Exploring the three flavor effects with future superbeams using liquid argon detectors

Recent measurement of a moderately large value of theta13 signifies an important breakthrough in establishing the standard three flavor oscillation picture of neutrinos. It has provided an opportunity to explore the sub-dominant three flavor effects in present and future long-baseline experiments. In this paper, we perform a comparative study of the physics reach of two future superbeam facilities, LBNE and LBNO in their first phases of run, to resolve the issues of neutrino mass hierarchy, octant of theta23, and leptonic CP violation. We also find that the sensitivity of these future facilities can be improved significantly by adding the projected data from T2K and NOvA. Stand-alone LBNO setup with a 10 kt detector has a mass hierarchy discovery reach of more than 7 sigma, for the lowest allowed value of sin^2theta23(true) = 0.34. This result is valid for any choice of true deltaCP and hierarchy. LBNE10, in combination with T2K and NOvA, can achieve 3 sigma hierarchy discrimination for any choice of deltaCP, sin^2theta23, and hierarchy. The same combination can provide a 3 sigma octant resolution for sin^2theta23(true) leq 0.44 or for sin^2theta23(true) geq 0.58 for all values of deltaCP(true). LBNO can give similar results with 10 kt detector mass. In their first phases, both LBNE10 and LBNO with 20 kt detector can establish leptonic CP violation for around 50% values of true deltaCP at 2 sigma confidence level. In case of LBNE10, CP coverage at 3 sigma can be enhanced from 3% to 43% by combining T2K and NOvA data, assuming sin^2theta23(true) = 0.5. For LBNO setup, CP violation discovery at 3 sigma is possible for 46% values of true deltaCP if we add the data from T2K and NOvA.


Introduction and Motivation
The discovery of neutrino oscillations over the past decade provides firm evidence for new physics. Recently, the unknown 1-3 lepton mixing angle has been measured quite precisely by the reactor experiments [1][2][3][4]. They have found a moderately large value, not too far from its previous upper bound. This represents a significant milestone towards addressing the remaining fundamental questions, in particular determining the neutrino mass hierarchy and searching for CP violation in the neutrino sector. Another recent and crucial development is the indication of non-maximal 2-3 mixing by the MINOS accelerator experiment [5,6], leading to the problem of determining the correct octant of θ 23 . It is possible to resolve all the above three issues by the observation of ν e appearance via ν µ → ν e oscillations. The determination of CP violation in particular requires the full interplay of three flavor effects in neutrino oscillations.
Oscillation data are insensitive to the lowest neutrino mass. However, it can be measured in tritium beta decay processes [7], neutrinoless double beta decay experiments [8], and from the contribution of neutrinos to the energy density of the universe [9]. Very recent data from the Planck experiment in combination with the WMAP polarization and baryon acoustic oscillation measurements have set an upper bound on the sum of all the neutrino mass eigenvalues of m i ≤ 0.23 eV at 95% C.L. [10]. But, oscillation experiments are capable of measuring the two independent mass-squared differences: ∆m 2 21 = m 2 2 − m 2 1 and ∆m 2 31 = m 2 3 − m 2 1 . ∆m 2 21 is required to be positive by the solar neutrino data but at present ∆m 2 31 can be either positive or negative. Hence, two patterns of neutrino masses are possible: m 3 > m 2 > m 1 , called normal hierarchy (NH) where ∆m 2 31 is positive and m 2 > m 1 > m 3 , called inverted hierarchy (IH) where ∆m 2 31 is negative. Leptonic CP violation can be established if CP violating phase δ CP in the mixing matrix, differs from both 0 and 180 • . So far, there is no constraint on δ CP . It can take any value in the range [−180 • , 180 • ]. Regarding θ 23 , all global fits [11][12][13]  Settling the issue of neutrino mass hierarchy is crucial to determine the structure of neutrino mass matrix. This structure will provide the fundamental input needed to develop the theory of neutrino masses and mixing [14]. Neutrino mass hierarchy is also a key parameter for neutrinoless double beta decay searches probing the Majorana nature of neutrinos [15]. Another fundamental issue that needs to be addressed in long-baseline experiments is to establish leptonic CP violation and measure δ CP . This new CP violation in the lepton sector may be able to explain the observed matter anti-matter asymmetry in the universe via leptogenesis [16]. A number of innovative ideas, such as µ ↔ τ symmetry [17], A 4 flavor symmetry [18], quark-lepton complementarity [19], and neutrino mixing anarchy [20,21] have been invoked to explain the observed pattern of one small and two large mixing angles in the neutrino sector. Measurements of the precise values of θ 13 and θ 23 will reveal the pattern of deviations from these symmetries and will lead to a better understanding of neutrino masses and mixing. In particular, the resolution of θ 23 octant will severely constrain the patterns of symmetry breaking. With the recent discovery of moderately large value of θ 13 , these three fundamental measurements fall within our reach.
The combined data from the current ν e appearance experiments, T2K [22,23] and NOνA [24][25][26], can provide a hint at 90% confidence level for neutrino mass ordering [27] and at 95% confidence level for octant of θ 23 [28,29]. They can determine these quantities at > 99% C.L. only for a very small range of favorable values of δ CP . Discovery of leptonic CP violation is possible at 95% C.L. only for values of δ CP close to ±90 • , i.e. where CP violation is maximum [27]. Hence, future facilities consisting of intense, high power wide-band beams and large smart detectors are mandatory to cover the entire parameter space at a high confidence level. In this paper, we explore the capabilities of future superbeam experiments with liquid argon detectors, LBNE [30][31][32][33][34] and LBNO [35][36][37][38][39] towards resolving these unknowns. We first present the stand-alone performances of these setups in their first phases. Then we examine how the addition of projected data from T2K and NOνA, can improve the sensitivity of these future facilities. We also study in detail how these sensitivities change as the true value of sin 2 θ 23 varies in its allowed 3σ range of 0.34 to 0.67.
We start with a brief discussion of ν µ → ν e oscillation channel in section 2. In section 3, we describe the important features of the experimental setups under consideration. Next, we introduce the concept of bi-events plots (ν e vs.ν e appearance events) to explain the underlying physics in section 4. In section 5, we present our results. Finally, we summarize and draw our conclusions in section 6.

Platinum Channel: Test Bed for Three Flavor Effects
A study of ν µ → ν e andν µ →ν e oscillations at long-baseline superbeam experiments is the simplest way to probe three flavor effects, including sub-leading ones. Such a study is capable of achieving all the three objectives mentioned in section 1. An approximate analytic expression for the oscillation probability, P µe , in matter [40][41][42], is given by  [43][44][45]. Here, A is the matter potential, expressed in terms of the electron density, N e , and the (anti-)neutrino energy E. It is positive for neutrinos and negative for anti-neutrinos. For anti-neutrinos, the term proportional to sin δ CP has the opposite sign. So far, it was possible to analyze the data from each oscillation experiment using an appropriate, effective two flavor oscillation approach because of the smallness of the mixing angle sin 2θ 13 0.3 and the ratio α 0.03. This method has been quite successful in measuring the solar and atmospheric neutrino parameters. The next step must involve probing the full three flavor effects, including the sub-leading ones proportional to α. This task will be undertaken, for the first time, by the current generation experiments T2K and NOνA.
In this paper, we consider two future long-baseline superbeam experiments with large matter effect. The matter effect increases P (ν µ → ν e ) oscillation probability for NH and decreases it for IH. For anti-neutrinos the situation is reversed. It can be seen from equation 2.1 that the dominant term (C 0 ) is driven by matter modified ∆m 2 31 and is proportional to sin 2 θ 23 sin 2 2θ 13 but the sub-dominant δ CP dependent terms (C − & C + ) are suppressed by α. Since the hierarchy and δ CP are both unknown, the interplay of the terms C 0 , C − , and C + in equation 2.1 gives rise to hierarchy-δ CP degeneracy [46]. If the matter effects are large enough, this degeneracy can be broken completely. This is not the case for T2K and NOνA, because of which their sensitivity to hierarchy is modest for about half the δ CP range. There is a similar octant-δ CP degeneracy also, which limits our ability to determine the correct octant of θ 23 . This problem can be solved by having substantial data in both ν andν channels [28]. Both the future facilities, LBNE (baseline of 1300 km) and LBNO (baseline of 2290 km) will operate at multi-GeV energies with very long-baselines. This will lead to a large enough matter effect which breaks the hierarchy-δ CP degeneracy completely. They are also scheduled to have equal ν andν runs, and can resolve the octant-δ CP degeneracy effectively. These experiments are planning to use liquid argon time projection chambers (LArTPCs) which have excellent kinematic reconstruction capability for all the observed particles. This feature helps in rejecting almost all of the large neutral current background.

Experimental Specifications
In this section, we briefly describe the key experimental features of the current (off-axis) and future (on-axis) generation long-baseline superbeam experiments that we use in our simulation.

Current Generation: T2K and NOνA
In Japan, the Tokai-to-Kamioka (T2K) experiment [22,23] started taking data in 2010. The NOνA experiment [24][25][26] in the United States is now under construction and will start taking data near the end of this year. The main goal of these experiments is to detect the electron neutrino appearance events in a ν µ beam using the classic off-axis beam technique [47] that delivers a beam with a narrow peak in the energy spectrum. The position of this peak is tuned to be close to the expected oscillation maximum. In our study, we have explored the improvement in the physics capabilities of LBNE and LBNO in their first phases, due to the addition of the projected data from T2K and NOνA experiments.
In the T2K experiment, a 2.5 • off-axis ν µ beam from J-PARC is observed in the Super-Kamiokande detector (fiducial volume 22.5 kt) at Kamioka, at a distance of 295 km [22]. The neutrino flux peaks sharply at the first oscillation maximum of 0.6 GeV. For mass hierarchy and CP violation studies, we consider 5 years of neutrino run with a beam power of 0.75 MW as officially announced. Recently, it has been shown in reference [28] that equal runs in neutrino and anti-neutrino modes in T2K experiments are vital to settle the octant ambiguity of θ 23 for all values of δ CP . Therefore, we assume equal neutrino and anti-neutrino runs of 2.5 years each for the T2K while exploring the octant sensitivity. The signal efficiency in T2K is around 87%. In our simulation, the background information and other details for T2K experiment are taken from [48,49].
In the NOνA experiment, the NuMI beam will be sent towards a 14 kt totally active scintillator detector (TASD) placed at a distance of 810 km from Fermilab, at a location which is 0.8 • off-axis from the beam. Due to the off-axis location, the flux is sharply peaked around 2 GeV, again close to the first oscillation maximum in P (ν µ → ν e ) channel. The experiment is scheduled to have three years run in neutrino mode first and then later, three years run in anti-neutrino mode. The NuMI beam power is 0.7 MW, which corresponds to 6 × 10 20 protons on target (p.o.t.) per year. See, reference [26] for details. After the discovery of moderately large value of θ 13 , NOνA has reoptimized its event selection criteria. A few cuts have been relaxed to allow more events in both signal and background. Additional neutral current backgrounds are reconstructed at lower energies and can be rejected by a kinematical cut. In our simulation, we use all these new features, the details of which are given in [27,50].

Future Generation: LBNE and LBNO
The Long-Baseline Neutrino Experiment (LBNE) [33,34] is one of the major components of Fermilab's intensity frontier program. In its first phase (LBNE10), it will have a new, high intensity, on-axis neutrino beam directed towards a 10 kt LArTPC located at Homestake with a baseline of 1300 km. This facility is designed for initial operation at a proton beam power of 708 kW, with proton energy of 120 GeV that will deliver 6 × 10 20 p.o.t. in 230 days per calendar year. In our simulation, we have used the latest fluxes being considered by the collaboration, which have been estimated assuming the smaller decay pipe and the lower horn current compared to the previous studies [51]. We have assumed five years each of ν andν runs. The detector characteristics have been taken from Table 1 of [52]. To have the LArTPC cross-sections, we have scaled the inclusive charged current (CC) cross sections of water by 1.06 (0.94) for the ν (ν) case [53,54].
The Long-Baseline Neutrino Oscillation Experiment (LBNO) [39] plans to use an experimental set-up where neutrinos produced in a conventional wide-band beam facility at CERN would be observed in a proposed 20 kt (in its first phase) LArTPC housed at the Pyhäsalmi mine in Finland, at a distance of 2290 km. The fluxes have been computed [55] assuming an exposure of 1.5 × 10 20 p.o.t. in 200 days per calendar year from the SPS accelerator at 400 GeV with a beam power of 750 kW. For LBNO also, we consider five years each of ν andν runs. We assume the same detector properties as that of LBNE10. In our calculations, we also consider a LBNO configuration reducing the detector mass to 10 kt which we denote as 0.5*LBNO. The exposure for this setup will be quite similar to LBNE10 which will enable us to perform a comparative study between these two setups at the same footing. The results presented in this paper are obtained using the GLoBES software [56,57].

Physics with Bi-events Plot
In this section, we attempt to understand the physics capabilities of 0.5*LBNO and LBNE10 setups with the help of bi-events plot. This kind of plot is quite useful to get a qualitative estimate of the physics sensitivity before performing a full ∆χ 2 calculation. In figure 1, we have plotted ν e vs.ν e appearance events, for 0.5*LBNO and LBNE10 for the four possible combinations of hierarchy and octant. Since δ CP is unknown, events are generated for the full range [−180 • , 180 • ], leading to the ellipses. The event rates are calculated using the following oscillation parameters: ∆m 2 21 = 7.5 × 10 −5 eV 2 , sin 2 θ 12 = 0.3 [13], ∆m 2 eff = ± 2.4 × 10 −3 eV 2 [6], and sin 2 2θ 13 = 0.089 [2]. ∆m 2 eff is the effective mass-squared difference measured using the ν µ survival probability and is a linear combination of ∆m 2 31 and ∆m 2 21 . The value of ∆m 2 31 is derived from ∆m 2 eff using the relation given in [58,59]. This relation leads to different magnitudes of ∆m 2 31 for NH and for IH. For sin 2 θ 23 , we choose the two degenerate best-fit values of the global fit [13]: 0.41 in the lower octant (LO) and 0.59 in the higher octant (HO). Note that, here we have plotted the total number of events, whereas the actual analysis will be done based on the spectral information. Nevertheless, the contours in this figure contain very important information regarding the physics capabilities of the experiments. An experiment can determine both the hierarchy and the octant, if every point on a given ellipse is well separated from every point on each of the other three ellipses. The larger the separation, the better is the confidence level with which the above parameters can be determined.
One can see from figure 1 that for 0.5*LBNO, the two (LO/HO)-IH ellipses are well separated from the two (LO/HO)-NH ellipses, in number of ν e events. Hence, 0.5*LBNO has excellent hierarchy determination capability with just ν data. However, ν data alone will not be sufficient to determine the octant in case of IH, because various points on (LO/HO)-IH ellipses have the same number of ν e events. Likewise, onlyν data cannot determine the octant in case of NH. Therefore, balanced ν andν data are mandatory to make an effective distinction between (LO/HO)-IH ellipses and also between (LO/HO)-NH ellipses. Figure 1 also depicts that the asymmetries between the neutrino and anti-neutrino appearance events are largest for the combinations: (NH, δ CP = −90 • ) and (IH, δ CP = 90 • ).
For LBNE10, ν data alone can not determine hierarchy because various points on LO-NH and HO-IH ellipses have the same number of ν e events (see figure 1). Thus,ν data is also needed. Even withν data, hierarchy determination can be difficult to achieve, if nature chooses LO and one of the two worst case combinations of hierarchy and δ CP which are (NH, 90 • ) or (IH, −90 • ). In such a situation, the ν e andν e events are rather close to each other and it will be very difficult for LBNE10 to reject the wrong combination. Regarding octant determination, the capability of LBNE10 is very similar to that of 0.5*LBNO because the separations between the ellipses, belonging to LO and HO are very similar for these two experiments.

Our Findings
Measurement of mass hierarchy and octant should be considered as a prerequisite for the discovery of leptonic CP violation. Now, it would be quite interesting to study whether the expected appearance data from the first phases of LBNE and LBNO experiments can resolve the issues of neutrino mass hierarchy and octant of θ 23 at 3σ to 5σ confidence level before they start probing the parameter space for leptonic CP violation. In this section, we address these issues in detail. We present the results for LBNE10 (10 kt), 0.5*LBNO (10 kt), and LBNO (20 kt) setups. We also study the improvement in their physics reach when the projected data from current generation experiments T2K and NOνA, is added. The impact of T2K and NOνA measurements on the performance of LBNE setup to determine the mass hierarchy and discover leptonic CP violation has been discussed recently in [60].

Discovery Reach for Neutrino Mass Hierarchy
We first focus on the discovery potential of future facilities to exclude the wrong hierarchy. It can be seen from equation 2.2 that the first term (C 0 ) dominates for large θ 13 and it is the leading term in platinum channel. This term contains the largest Earth matter effect which can therefore be used to unravel the sign of ∆m 2 31 . This term is also proportional to sin 2 θ 23 and therefore is quite sensitive to the choice of θ 23 value. If we vary sin 2 θ 23 in its 3σ allowed range of 0.34 to 0.67, then for LBNE10, the signal event rates in ν e appearance channel will increase from 122 to 231 (assuming NH and δ CP = 0 • ), an almost ∼ 90% enhancement in the statistics. For LBNO setup with 20 kt detector size, these numbers will change from 247 to 478 showing an almost ∼ 94% increase in the event numbers. ∆χ 2 is calculated for a given true combination of θ 23 -hierarchy, assuming the opposite hierarchy to be the test hierarchy. In the fit, we marginalize over test sin 2 θ 23 in its 3σ range. ∆m 2 eff and sin 2 2θ 13 are marginalized in their 2σ ranges. We consider 5% uncertainty in the matter density, ρ. Priors were added for ρ (σ = 5%), ∆m 2 eff (σ = 4%), and sin 2 2θ 13 (σ = 5%, as expected by the end of Daya Bay's run [61]). ∆χ 2 is also marginalized over the uncorrelated systematic uncertainties (5% on signal and 5% on background) in the set-ups, so as to obtain a ∆χ 2 min for every δ CP (true).
First, we consider two true values of sin 2 θ 23 : 0.41 (best-fit value in LO) and 0.5 (MM) giving us four true combinations of θ 23 -hierarchy: LO-NH, LO-IH, MM-NH and MM-IH. The hierarchy reach would suffer the most if sin 2 θ 23 (true) belongs to LO, hence we show the results for the best-fit value in LO. Here, we would like to mention that if we take sin 2 θ 23 (true) to be the best-fit value in HO, then the discovery reaches of these  experiments will be better than that for the case of MM. We elaborate on this point at the end of this section. Figure 2 depicts the discovery reach for hierarchy as a function of δ CP (true). We see that even 0.5*LBNO has 10σ 1 hierarchy discovery potential for all values of δ CP (true) and for all four true θ 23 -hierarchy combinations. The potential of LBNO, of course, is even better. The LBNO baseline is close to bimagic which gives it a particular advantage [63,64]. For LBNE10, a 5σ discovery of hierarchy is possible for only ∼ 50% of the δ CP (true), irrespective of these four true θ 23 -hierarchy combinations. For the unfavorable hierarchy-δ CP combinations [65], i.e. NH with δ CP in the upper half plane or IH with δ CP in the lower half plane, the performance of LBNE10 suffers. In particular, for LO and the worst case combinations [(NH, 90 • ) and (IH, −90 • )], LBNE10 will not be able to provide even a 3σ hierarchy discrimination. This suggests that additional data is needed for LBNE10 to have such a capability. In such a scenario, the projected data from T2K and NOνA can come to the rescue. Adding data from T2K (5 years of neutrino run) and NOνA (3 years of ν run and 3 years ofν run) helps LBNE10 setup to achieve more than 3σ discovery reach for mass hierarchy irrespective of the true choices of hierarchy and δ CP (see upper panels of figure 2), even if θ 23 is in the lower octant. Now, we ask the question, by how much does the sensitivity deteriorate if sin 2 θ 23 (true) turns out to be 0.34 in nature, which is its minimum value allowed in the 3σ range? We have  checked that even in this case, LBNO setup with 20 kt detector mass can give ∆χ 2 min 100 irrespective of the true choices of hierarchy, and δ CP . From figure 3, it can be seen that 0.5*LBNO can resolve the issue of mass hierarchy at more than 7σ confidence level for sin 2 θ 23 (true) = 0.34 independent of the choices of true hierarchy and δ CP . The most important message that is conveyed by figure 3 is that with the help of projected T2K and NOνA data, LBNE10 can still achieve 3σ mass hierarchy discovery for any combinations of true hierarchy-δ CP -sin 2 θ 23 . It clearly demonstrates the synergy between the current (off-axis) and future (on-axis) superbeam experiments and also proves that adding data from three different baselines (295 km, 810 km, and 1300 km) with completely different energy spectra is quite useful to kill the clone solutions for the unfavorable choices of the oscillation parameters.
The mass hierarchy discovery potential for all the three set-ups under consideration is remarkable if θ 23 happens to lie in HO. For sin 2 θ 23 (true) = 0.59 (the best-fit value in HO), even 0.5*LBNO can have ∆χ 2 min 130 irrespective of the true choices of hierarchy and δ CP . With this choice of sin 2 θ 23 (true), a 5σ discovery is not possible with LBNE10 for ∼ 30% values of true δ CP in the upper half plane for NH true and for ∼ 70% values of true δ CP in the lower half plane for IH true. We have checked that if we add the data from T2K and NOνA, LBNE10 can again provide 5σ discovery for mass hierarchy irrespective of the choices of true hierarchy and δ CP with sin 2 θ 23 (true) = 0.59. Next we turn our attention to the octant discovery potential of these setups.

Discovery Reach for θ 23 Octant
Here we discuss the discovery reach of future facilities for excluding the wrong octant. We consider the best-fit true values of sin 2 θ 23 = 0.41 (in LO) and 0.59 (in HO) resulting into  Figure 4 shows the discovery reach for octant as a function of δ CP (true). It can be seen that for (LO/HO)-IH true, the sensitivities of LBNE10 and 0.5*LBNO are quite similar whereas they are somewhat better for 0.5*LBNO if (LO/HO)-NH are the true combinations. For LO-(NH/IH), both LBNE10 and 0.5*LBNO have more than 3σ discovery of octant while for HO-(NH/IH), the ∆χ 2 min varies from ∼ 7 to 11 depending on the true value of δ CP . However, with full LBNO, we have more than 3.5σ discovery of octant for all true octant-hierarchy-δ CP combinations. A 5σ discovery of octant is possible only for LO-NH true for δ CP (true) ∈ (∼ 20 • to 150 • ).
In figure 5, we present the improvement in the octant discovery reach for 0.5*LBNO and LBNE10 with the addition of the projected data from T2K (2.5 years of ν run and 2.5 years ofν run) and NOνA (3 years of ν run and 3 years ofν run). Adding data from current generation experiments helps both 0.5*LBNO and LBNE10 to achieve more than 3σ discovery for all true octant-hierarchy-δ CP combinations. For LO-(NH/IH) true, these setups can provide close to 3.8σ discovery for octant irrespective of the choice of true δ CP .
In the discussion so far, we consider only the best-fit true values of sin 2 θ 23 in both    Figure 7 depicts the 3σ and 5σ octant resolution contours in true sin 2 θ 23 -true δ CP plane assuming NH as true hierarchy. The left (right) panel is for LBNE10 (0.5*LBNO) adding the expected data from T2K and NOνA. Octant resolution is only possible for points lying outside the contours. This figure again confirms that both LBNE10 and 0.5*LBNO in combination with T2K and NOνA data can provide octant discovery for global bestfit points at 3σ confidence level. We show the similar figure for the true IH choice in appendix A.

Discovery Reach for Leptonic CP Violation
A 'discovery' of leptonic CP violation, if it exists in Nature, means that we can reject both the CP-conserving values of 0 • , 180 • at a given confidence level. Obviously, this measurement becomes very difficult when δ CP approaches to 0 • , 180 • . Therefore, whilst it is possible to discover the mass hierarchy for all possible values of δ CP , the same is not true in the case of CP violation study. We have already emphasized that the present uncertainty in the knowledge of sin 2 θ 23 has a crucial impact on the discovery reach of mass ordering and octant of θ 23 for the experimental setups under consideration. This is also true for the CP violation discovery reach. We can see from the appearance probability expression in Results are shown for LBNE10 (10 kt), 0.5*LBNO (10 kt), and LBNO (20 kt) setups in the left, middle, and right upper panels respectively. In lower panels, we show the same including the projected data from T2K and NOνA experiments. The shaded band depicts the variation in ∆χ 2 min due to different true choices of sin 2 θ23 in its 3σ allowed range of 0.34 to 0.67. Inside the band, we show the results for three different true values of sin 2 θ23: 0.41, 0.5, and 0.59. equation 2.2 that both the CP-violating (C − ) and CP-conserving (C + ) terms depend on sin 2θ 23 , therefore these terms are not sensitive to the octant of θ 23 but they depend on the value of θ 23 . The leading term (C 0 ) in equation 2.2 is proportional to sin 2 θ 23 and therefore it is sensitive to both the octant and magnitude of θ 23 . In this paper for the first time, we study in detail the CP violation discovery reach by varying the true value of sin 2 θ 23 in its allowed 3σ range of 0.34 to 0.67. We follow the same marginalization scheme in the fit for oscillation parameters and systematic uncertainties as that in the case of mass hierarchy discovery study. For CP violation searches, the final ∆χ 2 is also marginalized over both the choices of hierarchy in the fit to obtain ∆χ 2 min . In figure 8, we present the CP violation discovery reach for various experimental setups under consideration as a function of true δ CP assuming NH as true hierarchy. Similar figure for the true IH choice is given in appendix B. The left, middle, and right upper panels of figure 8 show the results for LBNE10, 0.5*LBNO, and LBNO respectively. In lower panels, we depict the same results, combining the projected data from T2K and NOνA experiments. The shaded band in each panel reflects the variation in ∆χ 2 min due to different true choices of sin 2 θ 23 in its 3σ allowed range of 0. 34  the results for three different true values of sin 2 θ 23 : 0.41, 0.5, and 0.59. We summarize the main features of figure 8 in Table 1. In their first phases, both LBNE10 and LBNO will have CP violation reach for around 50% values of true δ CP at 2σ confidence level (see Table 1). At 3σ, their CP violation reach is quite minimal: only 3% for LBNE10 and 23% for LBNO. It is quite important to note that the addition of the projected T2K and NOνA data helps a lot to improve the CP coverage for these setups at 3σ confidence level for all possible true values of sin 2 θ 23 (see figure 8). For an example, LBNE10 (LBNO) can achieve CP violation discovery for 43% (46%) values of true δ CP at 3σ combining the expected data from the current generation experiments T2K and NOνA assuming sin 2 θ 23 (true) = 0.5. For 0.5*LBNO, we do not have any sensitivity at 3σ C.L. but, adding the T2K and NOνA data, 37% CP coverage can be obtained. All these results again clearly demonstrate that the projected data from the current generation off-axis superbeam experiments will be quite useful for future generation on-axis wide band superbeam setups to enhance their discovery reach at higher confidence level. Another important feature that emerges from figure 8 is that the CP violation discovery reach is quite sensitive to the true value of sin 2 θ 23 . The results are better if sin 2 θ 23 (true) belongs to LO compared to HO. The main reason behind this is that like in the case of θ 13 [66,67], the CP-asymmetry increases if we lower the value of θ 23 , reducing the strength of the leading term (C 0 ) in equation 2.2.

Concluding Remarks
With the recent measurement of θ 13 by reactor experiments, a clear and comprehensive picture of the three flavor leptonic mixing matrix has been established. This impressive result has crucial consequences for future theoretical and experimental efforts. It has opened up the possibility to probe the sub-dominant three flavor effects in both current and future long-baseline oscillation facilities. Another interesting piece of information on θ 23 has been provided by recently completed MINOS accelerator experiment. ν µ → ν µ disappearance data of MINOS points towards the deviation from maximal 2-3 mixing, causing the octant ambiguity of θ 23 . In this paper, we present a comparative study of the physics reach of two future superbeam facilities, LBNE and LBNO in their first phases of run, in addressing the issues of neutrino mass hierarchy, octant of θ 23 , and leptonic CP violation. We also demonstrate that the projected data from current generation experiments, T2K and NOνA will play a crucial role for these future facilities to achieve their milestones with higher confidence level. Also for the first time, we study in detail the impact of the present uncertainty in 2-3 mixing angle in resolving these fundamental issues. We find that in its first phase, even a 50% scaled down version of LBNO with 10 kt detector mass has more than 7σ mass hierarchy discovery reach for the lowest possible value of sin 2 θ 23 (true) = 0.34 in its presently allowed 3σ range. This result is valid for any choices of true δ CP and hierarchy. However, LBNE10 suffers in this regard and will not be able to provide a 5σ result for about 50% of the true δ CP range even for maximal mixing choice for sin 2 θ 23 (true). Moreover, it fails to achieve even a 3σ hierarchy discovery for the best-fit value in LO, sin 2 θ 23 (true) = 0.41 and the worst case combinations of the true parameters (NH, 90 • ) and (IH, −90 • ). In such a scenario, the projected data from T2K and NOνA can be extremely useful for LBNE10. Adding the expected informations from T2K and NOνA, LBNE10 can discover mass hierarchy at 3σ confidence level for any combinations of true hierarchy-δ CP and even for the most conservative choice of sin 2 θ 23 (true) = 0.34 in its present 3σ range. It clearly corroborates the synergy between the current (off-axis) and future (on-axis) superbeam experiments.
In their first phases, both LBNE10 and LBNO can establish leptonic CP violation for around 50% values of true δ CP at 2σ confidence level. At 3σ, their CP violation reach is quite minimal: only 3% for LBNE10 and 23% for LBNO. The expected measurements from present generation experiments T2K and NOνA can have dramatic impact on the CP violation discovery reach of the future facilities in their first phases of run. In case of LBNE10, CP coverage can be enhanced from 3% to 43% at 3σ combining T2K and NOνA data assuming sin 2 θ 23 (true) = 0.5. For LBNO setup, CP violation discovery is possible for 46% values of true δ CP at 3σ if we add the data from T2K and NOνA. The vertical lines correspond to the global best-fit values. We consider IH as true hierarchy. In producing all these plots, the projected data from T2K and NOνA have been added (see section 3 for details). 0.5*LBNO (right panel) assuming IH as true hierarchy. Variation of δ CP (true) in the range −180 • to 180 • leads to the band in ∆χ 2 values for a given true sin 2 θ 23 . The vertical lines indicate towards the global best-fit values. Here we add the projected data from T2K and NOνA to produce these results. For LBNE10, a 3σ octant resolution is possible for sin 2 θ 23 (true) ≤ 0.44 and for sin 2 θ 23 (true) ≥ 0.58 irrespective of the values of δ CP (true). For 0.5*LBNO, this is possible for sin 2 θ 23 (true) ≤ 0.44 and for sin 2 θ 23 (true) ≥ 0.57. We see that the results with IH(true) choice are quite similar to that of NH(true) (see figure 6). Figure 10 shows the 3σ and 5σ octant resolution contours in true sin 2 θ 23 -true δ CP plane considering IH as true hierarchy. The left (right) panel is for LBNE10 (0.5*LBNO) adding the expected data from T2K and NOνA. Octant resolution is only possible for points lying outside the contours. This figure again suggests that for IH(true) case, both LBNE10 and 0.5*LBNO in combination with T2K and NOνA data can provide octant discovery for global best-fit points at 3σ confidence level.
B CP Violation discovery as a function of true δ CP for IH(true) In figure 11, we give the CP violation discovery reach for various experimental setups under study as a function of true δ CP considering IH as true hierarchy. Like in figure 8, the left, middle, and right upper panels of figure 11 present the results for LBNE10, 0.5*LBNO, and LBNO respectively. In lower panels, we depict the same combining the projected data from T2K and NOνA experiments. The shaded band in each panel reflects the variation in ∆χ 2 min due to different true choices of sin 2 θ 23 in its 3σ allowed range of 0.34 to 0.67. Inside the band, we give the results for three different true values of sin 2 θ 23 : 0.41, 0.5, and Here, we assume IH as true hierarchy. In generating all these plots, the projected data from T2K and NOνA have been added (see section 3 for details).  Figure 11: CP Violation discovery reach as a function of true value of δCP assuming IH as true hierarchy.
Results are shown for LBNE10 (10 kt), 0.5*LBNO (10 kt), and LBNO (20 kt) in the left, middle, and right upper panels respectively. In lower panels, we depict the same adding the information from T2K and NOνA experiments. The shaded band depicts the variation in ∆χ 2 min due to different true choices of sin 2 θ23 in its 3σ allowed range of 0.34 to 0.67. Inside the band, we show the results for three different true values of sin 2 θ23: 0.41, 0.5, and 0.59.