the statistics limits only, whereas the right edges are obtained after successively switching on systematics, correlations, and degeneracies, i.e., they correspond to the final sin2 213 sensitivity limits. The gray-shaded area shows the current sin2 213 excluded region sin2 213 0.14 at the 90% CL [42]. For the true values of the oscillation parameters, we use the current best-fit values Eq. (3) and a normal mass hierarchy.

Figure 3: The sin2 2

the next generation of experiments to increase the sin2 213 sensitivity. Especially, the offaxis technology to suppress backgrounds and more optimized detectors could help to improve the performance. Amongst other experiments, we discuss the corresponding superbeams, which are using these improvements, in the next section.

6

Further improvement of the sin2 213 b ound

After the discussion of the conventional beams in the last section, we here discuss the final bound on sin2 213 in ten years from now, if no finite value will be found (we will in the next section consider the case of a large 13 ). We first discuss in Section 6.1 the potential of a new reactor neutrino experiment, whereas we compare in Section 6.2 the sin2 213 limits from conventional beams, reactor experiments, and superbeams. 6.1 Characteristics of reactor neutrino experiments

In Figure 5, we show the sin2 213 sensitivity from reactor neutrino experiments as a function of the integrated luminosity measured in t (fiducial far detector mass) з GW (thermal reactor power) з yr (time of data taking).2 We consider two options of the far detector baseline: LFD = 1.05 km, corresponding to the baseline of the CHOOZ site, and LFD = 1.7 km, which is optimized for values of m21 (2 - 4) З 10-3 eV2 [20]. A crucial parameter for 3
Note that we assume 100% detection efficiency in the far detector. For smaller efficiencies, one needs to re-scale the luminosity.
2

13

3 10

4

MINOS & ICARUS & OPERA

2 10 True value of m21 2 eV2

4

LMA II

10

4

7 10

5

LMA I
Systematics Correlation Degeneracy

4 10

5

0.01

0.02

0.03 0.05 sin2 213 sensitivity limit

0.1

0.2

The sin2 213 sensitivity limit at 90% CL for MINOS, ICARUS, and OPERA combined as function of the true value of m21 (five years running time). The left curve is obtained for the statistics 2 limit only, whereas the right curve is obtained after successively switching on systematics, correlations, and degeneracies, i.e., it corresponds to the final sin2 213 sensitivity limit. The dark gray-shaded area shows the current sin2 213 excluded region sin2 213 0.14 at the 90% CL, and the light gray-shaded area refers to the LMA-excluded region at 3 , where the best-fit value is marked by the horizontal line [42]. For the true values of the un-displayed oscillation parameters we use the current best-fit values in Eq. (3) and a normal mass hierarchy.

Figure 4:

the sin2 213 sensitivity is the uncertainty of the relative normalization between the near and far detectors. We show the sensitivity for two representative values for this relative normalization uncertainty: First, rel = 0.6% is a realistic value for two identical detectors [23]. Second, in order to illustrate the improvement of the performance of an reactor experiment with a reduced normalization error, we consider the very optimistic assumption of rel = 0.2%. Such a small value might be achievable with movable detectors, as discussed for some proposals in the US [24]. The shaded regions in Figure 5 correspond to the range of possible sensitivity limits for different assumptions of systematical errors and backgrounds. For the optimal case (lower curves), we only include the absolute flux and relative detector uncertainties abs and rel . For the worst limits (upper curves) we include in addition an error on the spectral shape shape = 2%, the energy scale uncertainty cal = 0.5%, and various backgrounds as discussed in Appendix B. The first observation from Figure 5 is that the shaded regions in the left-hand panel are significantly wider than in the right-hand panel, which demonstrates that a reactor experiment at 1.05 km is more sensitive to systematical errors. This reflects the fact that the baseline of 1.7 km is better optimized for the used value of |m21 | = 2 З 10-3 eV2 , such 3 that the oscillation minimum is well contained in the center of the observed energy range. In contrast, for the baseline of 1.05 km, the signal is shifted to the low energy edge of the spectrum. This implies that the interplay of background uncertainties, energy calibration, and shape error has a larger impact on the final sensitivity limit. 14

Sensitivity limit on sin2 213 at 90% CL

D CHOOZ

Sensitivity limit on sin2 213 at 90% CL

10

1

Far detector at L 1.05 km

10

1

Far detector at L 1.7 km

10

2

10

2

rel 0.6% rel 0.2% 10
1

rel 0.6% rel 0.2% 10
1

Reactor II 10
4

102 103 Luminosity t GW yr

10

4

102 103 Luminosity t GW yr

sensitivity at the 90% CL. Here m21 = 2 З 10-3 eV2 is 3 assumed to be known within 5%, LND = 0.15 km, and LFD = 1.05 (1.7) km in the left (right) panel. The number of events in the near detector is fixed to 2.94 З 106 . We use abs = 2.5% and rel = 0.2% (0.6%) for the light (dark) shaded regions. The upper edge of each region is calculated for shape = 2%, cal = 0.5%, and backgrounds as given in Table 6 in Appendix B. For the lower edges, we set shape = cal = 0 and do not include backgrounds. The dots mark the Double-Chooz and Reactor-II setups.
13

Figure 5: Luminosity scaling of the sin2 2

However, from the left-hand panel, one finds that for experiments of the size of Double-Cho oz, the impact of systematics is rather mo dest; the sin2 213 sensitivity of 0.024 for normalization errors only deteriorates to 0.032 if all systematics errors and backgrounds are included. We conclude that the proposed Double-Cho oz pro ject is rather insensitive to systematical effects and will be able to provide a robust limit sin2 213 0.032, although the far detector baseline is not optimized. In contrast, if one aims at higher luminosities, the systematics will have to be well under control at a non-optimal baseline such as at the CHOOZ site. In that case, it is saver to use a longer baseline. We note that the main limiting factor for large luminosities in the right-hand panel of Figure 5 is the error on a bin-to-bin uncorrelated background. Furthermore, comparing the light and dark shaded regions in that plot, it is obvious that a smaller relative normalization error will significantly improve the performance of a large experiment at 1.7 km, and will further reduce the impact of systematics and backgrounds. With the ambitious value of rel = 0.2%, sensitivity limits of sin2 213 7 З 10-3 could be obtained with a Reactor-I I-type experiment. Eventually, we have demonstrated that the Double-Cho oz experiment could give a robust sin2 213 sensitivity limit. In fact, one can read off Figure 5 (D-Cho oz-dot) that our assumptions about Double-Cho oz are rather conservative. Since a Letter of Intent for this experiment is in preparation, we use it in the next subsection for a direct quantitative comparison to the superbeams. However, as one can also learn from Figure 5, luminosity and different systematics sources are important issues for a reactor experiment. Therefore, one should keep in mind that much better sin2 213 sensitivity limits could be obtained from reactor experiments, such as the Reactor-I I setup. However, the exact final sensitivity limits will in these cases depend on many sources, which means that they are hardly predictable right now. 15

sensitivity limit at the 90% CL for MINOS, ICARUS, and OPERA combined, Double-Chooz, JPARC-SK, and NuMI. The left edges of the bars are obtained for the statistics limits only, whereas the right edges are obtained after successively switching on systematics, correlations, and degeneracies, i.e., they correspond to the final sin2 213 sensitivity limits. The gray-shaded region corresponds to the current sin2 213 bound at 90% CL. For the true values of the oscillation parameters, we use the current best-fit values in Eq. (3) and a normal mass hierarchy.
13

Figure 6: The sin2 2

6.2

The sin2 2

13

bound from different experiments in ten years from now

Let us now assume that the conventional beam experiments MINOS, ICARUS, and OPERA have been running five years each, and that the Double-Cho oz experiment has accumulated three years of data. In addition, we assume that the superbeam experiments JPARC-SK and NuMI have reached the integrated luminosities as given in Table 1. (For earlier, more extensive discussions of the potential of superbeam experiments, we refer to Ref. [26].) In Figure 6, we show the sin2 213 sensitivity for the considered experiments. The final sensitivity limit is obtained after successively switching on systematics, correlations, and degeneracies as the rightmost edge of the bars.3 Figure 6 demonstrates that the beam experiments are dominated by correlations and degeneracies, whereas the reactor experiments are dominated by systematics. It can be clearly seen that the (sin2 213 )eff sensitivity limit (between systematics and correlation bar), or the precision of a combination of parameters leading to a positive signal, is much better for the superbeams than for the reactor experiments. Therefore, though the reactor experiments have a go od potential to extract sin2 213 directly, the superbeams results will in addition contain a lot of indirect information about CP and the mass hierarchy, which might be resolved by the combination with complementary information. We call this gain in the physics potential which go es beyond the simple addition of statistics for the combination of experiments "synergy". In Section 7, we will discuss this further for the case if sin2 213 turns out to be large.
Note that earlier similar figures, such as in Refs. [20, 26], are computed with different parameter values, which leads to changes of the final sensitivity limits. The largest of these changes come from the adjusted atmospheric best-fit values and NuMI parameters.
3

16

Another conclusion from Figure 6 is that it is very important to compare the sin2 213 sensitivities of different experiments which are obtained with equal metho ds. In particular one clearly has to distinguish between the (sin2 213 )eff sensitivity limit (between systematics and correlation bar) and the final sin2 213 sensitivity limit, including correlations and degeneracies. For example, by accident the (sin2 213 )eff sensitivity limit from the combined MINOS, ICARUS, and OPERA experiments is very close to the final sensitivity limit of JPARC-SK or NuMI. Thus, one may end up with two similar numbers, which however, refer to different quantities and are not comparable. A very important parameter for future sin2 213 measurements is the true value of m21 , 3 which currently is constrained to the interval 0.0011 eV2 |m21 | 0.0032 eV2 at 3 [2]. 3 From Figure 7, one can can easily see that the true value of m21 strongly affects the sin2 213 3 sensitivity limit. The left-hand plot in this figure demonstrates that for all experiments the sin2 213 sensitivity becomes worse for small values of |m21 | within the currently allowed 3 range. However, since also the current sin2 213 bound (dark-gray shaded region) is worse for small values of |m21 | than for large values, the relative improvement of the current 3 sin2 213 bound might be a more appropriate description of the experiment performance. This relative improvement as function of the true value of |m21 | is shown in the right3 hand plot of Figure 7, where a factor of unity corresponds to no improvement. From this plot, one can read off an improvement by a factor of two for the conventional beams, a factor of four for Double-Cho oz, and a factor of six for the superbeams at the atmospheric best-fit value (vertical line). Nevertheless, the conventional beams might not improve the current 2 bound at all for small values of |m31 | within the atmospheric allowed range, whereas any of the other experiments would improve the current bound at least by a factor of two. Thus, though the sin2 213 sensitivity limit could be as be as large as sin2 213 0.1 for small values of |m21 | for the superbeams or Double-Cho oz, those experiments would still improve the 3 current bound by a factor of two.

7

Opp ortunities if sin2 213 is just around the corner

In Section 6, we have discussed how much the sin2 213 bound could be improved if the true value of sin2 213 were zero. There are, however, very go o d theoretical reasons to expect sin2 213 to be finite, such that the experiments under consideration could establish sin2 213 > 0. In this case, one could aim for the sin2 213 precision, CP violation, CP precision measurements, and the mass hierarchy determination. Though it has been shown that CP and mass hierarchy measurements are very difficult for the first-generation superbeams and new reactor experiments [19, 20, 26, 27, 48], we will demonstrate in this section that we could still learn something about these parameters if sin2 213 turns out to be large. In particular, we discuss the combination of the discussed experiments for the case sin2 213 = 0.1. This would imply that a positive sin2 213 signal could already be seen with the next generation of experiments. As discussed in Section 2, we assume here that a large reactor experiment Reactor-I I will be available at the end of the perio d under consideration to resolve the correlation between sin2 213 and CP . We note again that similar results can be obtained by the superbeams in the antineutrino mo de using higher target powers or

17

sin2 213 sensitivity limit
0.005
CHOOZ Solar excluded at 90% CL

Relative improvement of sin2 213 bound
7
New bound

Atmosph. excluded 3

NuMI 0.004 m2 eV2 31 J PARC SK D CHOOZ Conv. Beams 0.003

6 5 4 3 2 1 0

True value of

0.002

0.001
Atmospheric excluded at 3 CL

sin2 213

Current bound

sin2 213

No improvement of current bound

0.01

0.02 0.03 0.1 sin2 213 sensitivity limit

0.2

0.3

0.001

0.002 0.003 0.004 True value of m2 eV2 31

0.005

Figure 7: Left panel: The sin2 213 sensitivity limits at 90% CL from the experiments NuMI, JPARC-SK,
Double-Chooz, and the combined conventional beams (MINOS, ICARUS, OPERA) as function of the true value of |m21 |. The dark-gray shaded region refers to the current sin2 213 bound from CHOOZ and 3 the solar experiments (90% CL) [42]. Right panel: The relative improvement of the sin2 213 sensitivity limit with respect to the current bound from CHOOZ and solar experiments, where the dark-gray region corresponds to no improvement. The light-gray shaded regions in both panels refer to the atmospheric excluded regions (3 ), and the lines in the middle mark the current atmospheric best-fit value.

detector upgrades.4 The superbeam appearance channels will lead to allowed regions in the sin2 213 -CP -plane, similar to the allowed regions for solar and atmospheric oscillation parameters from current data. We show the results of JPARC-SK, NuMI, and Reactor-I I for the true values sin2 213 = 0.1 and CP = 90 in Figure 8, and CP = -90 in Figure 9. For the right-most plots in these figures, we combine all experiments including the conventional beams MINOS, ICARUS, and OPERA, although they do not contribute significantly to the final result. Since we assume a normal mass hierarchy to generate the data, the best-fit is obtained by fitting with the normal hierarchy; the corresponding regions are shown by the black curves. The sgn(m21 )-degenerate regions are obtained by fitting the data assuming an 3 inverted hierarchy (gray curves). Thus, the best-fit and degenerate manifolds, which are disconnected in the six-dimensional parameter space, are shown in the same plots. Similar to Figure 1 we demonstrate the difference between a section of the fit manifold (upper rows) and a pro jection (lower rows) in these figures. As far as the measurement of sin2 213 is concerned, any of the experiments in Figures 8 and 9 can establish sin2 213 > 0 for sin2 213 = 0.1 at 3 . The sin2 213 -precision can
In fact, one could already obtain some CP-conjugate information by running NuMI at L = 712 km with antineutrinos only [48]. However, we do not consider an option with a very extensive a priori NuMI antineutrino running in this study, since the risk of this configuration is too high as long as sin2 213 > 0 is not established.
4

18

J PARC SK: Section
150 100 50 0 50 100 150 0 0.05 0 150 100 50 0 50 100 150 0

NuMI: Section
150 100 50 0 50 100 150 0

Reactor II: Section
150 100 50 0 50 100 150 0

Combined: Section

CP Degrees

CP Degrees

CP Degrees

0 0.05 0.1 0.15 sin2 213 0.2

CP Degrees

0.1 0.15 sin2 213

0.2

0.05

0.1 0.15 sin2 213

0.2

0.05

3.1 0.1 0.15 sin2 213

0.2

J PARC SK: Projection
150 100 50 0 50 100 150 0 0.05 0 150 100 50 0 50 100 150 0

NuMI: Projection
150 100 50 0 50 100 150

Reactor II: Projection
150 100 50 0 50 100 150 0

Combined: Projection

CP Degrees

CP Degrees

CP Degrees

0 0.05 0.1 0.15 sin2 213 0.2

CP Degrees

0.1 0.15 sin2 213

0.2

0

0.05

0.1 0.15 sin2 213

0.2

0.05

3.1 0.1 0.15 sin2 213

0.2

Figure 8: The 90% CL (solid curves) and 3 (dashed curves) allowed regions (2 d.o.f.) in the sin2 213 CP -plane for the true values sin2 213 = 0.1 and CP = 90 for JPARC-SK, NuMI, Reactor-II. The right-most plots are calculated for the shown experiments in combination with the conventional beams. For the true values of the un-displayed oscillation parameters, we choose the current best-fit values and a normal mass hierarchy. The black curves refer to the allowed regions for the normal mass hierarchy, whereas the gray curves refer to the sgn(m21 )-degenerate solution (inverted hierarchy), where the pro jections of the minima 3 onto the sin2 213 -CP -plane are shown as diamonds (normal hierarchy) and triangles (inverted hierarchy). For the latter, the 2 -value with respect to the best-fit point is also given. The upper row shows the fit manifold section (with the un-displayed oscillation parameters fixed at their true values), and the lower row shows the pro jection onto the sin2 213 -CP -plane as the final result.
J PARC SK: Section
150 100 CP Degrees CP Degrees 50 0 50 100 150 0 0.05 0.1 0.15 sin2 213 0.2 0 150 100 CP Degrees 50 0 50 100 150 0 0.05 0.1 0.15 sin2 213 0.2 0

NuMI: Section
150 100 50 0 50 100 150 0

Reactor II: Section
150 100 CP Degrees 50 0 50 100 150 0.05 0.1 0.15 sin2 213 0.2 0

Combined: Section

4.9 0.05 0.1 0.15 sin2 213 0.2

J PARC SK: Projection
150 100 CP Degrees CP Degrees 50 0 50 100 150 0 0.05 0.1 0.15 sin2 213 0.2 0 150 100

NuMI: Projection
150 100 CP Degrees 50 0 50 100 150 0 0.05 0.1 0.15 sin2 213 0.2

Reactor II: Projection
150 100 CP Degrees 50 0 50 100 150 0 0.05 0.1 0.15 sin2 213 0.2 0

Combined: Projection

50 0 50 100 150 0

4.9 0.05 0.1 0.15 sin2 213 0.2

Figure 9: The same as Figure 8 but for the true value

CP

= -90 .

19

be read off from the figures as pro jection of the bands onto the sin2 213 -axis.5 The band structures of JPARC-SK and NuMI come from the CP phase dependency in Eq. (1). Because of the larger matter effects, the degenerate solution for NuMI is rather different from the best-fit solution, whereas it is very similar to the best-fit solution for JPARC-SK. For Reactor-I I, the sin2 213 -precision can be read off directly, since a reactor experiment is not affected by CP (see Eq. (2)), and the mass hierarchy has essentially no effect. Note that the 2 treatment of the sgn(m31 )-degeneracy in such a situation as shown in Figures 8 and 9 is a matter of definition: One could either return two different intervals for normal and inverted mass hierarchies, or one could return the union of the two fit intervals as more condensed information. The figures show that for CP , none of the individual experiments can give any information, since no substantial fraction of antineutrino running is involved. However, there is some information on CP for the combination of all experiments, since the complementary information from the reactor experiment helps to resolve the superbeam bands. Note that the overall performance for the considered experiments (including the sgn(m21 )-degeneracy) 3 is usually better close to the true value CP = -90 than close to the true value CP = 90 , since the degeneracy includes for CP = 90 very different values of CP far away from the best-fit manifold. This can, for example, be understo o d in terms of bi-rate graphs (cf., Refs. [38, 48]). From a separate analysis of the CP precision, we find that one could exclude as much as up to 40% of all values of CP at the 90% confidence level (1 d.o.f., close to CP = -90 ). However, if CP turns out to be close to 0 or , we find that one could not obtain any information on CP . Furthermore, one can directly read off from Figures 8 and 9 that CP violation measurements will not be possible with the considered experiments at the 90% confidence level (2 d.o.f. in these figures), since for the true values CP = Б90 corresponding to maximal CP violation, the pro jected allowed regions (even the best-fit solutions) include at least one of the CP conserving cases CP {0, 180}. One can show that even for one degree of freedom, there is no CP violation sensitivity with the discussed experiments at the 90% confidence level. Another important issue for the next generation long-baseline experiments is the mass hierarchy determination. In Figures 8 and 9 we give the 2 -values for the minimum in the fit manifold corresponding to the sgn(m21 )-degenerate solution (i.e., for the inverted mass 3 hierarchy) with respect to the best-fit minimum for the normal hierarchy (2 = 0), which is the relevant number for the sensitivity to a normal mass hierarchy. Obviously, none of the individual experiments has a mass hierarchy sensitivity, but their combination has some. The mass hierarchy sensitivity becomes only possible because of the long NuMI baseline L = 812 km [26, 29, 30], since matter effects differ for the normal and inverted mass hierarchies. Eventually, a NuMI baseline even longer than L = 812 km could further improve the mass hierarchy sensitivity [26, 48]. We note that the ability to identify the mass hierarchy strongly depends on the (unknown) true value of CP . The mass hierarchy determination at the combined superbeams is close to the optimum for CP = -90 , and close to the
Note that these figures with one degree of freedom (2 = 4.61) is close to the of comparison, we also use 2
5

are computed for two degrees of freedom, which means that the pro jections are slightly smaller. In fact, the 90% CL contour for two degrees of freedom 2 contour for one degree of freedom (2 = 4.00). In particular, for the sake d.o.f. for Reactor-II, although it does not depend on CP .

20

minimum for CP = 90 [38, 48]. In fact, one could have a better sensitivity to the normal mass hierarchy for CP = -90 (2 = 4.9, see Figure 9) than for CP = 90 (2 = 3.1, see Figure 8) at the 90% confidence level (2 = 2.71 for 1 d.o.f.).

8

Summary and conclusions

This study has fo cused on the future neutrino oscillation long-baseline experiments on a timescale of about ten years. The primary ob jective has been the search for sin2 213 , but we have also analyzed the "atmospheric" parameters 23 and m21 . The main selection 3 criterion for the different experiments has been the availability of specific studies, such as LOIs or proposals, or that they are even being under construction. We assume that an experiment (including data taking and analysis) will only be feasible within the coming ten years, if it is already now actively being planned. The next long-baseline experiments will be the conventional beam experiments MINOS, ICARUS, and OPERA which are currently under construction. In addition, the JPARC-SK and NuMI superbeam experiments are under active consideration with existing proposals and will most likely provide results within the next ten years. Furthermore, new reactor neutrino experiments are actively being discussed. In this study, we have considered the Double-Cho oz pro ject, which will probably deliver results in the anticipated timescale, since infrastructure (such as the detector cavity) of the original CHOOZ experiment can be re-used. First, we have investigated the possible improvement of our knowledge on the leading spheric oscillation parameters. We have found that the conventional beams and super will reduce the error on m21 by roughly an order of magnitude within the next ten 3 The precision of 23 is dominated by JPARC-SK and will improve only by a factor (cf., Table 4). atmobeams years. of two

As the next important issue, we have investigated the potential of the conventional beams, i.e., MINOS, ICARUS, and OPERA, to improve the current sin2 213 bound from CHOOZ and the solar experiments in a complete analysis taking into account correlations and degeneracies. Since the final luminosities of these experiments are not yet determined, we have discussed the results as function of the total number of protons on target. We have found that MINOS could improve the current bound after a running time of about two years, and ICARUS and OPERA combined after about one and a half years. In addition, we have discussed the maximal potential of all three conventional beams combined with a running time of five years each, leading to a final sensitivity limit of sin2 213 0.061 (all sensitivity limits at 90% CL). This final sensitivity limit includes correlations and degeneracies, which means that it reflects the experiment's ability to extract the parameter sin2 213 from the appearance information. Since correlations and degeneracies could be reduced by later experiments, another interesting measure is the systematics-only sin2 213 limit for fixed oscillation parameters, i.e., the sensitivity limit to a specific combination of parameters, which we have called (sin2 213 )eff . We have found a (sin2 213 )eff sensitivity limit for the conventional beams of 0.026, illustrating that correlations and degeneracies have a rather large impact on the sin2 213 limit from conventional beams. Note that it is important to compare different experiments with equal methods, which means that only

21

Current Beams D-Chooz JPA sin 213 sensitivity limit (90% CL) sin2 213 0.14 0.061 0.032 2 (sin 213 )eff 0.14 0.026 0.032 Allowed ranges for leading atmospheric parameters
2 |m21 | 3 10-3 eV2

RC-SK 0.023 0.006 (3 )
0 2+0..15 - 09 .13 .10

NuMI 0.024 0.004
43 2+0..07 -0

Reactor-I I (0.009) (0.009) -

Comb. (0.009) (0.003)
0. 0. +0. )-0. 4

23

(
13

1.2 0.9 +0.20 )-0.20 4

2+ -

Measurements for large s sin 2
2

CP CP violation sgn(m21 ) 3

Combination can exclude up to 40% of all values No sensitivity to CP violation of any tested exp eriment or combination Combination has sensitivity to normal mass hierarchy

-

0.34 0.18 ( )+0.22 4 -0.19 in2 213 = 0.1+0.104 -0.052

2+ -

-

2+ -

0.1 (90% CL) 0.1+ -
0.034 0.033

-

0 ( )+0 4-

( )+ 4- 0.1+ -

0.24 0.21 0 0.1+0 -

-
.010 .008

(

12 06 13 10

0.1+ -

0.067 0.034

0.083 0.043

0.1+ -

0.010 0.008

Table 4: Summary table of this study. The numbers which are printed boldface represent the best individual results within each row. For the true values of the oscillation parameters, we use the current best-fit values from Eq. (3) and a normal mass hierarchy. The precisions for sin2 213 do not include the sgn(m21 )-degeneracy and are computed for the true value CP = 0. If one does not use Reactor-II for the 3 combination of all experiments, but Double-Chooz instead, one obtains the following values: 0.016 for the sin2 213 limit, 0.003 for the (sin2 213 )eff limit, and 0.1+0.025 for the sin2 213 precision. -0.021 sin2 213 or (sin2 213 )eff limits should be compared with each other. teresting to observe that the final sin2 213 sensitivity limit increases within the solar allowed region, whereas the (sin2 213 )eff sensitivity can be understo o d by the amplitude of the CP -terms which is propo In addition, it is inwith increasing m21 2 limit decreases. This rtional to m21 . 2

Furthermore, we have investigated the sin2 213 -limit obtainable by nuclear reactor experiments. A thorough analysis of the Double-Cho oz configuration including systematics and backgrounds, demonstrates that a robust limit of sin2 213 0.032 can be obtained in spite of the non-optimal baseline of 1.05 km. If one aims, however, to significantly higher luminosities than the 60 000 events anticipated by Double-Cho oz, the systematics has to be well under control. In this case, a more optimized baseline of 1.7 km helps to reduce the impact of systematics and backgrounds, and limits of the order of sin2 213 0.014 could be achievable. If in ten years from now no finite value is established, sin2 213 bounds from the conventional beams (MINOS, ICARUS, OPERA), from reactor experiments, such as Double-Cho oz, and from the superbeams JPARC-SK and NuMI will be available. We have demonstrated that the conventional beams could improve the current sin2 213 bound by about a factor of two, the Double-Cho oz experiment by about a factor of four, and the superbeams by about a factor of six. We have also shown that these results apply to a large range within the allowed interval for m21 , since not only the experiment's potential decreases for small values of 3 m21 , but also the current sin2 213 bound. For m21 = 2 З 10-3 eV2 we have found a 3 3 final sin2 213 sensitivity limit of sin2 213 0.02 for the superbeams. Note that, though the Double-Cho oz setup is not as go o d as the superbeams, its results are not affected by the true 22

value of m21 within the solar-allowed range [20], which means that a reactor experiment 2 is more robust with respect to the true parameter values. Moreover, because correlations and degeneracies do not effect the sin2 213 limit from reactor experiments, the sin2 213 and (sin2 213 )eff limits are almost identical for Double-Cho oz. In contrast, for the superbeams the (sin2 213 )eff limit is nearly one order of magnitude smaller than the sin2 213 limit (cf., Table 4), demonstrating that correlations and degeneracies are crucial for them. In order to illustrate where we could stand in ten years from now if sin2 213 were close to the current bound, we have also performed an analysis by assuming sin2 213 = 0.1. In this case, all the considered experiments will establish the finite value of sin2 213 and measure it with a certain precision (cf., Table 4). In this situation, which is theoretically well motivated (cf., Table 1 of Ref. [16]), one could even aim to learn something about CP and the neutrino mass hierarchy with the next generation of experiments. Since the results of superbeam experiments will lead to strong correlations between CP and sin2 213 , it is well known that complementary information is needed to disentangle these two parameters. One can either use extensive antineutrino running at the superbeams (which, however might not be possible at the time scale of ten years, because of the lower antineutrino cross sections), or a large reactor experiment to measure sin2 213 . In this study, we have demonstrated the potential for CP by assuming such a large reactor experiment at an ideal baseline of L = 1.7 km, which we call Reactor-I I. Though such an experiment might not exactly fit into the discussed timescale, it might be realized so on thereafter. Possible sites for such an experiment are under investigation [16] (some proposals, which are, for example, discussed in the US, are similar to our Reactor-I I setup). Indeed, we find that in this optimal situation (sin2 213 = 0.1), up to 40% of all possible values for CP could be excluded (90 % CL). This result, however, depends strongly on the true value of CP , and applies to maximal CP violation. For the case of CP conservation (true parameter value), however, nothing at all could be learned about CP . In either case, a sensitivity to CP violation would not be achievable with the discussed experiments because of to o low statistics. For the mass hierarchy determination, we have found that one would be sensitive to a normal mass hierarchy at the 90% confidence level, where the sensitivity to the inverted mass hierarchy would be somewhat worse [48]. Note that the sensitivity to the mass hierarchy is mainly determined by matter effects in NuMI, and could even be better for NuMI-baselines larger than 812 km. To summarize, from the current perspective neutrino oscillations will remain a very exciting field of research, and the experiments considered within the next ten years will significantly improve our knowledge. Eventually, these experiments could indeed restrict CP and determine the neutrino mass hierarchy within the coming ten to fifteen years if sin2 213 turns out to be sizeable. The remaining ambiguities could be resolved by the subsequent generation of experiments, such as superbeam upgrades, beta beams, or neutrino factories [29, 49]. Acknowledgments We want to thank M. Go o dman and K. Lang for providing input data and useful information about the MINOS experiment, especially the PH2low beam flux data. Furthermore, we thank T. Lasserre, H. deKerret and L. Oberauer for very useful discussions on the Double23

Cho oz pro ject. This study has been supported by the "Sonderforschungsbereich 375 fur ? Astro-Teilchenphysik der Deutschen Forschungsgemeinschaft".

24

A

Simulation details of the conventional b eam exp eriments

In this appendix, we describe our simulations of the conventional beam experiments MINOS, ICARUS, and OPERA in greater detail. In Appendix A.1 we give the numbers and references for the experimental parameters used, and in Appendix A.2 we demonstrate that our calculations repro duce the results of the simulations of the experimental collaborations to go o d accuracy. A.1 Description of the experiments and experimental parameters

The MINOS experiment will use both a near and far detector. The near detector allows to measure the neutrino flux and energy spectrum. In addition, other important characteristics, such as the initial e contamination of the un-oscillated neutrino beam can be extracted with go o d precision. Besides the smaller detector mass of 1 kt, it is constructed as identical as possible to the far detector in order to suppress systematical uncertainties. The far detector is placed 713 m deep in a newly built cavern in the Soudan mine in order to suppress cosmic ray backgrounds. It is an o ctagonal, magnetized iron calorimeter with a diameter of 8 m, assembled of steel layers alternating with scintillator strips with an overall mass of 5.4 kt. The construction of the far detector was finished in spring of 2003 and it is now taking data on atmospheric neutrinos and muons. The mean energy of the neutrino beam pro duced at Fermilab can be varied between 3 and 18 GeV. The beam is planned to start with the low energy configuration (PH2low), with the peak neutrino energy at E 3 GeV. In our simulation we use the official PH2low beam configuration [44], which means that we do not include a hadronic hose or different beam-plugs in the beam line setup. These mo difications would lead to a better signal to background ratio. However, as discussed in Ref. [44], they affect the sensitivity limits to sin2 213 only marginally. The NuMI PH2low beam flux data, as well as the detection cross sections have been provided by Ref. [50]. We use 30 energy bins in the energy range between 2 GeV and 6 GeV. In addition, the energy resolution is assumed to be E = 0.15 З E [11]. The NuMI beam will have a luminosity of 3.7 З 1020 pot y-1 . In addition to the Е e appearance channel most relevant for the sin2 213 measurement, we include also the Е Е disappearance channel with an efficiency of 0.9, and we take into account that a fraction of 0.05 of the neutral current background events will be misidentified as signal events. For the CNGS experiments, we use the flux and cross sections from Ref. [51]. For both ICARUS and OPERA, we use an energy range between 1 and 30 GeV, which is divided into 80 bins. For ICARUS, we assume an energy resolution of E = 0.1 З E [45], and for OPERA E = 0.25 З E . The latter might be somewhat overestimated [13]. However, our 13 limit at OPERA changes less than 5% for values of the energy resolution up to E = 0.4 З E . For the CNGS beam, we assume a nominal luminosity of 4.5 З 1019 pot y-1 .

The original purpose of the CNGS experiments is the observation of Е appearance. The OPERA detector is an emulsion cloud chamber, and the extremely high granularity of the emulsion allows to detect the events directly by the so-called "kink", which comes from the semi-leptonic decay of the tauons. In order to reach a significant detector mass, the emulsion layers are separated by lead plates of 1 mm thickness. The total fiducial mass 25

of the detector will be 1.8 kt. However, during the extraction of the data, the detector mass will change as a function of time. Therefore, we use the time averaged fiducial mass of 1.65 kt for our analysis. A main challenge in the OPERA experiment is the automated scanning of the emulsions. The ICARUS detector uses a different approach: it is a liquid Argon TPC, which allows to reconstruct the three dimensional topology of an event with a spacial resolution of roughly 1 mm on an event by event basis. The detection is performed by a full kinematical analysis. The fiducial mass will be 2.35 kt. For the OPERA experiment, we include the information from the Е channel by assuming an efficiency of 0.11, and a fraction of 3 З 10-5 of misidentified neutral current events. For the ICARUS experiment, we use an efficiency of 0.075 for this channel with a background fraction of 8.5 З 10-5 of the neutral current events [12]. Although the ICARUS and OPERA detectors are optimized to observe the decay properties of -leptons, they also have very go o d abilities for muon identification, which allows to measure also Е disappearance. We therefore include the Е Е CC channel in both CNGS experiments, assuming a detection efficiency of 0.9 and taking into account a fraction of 0.05 of all neutral current events as background. As a matter of fact, the measurement of the atmospheric parameters also contributes to the sin2 213 sensitivity limit, since correlation effects decrease with a higher precisions on the atmospheric parameters. Therefore, the sin2 213 sensitivity at ICARUS and OPERA is considerably improved by including (besides the Е e channel) the Е appearance and the Е disappearance channels in the fit. We have checked for all setups that the results do not depend significantly on the energy range, energy resolution, and bin size as long as the energy information is sufficient to distinguish the shape of the signal from the shape of the background.

The sin2 213 sensitivity of the different experiments is provided mainly by the information from the Е e appearance channel. Because of the small value of sin2 213 , the number of Е e CC events will be very small compared to the Е Е CC and NC events. Furthermore, the events from the intrinsic e component of the beam create a background to the oscillation signal. Thus, in our simulation, we consider as possible backgrounds: Beam e CC events, misidentified Е CC events, misidentified CC events (mainly for CNGS), and misidentified NC events. We have calibrated the various background sources in our simulation carefully with respect to the information given in the literature. The corresponding references are for MINOS Table 3 of Ref. [44], for ICARUS Ref. [12], and for OPERA Table 4 of Ref. [45]. Using this information, we can repro duce with high accuracy the numbers of signal and background events provided by the experimental collaborations, which can be found in Table 5. A.2 Reproduction of the analyses performed by the experimental collaborations

In order to demonstrate the reliability and accuracy of our calculations, we use in this appendix the analysis techniques from Refs. [12, 44, 45], and compare our results with the ones in these references. For this purpose, we neglect all correlations and degeneracies, i.e., we set the solar mass splitting to zero, which also eliminates the solar mixing angle and CP effects. In addition, we fix the atmospheric mixing angle to /4. Thus, the only remaining 26

Experiment MINOS ICARUS OPERA

Reference NuMI-L-714 [44] T600 proposal [12] Komatsu et al. [45]

Signal Background Е e e e Е Е Е NC Total 8.5 5.6 3.9 3.0 27.2 39.7 51.0 79.0 76.0 - 155.0 5.8 18.0 1.0 4.6 5.2 28.8

Table 5: The signal and background events for the three conventional beam experiments. The reference
points are m21 = 3.0 З 10-3 eV2 , sin2 13 = 0.01 for MINOS, m21 = 3.5 З 10-3 eV2 , sin2 213 = 0.058 3 3 for ICARUS, m21 = 2.5 З 10-3 eV2 , sin2 213 = 0.058 for OPERA, and sin2 223 = 1, m21 = sin2 212 = 3 2 CP = 0 in all three cases. The nominal exposures are 10 kt y (MINOS), 20 kt y (ICARUS), and 8.25 kt y (OPERA). Note that these numbers are different from the ones in Table 3, since different reference points and luminosities are used.

parameters are 13 and m21 , where m21 is assumed to be exactly known. For both MINOS 3 3 and the CNGS experiments, we use the background uncertainties given in Refs. [12, 44, 45], i.e., 10% for MINOS and 5% for ICARUS and OPERA. Then we simulate data for each value of m21 with 13 = 0, and fit these data with 13 as the only free parameter. This simplified 3 pro cedure leads to a limit similar to (sin2 213 )eff , which represents the ability to identify a signal (but not to extract sin2 213 ), and is similar to a simple estimate of S/ S + B . In Figure 10, we compare the discussed effective sin2 213 limit to the ones of the experimental collaborations. The solid black curves represent our results, whereas the dashed gray curves are taken from Refs. [12, 44, 45]. Within the Super-Kamiokande allowed atmospheric region, our simulation is in very go o d agreement with the results of the different collaborations. The slight deviation in the OPERA curve at large values of m21 comes from the 3 efficiencies in Ref. [45], since they are only given as energy-integrated quantities. Thus, it is not possible to fully repro duce the energy dependence of the events. This effect becomes stronger if the oscillation maximum is shifted to higher energies compared to the reference point used in Ref. [45]. However, the influence on our results is marginal, since OPERA do es not contribute significantly to the 13 sensitivity. Note that the numbers given in Table 5 and the results shown in Figure 10 do not allow a comparison of the different experiment performances, because the reference points used for the calculation of Table 5 are rather different, and so are the integrated luminosities. For a comparison on equal fo oting we refer to Table 3 and the discussion in Section 5.

B

Simulation of the reactor exp eriments

For our simulation of the reactor neutrino experiments, we closely follow our previous work in Ref. [20]. For the analyses presented here, we assume a near detector baseline of LND = 0.15 km and we consider two options for the far detector baseline: LFD = 1.05 km corresponds to the baseline at the CHOOZ site, whereas a baseline LFD = 1.7 km is close to the options considered for several other sites. We always fix the number of reactor neutrino events in the near detector to 2.94 З 106 , which implies that it has the same size as the far detector at LFD = 1.05 km with 60 000 events (assuming the same efficiencies in both

27

The effective sin2 213 sensitivity limit (as discussed in the main text) at 90% CL as a function of the true value of m21 for the conventional beam experiments. The exposure is 10 kt y for 3 MINOS, 20 kt y for ICARUS and a nominal running time of five years for OPERA, corresponding to an exposure of 8.25 kt y. The dashed gray curves come from the collaborations of the individual experiments and are taken from Ref. [44] for MINOS, Ref. [12] for ICARUS, and Ref. [45] for OPERA. The black curves are obtained for sin2 223 = 1 and m21 = sin2 212 = CP = 0 for systematics only, i.e., correlations and 2 degeneracies are not included, as for the dashed curves.

Figure 10:

detectors6 ). We allow an uncertainty of the overall reactor neutrino flux normalization of abs = 2.5%. For the normalization error between the two detectors, we use a typical value of rel = 0.6%. As shown in Ref. [20], this roughly corresponds to an effective normalization error of norm 0.8%. The total range for the visible energy Evis = E - + me (where ? is the neutron-proton mass difference, and me is the electron mass) from 0.5 MeV to 9.2 MeV is divided into 31 bins. Furthermore, we assume a Gaussian energy resolution with res = 5%/ Evis [MeV]. We remark that our results do not change if a smaller bin width is chosen, as it would be allowed by the go o d energy resolution and the large number of events. Furthermore, we take into account an uncertainty on the energy scale calibration cal = 0.5%, and an uncertainty on the expected energy spectrum shape shape = 2%, which we assume to be uncorrelated between the energy bins, but fully correlated between the corresponding bins in near and far detectors (see Ref. [20] for details). In addition to the analysis as performed in Ref. [20], we have investigated in greater detail the impact of a background for a reactor experiment of the Double-Cho oz type. We take into account four different background sources with known shape: З A background from spallation neutrons coming from muons in the ro ck close to the detector. This background can be assumed to be flat as a function of energy to a first approximation (see, e.g., Figure 48 of Ref. [10]). З A background from accidental events. A from radioactivity is followed by a second random with more than 6 MeV faking a neutron signal. Those events are important for low energies.
Due to a higher background rate in the near detector, there will more dead time than in the far detector. This reduces the number of events in the near detector roughly by a factor of two. We have checked that this has a very small impact on the final sensitivity.
6

28

З Two correlated backgrounds from cosmogenic 9 Li and 8 He nuclei. Both are created by through-going muons and give -spectra with end points of 13.6 and 10.6 MeV, respectively. In Table 6, we give for each background a realistic estimate [52] for the expected number of events in near and far detectors relative to the number of reactor neutrino events. Since the near detector will have less ro ck overburden than the far detector, more background events are expected. They are, however, compensated by the much larger number of reactor neutrino events in the near detector. Therefore, we assume to a first approximation the same relative sizes for the backgrounds in near and far detector. In Figure 11, the spectral shape of these backgrounds is shown. We assume that these shapes are exactly known, however, the overall normalization of each of the four background components in the two detectors is allowed to fluctuate independently with an error of BG = 50%. In addition to these backgrounds with known shape, we include a background from an unidentified source with a bin-to-bin uncorrelated error of 50%. We assume a total number of background events of 0.5% of the reactor signal in both detectors, and a flat energy shape for this background. As a general trend, we find that backgrounds with known shape do not significantly affect the sensitivity. This holds independently of the integrated luminosity. Even increasing the numbers given in Table 6 by a factor five do es not change the picture. This behavior can be understo o d in terms of Figure 11, where we show the signal (the spectrum without oscillation minus the spectrum for sin2 213 = 0.05) and its statistical error compared to the various background spectra. For illustration, background levels significantly larger than in Table 6 are assumed. From this figure, it is obvious that the spectral shape of the signal is very different from that of all of the background components. Already at mo dest luminosities, such as for Double-Cho oz, enough spectral information is available to determine the backgrounds with sufficient accuracy, which means that it is not possible to fake the Background type Spectral shape Backgrounds with known shape Spallation neutrons Flat Accidentals Low energies 9 Cosmogenic Li -spectrum (end point 13.6 MeV) 8 Cosmogenic He -spectrum (end point 10.6 MeV) Bin-to-bin correlated BG total: Bin-to-bin uncorrelated background Unknown source Flat BG/Reactor events 0 0 0 0 1 .4 .2 .2 .2 .0 B
G

% 50% % 50% % 50% % 50% % 50%

0.5%

Table 6: Backgrounds included in our reactor experiment analysis. For each background source, the column "BG/Reactor events" refers to the total number of background events in the energy range between 0.5 and 9.2 MeV relative to the total number of reactor neutrino events for no oscillations [52]. We assume the same magnitudes of the backgrounds relative to the total events in the near and far detectors. For the backgrounds with known shape, BG is the uncertainty of the overall normalization. For the uncorrelated background, BG is the error on the number of events in each bin, which is uncorrelated between different bins (31 bins). All backgrounds are uncorrelated between the two detectors. 29

Energy spectrum of backgrounds and signal
400 Number of events / MeV Signal

300

200

Accidentals
100

Total BG (3.6%) Spallation neutrons (2%)

(0.8%)
Cosmogenics (0.4% + 0.4%) 0 1 2 3 4 E 5 6 [MeV] 7 8 9 10

vis

Figure 11: Energy spectrum of the backgrounds from spallation neutrons, accidentals, and cosmogenic
Li and 8 He. The percentage relative to the total number of spectrum. The curve labeled where N (Evis ; sin2 213 ) is the
9

given for each curve corresponds to the total number of background events reactor neutrino events for no oscillations. Also shown is the total background "signal" corresponds to N (Evis ; sin2 213 = 0) - N (Evis ; sin2 213 = 0.05), energy spectrum for given sin2 213 . The shaded region is the statistical error
13

band at 1 , i.e., Б N (Evis ; sin2 2 exaggerated in this figure.

= 0). Note that the absolute normalizations of the backgrounds are

signal within the statistical error by fluctuations of the background components. In contrast, we find that the bin-to-bin uncorrelated background only plays a minor role for experiments of the size of Double-Cho oz, whereas it becomes important for large experiments, such as Reactor-I I. In the latter case, a background level of 0.5% with a bin-to-bin uncorrelated error larger than about 20% would significantly affect the sensitivity. We conclude that for large reactor experiments, the shape of the expected background has to be well under control.7 In Table 7, we summarize the experimental parameters which we use for the two setups Double-Cho oz and Reactor-I I in the main text of this study. For the Double-Cho oz setup, we stick closely to the configuration discussed in Ref. [23]. We have checked that the effect of the slightly different distances (1.0 km and 1.1 km) of the far detector lo cation from the two different reactor cores at the CHOOZ site is very small. Hence it is a go o d approximation to consider the average baseline of 1.05 km for both cores. In order to obtain robust results, we include all systematical errors as well as backgrounds. The large reactor experiment Reactor-I I corresponds to the same setup as already used in Ref. [20]. It represents an ideal configuration without backgrounds and any systematical errors beyond overall normalization errors. This setup has been chosen to illustrate how
Note that the above statements quantitatively depend to some extent on the chosen number of bins. For example, a bin-to-bin uncorrelated error of 20% for 10 bins has, in general, a different impact than such an error for 60 bins. This can be understood by the fact that for a large number of bins, the simultaneous fluctuation of neighboring bins becomes unlikely. The same argument holds for the flux shape uncertainty shape .
7

30

Luminosity L Number of events in ND Number of events in FD Near detector baseline Far detector baseline Energy resolution Visible energy range Individual detector normalization Flux normalization Flux shape uncertainty Energy scale error Backgrounds included

Double-Cho oz Reactor-I I 288 t G W y 8000 t G W y 2.94 З 106 2.94 З 106 6 З 1 04 6.36 З 105 0.15 km 0.15 km 1.05 km 1.70 km res = 5%/ E [MeV] 0.5 - 9.2 MeV (31 bins) rel = 0.6% rel = 0.6% abs = 2.5% abs = 2.5% shape = 2% shape = 0 cal = 0.5% cal = 0 Yes No

Table 7: Characteristics of the two reactor experiments Double-Chooz and Reactor-II. an optimal reactor experiment would fit into the general picture of the next ten years of oscillation physics and, to obtain CP-complementary information. Several proposals which are close to our Reactor-I I setup are currently discussed [16].

C

The definition of the sin2 213 sensitivity limit

In this appendix, we discuss the definition of the sin2 213 sensitivity limit. Although this definition is very general, we mainly fo cus on the Е e appearance channel, since one has to deal extensively with parameter correlations and degenerate solutions in this case. Let us first define our sin2 213 sensitivity and then discuss its properties. Definition 1 We define the sin2 213 sensitivity limit as the largest value of sin2 213 , which fits the true value sin2 213 = 0 at the chosen confidence level. The largest value of sin2 213 is obtained from the projections of al l (disconnected) fit manifolds (best-fit manifold and degeneracies) onto the sin2 213 -axis. Since for future experiments no data are available, one has to simulate data by calculating a "reference rate vector" for a fixed set of "true" parameter values. In general, the experiment performance depends on the chosen set of true parameter values, and it is interesting to discuss this dependency in many cases. It is especially relevant for the true values of m21 2 and m21 , which we usually cho ose within their currently allowed ranges. According to 3 Definition 1, we cho ose the true value sin2 213 = 0 to calculate the sin2 213 limit, since we are interested in the bound on sin2 213 if no positive signal is observed. Moreover, this choice has the following advantages: З Since for sin2 213 = 0 the phase CP becomes unphysical, the sensitivity limit will be independent of the true value of CP . 31

З For sin2 213 = 0, the reference rate vectors for the normal and the inverted mass hierarchies are approximately equal, which implies that the sensitivity limit hard ly depends on the true sign of m21 (see also the discussion related to Figure 12 later). 3 Once the reference rate vector has been obtained, the fit manifold in the six-dimensional space of the oscillation parameters is given by the requirement 2 CL (e.g., at the 90% confidence level, we have CL = 2.71 for 1 d.o.f.). In addition to the allowed region which contains the best-fit point ("best-fit manifold"), one or more disconnected regions ("degenerate solutions") will exist, and each of them may have a rather complicated shape in the six-dimensional space ("correlations"). The final sensitivity is given by the largest value of sin2 213 which fits sin2 213 = 0. It is obtained by pro jecting al l these disconnected fit regions onto the sin2 213 -axis, where the pro jection takes into account the correlations. Hence, this pro cedure provides a straightforward metho d to take into account correlations and degeneracies. Thus, for the case of the Е e appearance channel, our definition of the sin2 213 sensitivity limit includes the intrinsic structure of Eq. (1). This equation reflects that an appearance experiment is only sensitive to a particular combination of parameters. The pro jection onto the sin2 213 -axis takes into account that all the other parameters can be only measured with a certain accuracy by the experiment itself. Moreover, in complicated cases (e.g., for neutrino factories) lo cal minima may appear in the pro jection of the 2 function onto the sin2 213 -axis, and the 2 -function can intersect the chosen confidence level multiple times. In this case, we cho ose by definition the rightmost of these intersections. Hence, the sensitivity limit, as defined above, refers to the potential of an experiment (or combination of experiments) to extract the value of the parameter sin2 213 from Eq. (1) convolved with all the simulation information. In this study, we compare the sin2 213 sensitivity limit of a given experiment to a socalled (sin2 213 )eff sensitivity limit in some cases. The (sin2 213 )eff sensitivity limit roughly corresponds to the potential of a given experiment to observe a positive signal, which is parameterized by some (unphysical) mixing parameter (sin2 213 )eff : Definition 2 The (sin2 213 )eff sensitivity limit is defined as the sensitivity limit from statistics and systematics only which is computed for CP = 0 by fixing al l other oscil lation parameters to their true values. In order to illustrate the impact of systematics, correlations, and degeneracies, we often use "bar charts" (see, for example, Figures 3 and 6), where the final sin2 213 sensitivity is obtained by successively switching on systematics, correlations, and degeneracies. In these bar charts, the statistics-only sin2 213 sensitivity (left edge of the bar) is computed for all oscillation parameters fixed and CP = 0, the statistics+systematics sensitivity limit corresponds to the (sin2 213 )eff sensitivity limit, the statistics+systematics+correlations limit corresponds to the sensitivity limit for the best-fit manifold only (no degenerate solutions included), and the final sensitivity limit (right edge of the bar) corresponds to Definition 1. In the following, we illustrate in greater detail how the sin2 213 limit is obtained, how the bar charts are constructed, and how the sin2 213 and (sin2 213 )eff limits are related to each other at the example of the JPARC-SK experiment. We fo cus mainly on the sgn(m21 )3 32

The 2 as function of sin2 213 for JPARC-SK. For the true values of the oscillation parameters, we choose the current best-fit values from Eq. (3), sin2 213 = 0, CP = 0 (for curves without correlations only), and normal (upper plot) or inverted (lower plot) mass hierarchies. The solid curves in each plot are obtained by fitting with the same mass hierarchy as has been used to calculate the reference rate vector ("right-sign"), whereas for the dashed curves the wrong mass hierarchy has been used ("wrongsign"). Within each group of solid or dashed curves, the left curve determines the statistics-only limit, the middle curve the statistics+systematics limit, and the right curve the statistics+systematics+correlations limit. Note that the wrong-sign minimum has not exactly the same position in parameter space as the original minimum.

Figure 12:

degeneracy and the correlation between 13 and CP , which is of particular relevance for the Е e appearance channel at superbeams.

In Figure 12, the 2 is shown as a function of sin2 213 for the "right-sign" and "wrongsign" solutions, where in the upper (lower) plot the normal (inverted) hierarchy has been chosen to calculate the reference rate vector. The right-sign solution is obtained by fitting with the same sign of m21 as the reference rate vector has been calculated with, i.e., 3 the "right" neutrino mass hierarchy is used, whereas the wrong-sign solution is obtained by fitting with the opposite sign of m21 , i.e., the "wrong" mass hierarchy is used. The 3 different curves in each group with the same curve style correspond, from the left to the right, to the statistics-only, statistics+systematics, and statistics+systematics+correlations 33

Figure 13: The 90% CL fit manifold (1 d.o.f.) in the sin2 213 -CP -plane for JPARC-SK. For the true
values of the oscillation parameters, we choose the current best-fit values from Eq. (3) different curves correspond to various sections (un-displayed oscillation parameters (minimized over un-displayed oscillation parameters) as described in the plot legend. the individual contributions to the final sin2 213 sensitivity limit. Note that for the solution, we only show the final pro jection. and sin2 213 = 0. The fixed) and pro jections The bars demonstrate sgn(m21 )-degenerate 3

sensitivity limits, where these limits are obtained from the intersection of the 2 with the 2 = 2.71 line. The bar charts are constructed from the corresponding curves, as one can easily read off the figure. Comparing the normal and inverted mass hierarchy plots in Figure 12, one can observe a symmetry between the right- and wrong-sign solutions: The curves for the normal mass hierarchy and m21 > 0 (right sign) are very similar to the ones of the inverted mass 3 hierarchy and m21 > 0 (wrong sign). This can be understo o d in terms of the identical 3 appearance rate vectors for the normal and inverted mass hierarchies for the true value of sin2 213 = 0. However, since the role of the m21 > 0 curves is different for the normal 3 and inverted mass hierarchies, i.e., they either correspond to the best-fit manifold (right sign) or the sgn(m21 )-degeneracy (wrong sign), the bar charts are, by definition, very 3 different, since they are originally determined by the best-fit solution. However, one can easily see that the final sensitivity limit do es not depend on the mass hierarchy [26]. This property comes from the fact that the degeneracy part do es not contribute to the final sensitivity if the best-fit sin2 213 sensitivity is already worse than the degenerate solution sensitivity. Since there is hardly a difference between final sensitivity limits for the different mass hierarchies, we usually show the normal mass hierarchy sensitivity limit. In fact, there is a small difference between the final sensitivity limits for the different mass hierarchies, which mainly comes from the disappearance channels. Let us now illustrate the impact of the correlation between sin2 213 and CP . Therefore, we show in Figure 13 the fit manifold in the sin2 213 -CP -plane. The sin2 213 sensitiv34

ity limit is again obtained from the pro jection onto the sin2 213 -axis. In Figure 13, the individual contributions to the bar chart are illustrated by showing different sections (undisplayed oscillation parameters fixed, i.e., no correlations) and pro jections (minimized over un-displayed oscillation parameters, i.e., they include correlations) of the fit manifold. One can see that both edges of the leftmost (blue) bar are computed for CP = 0. This illustrates that if CP and all the other oscillation parameters except sin2 213 are fixed at the true values, much stronger bounds on sin2 213 can be obtained, corresponding to the (sin2 213 )eff limit. The limit gets considerably weaker if the 2 -function is minimized over CP , as well as all oscillation parameters which are not shown, which leads to the "correlation bar". In fact, from Figure 13, one can see that the largest part of the correlation bar comes from the correlation with CP [53], and only the small difference between the dark dashed and the light solid curves comes from the correlation with the other oscillation parameters. The final sensitivity limit is then obtained as the maximum value of sin2 213 which fits sin2 213 = 0 including all degenerate solutions.

35

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