# A Comprehensive Study of the Discovery Potential of NOνA, T2K, and T2HK Experiments

Authors: C. Soumya; K. N. Deepthi; R. Mohanta
Journal: Advances in High Energy Physics
 (2016)

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## Abstract

With the recent measurement of reactor mixing angleθ13 the knowledge of neutrino oscillation parameters has improved significantly except the CP violating phase δCP, mass hierarchy, and the octant of the atmospheric mixing angle θ23. Many dedicated experiments are proposed to determine these parameters which may take at least 10 years from now to become operational. It is therefore very crucial to use the results from the existing experiments to see whether we can get even partial answers to these questions. In this paper we study the discovery potential of the ongoing NOνA and T2K experiments as well as the forthcoming T2HK experiment in addressing these questions. In particular, we evaluate the sensitivity of NOνA to determine neutrino mass hierarchy, octant degeneracy, and δCP after running for its scheduled period of 3 years in neutrino mode and 3 years in antineutrino mode. We then extend the analysis to understand the discovery potential if the experiments will run for (5ν+5ν¯) years and (7ν+3ν¯) years. We also show how the sensitivity improves when we combine the data from NOνA, T2K, and T2HK experiments with different combinations of run period. The CP violation sensitivity is marginal for T2K and NOνA experiments even for ten-year data taking of NOνA. T2HK has a significance above 5σ for a fraction of two-fifths values of the δCP space. We also find that δCP can be determined to be better than 35°, 21°, and 9° for all values of δCP for T2K, NOνA, and T2HK respectively.


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## Body

## 1. Introduction

The discovery of neutrino oscillations has firmly established that neutrinos are massive. It has marked the beginning of many neutrino oscillation experiments. The mixing of three neutrino flavors can be described by Pontecorvo-Maki-Nakagawa-Sakata matrixUPMNS [1, 2], which is parameterized in terms of three rotation angles θ12, θ23, and θ13 and three CP violating phases, one Dirac type (δCP) and two Majorana types (ρ and σ). The neutrino oscillation data accumulated over many years allows us to determine the solar and atmospheric neutrino oscillation parameters with very high precision. Recently, the reactor mixing angle θ13 has been measured precisely [3–7] with a moderately large value, quite close to its previous upper bound. The observation of the largish value of θ13 has attracted a lot of attention in recent times to understand the mixing pattern in the lepton sector. Furthermore, it also opens up promising prospects for the observation of leptonic CP violation [8, 9]. As θ13 is nonzero, there could be CP violation in the lepton sector, analogous to the quark sector, provided the CP violating phase δCP is not vanishingly small.The current results from recent neutrino oscillation experiments [10–13] and their global analysis [14–17] performed by several groups have implied that the minimal three-neutrino framework is adequate to describe the observed oscillation phenomenology. The best-fit values and the 3σ ranges of the oscillation parameters from [17] are presented in Table 1.Table 1
The best-fit values and the3σ ranges of the neutrino oscillation parameters from [17].
Mixing parameters
Best-fit value
3
σ range
sin
2
⁡
θ
12
0.323
0.278
→
0.375
sin
2
⁡
θ
23 (NH)
0.567
0.392
→
0.643
sin
2
⁡
θ
23 (IH)
0.573
0.403
→
0.640
s
i
n
2
θ
13 (NH)
0.0234
0.0177
→
0.0294
sin
2
⁡
θ
13 (IH)
0.0240
0.0183
→
0.0297
Δ
m
21
2
/
1
0
-
5 eV2
7.6
7.11
→
8.18
|
Δ
m
31
|
2
/
1
0
-
3 eV2 (NH)
2.48
2.30
→
2.65
|
Δ
m
31
|
2
/
1
0
-
3 eV2 (IH)
2.38
2.20
→
2.54Another important discovery in recent times is the precision measurement ofsin2⁡θ23 by MINOS experiment [18], which is found to be nonmaximal. Using the complete set of accelerator and atmospheric data they disfavored the maximal mixing by -2Δlog⁡(L)=1.54. They obtained the best-fit value for the mixing angle θ23 as sin2⁡θ23=0.41, known as lower octant (LO) and sin2⁡θ23=0.61, the so-called higher octant (HO) values.With these exciting discoveries of nonzeroθ13 and nonmaximal θ23, the focus of neutrino oscillation studies has now been shifted towards the determination of other unknown parameters. These include the determination of mass hierarchy, octant of the atmospheric mixing angle θ23, discovery of CP violation, and the magnitude of the CP violating phase δCP. In this paper we would like to investigate the prospects of addressing these issues with the off-axis long-baseline experiments T2K, NOνA, and T2HK with updated experimental specifications. The experimental specifications of these experiments are briefly described below.(i)
NOνA [19, 20] is an off-axis long-baseline neutrino oscillation experiment designed to study νμ→νe appearance measurements using Fermilab NuMI muon neutrino beam (νμ). Its secondary aim is to precisely measure νμ disappearance parameters. It uses a high intensity proton beam with a beam power of 0.7 MW with 6×1020 POT/year. Its detector is a 14 kt totally active liquid scintillator detector (TASD) located at Ash River, 810 km from Fermilab. The detector is located slightly off the centerline (14 mrad) to the neutrino beam where one can find a large flux of neutrinos of 2 GeV energy. The oscillation from νμ→νe is expected to be maximum at this energy. It is scheduled to run 3 years in ν mode followed by 3 years in ν¯ mode. The detector properties of NOνA considered in our simulations are taken from [21] with the following characteristics as given in Table 2.(ii)
T2K (Tokai-to-Kamiokande) is a currently running long-baseline experiment designed to study neutrino oscillations. An intenseνμ beam of 0.77 MW power is directed from J-PARC to Super-Kamiokande detector, 295 km away. It has a 22.5 kt water Cherenkov detector. The details of T2K experiment can be found in [22]. We have considered input files for T2K from the General Long-Baseline Experiment Simulator (GLoBES) package [22–24] and the updated experimental description of T2K is taken from [25]. We have matched our results with the ones presented in [25]. In this analysis, we have used (3ν+2ν¯) running modes for T2K.(iii)
T2HK (Tokai-to-Hyper-Kamiokande) is a future long-baseline experiment which is expected to be operational around 2023. It can be considered a natural advancement to the ongoing T2K experiment. It has the same baseline and off-axis angle as T2K experiment. It uses J-PARC’s neutrino experimental facilities with an improved beam power (7.5 MW) and 1 Mt volume water Cherenkov detector, Hyper-Kamiokande (Hyper-K). We have considered a fiducial volume of 0.56 Mt and beam power of 7.5 MW and other specifications are taken from [26]. Hence, T2HK will have high statistics of neutrino events compared to T2K. These features of T2HK make it one of the most sensitive experiment to probe neutrino CP violation. The input files for T2HK are obtained from GLoBES package [22–24]. The primary objective of this experiment is the discovery of CP asymmetry.Table 2
Details of NOνA detector characteristics considered in this analysis.
Signal efficiency
45% forνe and ν-e signal
100%νμ CC and ν-μ CC
Background efficiency
0.83%νμ CC, 0.22%  ν-μ CC
2%νμ NC, 3%  ν-μ NC
26% (18%)νe (ν-e) beam contamination
NC background smearing
Migration matrices
Systematics
5% signal normalization error
10% background normalization errorSince these experiments useνμ beam and also will run in antineutrino mode their main focus is to study the appearance (νμ→νe) and the disappearance channels (νμ→νμ) along with their antineutrino counterparts. Since the leading term in the appearance channels νμ→νe(Pμe) and the corresponding antineutrino mode ν¯μ→ν¯e(Pμ¯e¯) is proportional to sin2⁡2θ13sin2⁡θ23 and with the observation of moderately large value of θ13, these experiments are well-suited for the determination of mass hierarchy and the octant of θ23. Although the ongoing NOνA and T2K experiments are not planned to measure δCP or to explore CP violation in the neutrino sector, we would like to investigate whether it is possible to constrain the δCP phase using the data from these two experiments. In other words, how much of the δCP space can be ruled out by these experiments within the next 10 years? In particular, we would like to investigate(i)
whether the combination of T2K (3+2) and NOνA (3+3) provide more quantitative answer on the above posed questions than each one of these experiments,(ii)
how the sensitivity onδCP, mass hierarchy, and θ23 octant will improve if NOνA runs for 10 years in the (5+5) and (7+3) combination of modes,(iii)
the sensitivities of T2HK experiment for its scheduled run of 3 years in neutrino and 7 years in antineutrino mode.The paper is organized as follows. In Section2 we briefly describe the physics reach of these experiments. The prospect of octant resolution and mass hierarchy determination are discussed in Sections 3 and 4. Section 5 contains the CP violation discovery potential and the correlations between the CP violating phase δCP and the mixing angles θ13 and θ23. We summarize our results in Section 6.


## 2. Physics Reach

As discussed before, the determination of the mass hierarchy, octant of the atmospheric mixing angleθ23 and the search for CP violation in the neutrino sector are the important physics goals of the current and future oscillation experiments. A simple way to achieve the above three goals is to measure the oscillation probabilities P(νμ→νe) and P(ν¯μ→ν¯e). This can be seen from the expression for probability of oscillation from νμ(ν¯μ)→νe(ν¯e) [27–29], where we have kept terms only first order in sin⁡θ13 and α=Δm212/Δm312:(1)Pνμ⟶νe≈sin2⁡2θ13sin2⁡θ23sin2⁡A^-1ΔA^-12+αcos⁡θ13sin⁡2θ12sin⁡2θ13sin⁡2θ23sin⁡A^ΔA^sin⁡A^-1ΔA^-1cos⁡Δ+δCP,where Δmij2=mi2-mj2, Δ=Δm312L/4E, and A^=22GFneE/Δm312. GF is the Fermi coupling constant and ne is the electron number density. The transition probability can be enhanced or suppressed depending on the oscillation parameters θ13, θ23, mass hierarchy, that is, the sign of Δm312 and CP violation phase δCP. Parameters α, Δ, and A^ are sensitive to neutrino mass ordering. For neutrinos, A^ is positive for normal hierarchy (NH) and negative for inverted hierarchy (IH), while its sign changes when we go from neutrino to antineutrino mode. Moreover, sign of δCP is reversed for antineutrinos.It should be noted from (1) that the leading term in the transition probability P(νμ→νe) is proportional to sin2⁡2θ13sin2⁡θ23. Therefore, the observed moderately large value of θ13 makes it possible for the current generation long-baseline experiments to address the problems of hierarchy and the octant of θ23 determination. The second term in (1) shows the prominence of matter effect on the oscillation probability. The dependency of all the terms on a moderately large reactor neutrino mixing angle θ13 suggests that NOνA detector will be able to collect a good number of νμ(ν¯μ)→νe(ν¯e) events.First, we will try to see whether the energy spectrum information will help us in resolving the octant degeneracy and mass hierarchy. We use GLoBES package [30, 31] for the simulation to obtain the energy spectra. In our analysis, we consider the true values of oscillation parameters as provided in Table 3, unless mentioned otherwise.Table 3
The true values of oscillation parameters considered in the simulations.
sin
2
⁡
θ
12
0.32
sin
2
⁡
2
θ
13
0.1
sin
2
⁡
θ
23
0.41 (LO), 0.59 (HO)
Δ
m
a
t
m
2
2.4
×
1
0
-
3 eV2 for NH
-
2.4
×
1
0
-
3 eV2 for IH
Δ
m
21
2
7.6
×
1
0
-
5 eV2
δ
C
P
0°Figure1 shows the energy spectrum of the appearance probabilities P(νμ→νe) for neutrino (left panel) and P(ν¯μ→ν¯e) for antineutrino (right panel) for NOνA experiment, where we have varied δCP within the range -π to π. In the upper panel the red (blue) band is for NH (IH). Furthermore, in each band the probability for δCP=90∘ and δCP=-90∘ cases are shown explicitly by the magenta and green lines. Due to matter effect the probability Pμe increases for NH and decreases for IH and vice versa for Pμ¯e¯. Thus, for δCP lying in the lower half plane (LHP), that is, -180∘≤δCP≤0, Pμe is larger and, for δCP in the upper half plane (UHP) (0≤δCP≤180∘), Pμe is much lower. The situations reverse for the antineutrino probability Pμ¯e¯. Thus, LHP is the favorable half plane for NH and UHP is for IH for neutrino mode. However, the most unfavorable condition is (NH, δCP=90∘) and (IH, δCP=-90∘) as the bands almost overlap with each other for the entire energy range. In the lower panels of Figure 1, we show the energy spectrum of Pμe and Pμ¯e¯ for two different values of θ23 assuming NH to be true hierarchy. The blue band in both of the panels is for θ23 in the LO and red band is for θ23 in the HO. As can be seen from the figures the two bands overlap with each other for some values of δCP and are distinct for others. The overlap regions are the unfavorable ones for the determination of the θ23 octant.Figure 1
P
μ
e energy spectrum for NOνA experiment. The left (right) panel is for neutrino (antineutrino). The red (blue) band in the top panel corresponds to NH (IH), where we have used sin2⁡θ23=0.5, sin2⁡2θ13=0.1, and baseline L=810 km and vary δCP between -π and π. The red (blue) band in the bottom panel is for HO (LO), where we have used sin2⁡θ23=0.41 (0.59) for LO (HO) and keep the hierarchy as normal. Inside each band the probability for δCP=90∘(-90∘) case is shown by magenta (green) line.
(a)
(b)
(c)
(d)


## 3. Octant Resolution as a Function ofθ23

In this section we present the results of our analysis on octant sensitivity ofθ23 for T2K, NOνA, and T2HK experiments. We also show the results when the data from all the experiments are combined. Although the octant sensitivity of various long-baseline experiments has been discussed extensively by many authors [32–34], here we would like to revisit the octant resolution potential of these experiments with the updated specification details. For NOνA, we consider its scheduled (3ν+3ν¯) years of run, for T2K (3ν+2ν¯) years of run, and for T2HK (3ν+7ν¯) years of run. Furthermore, we also investigate the following situation: if NOνA continues to run for the next 10 years what would be the potential for resolving octant degeneracy for (5ν+5ν¯) as well as (7ν+3ν¯) years of running? We also see the synergy between T2K, NOνA, and T2HK experiments for their scheduled runs.The indistinguishability ofθ23 and (π/2-θ23) is known as octant degeneracy. The relevant oscillation probability expressions for long-baseline experiments NOνA, T2K, and T2HK with negligible matter effects are given as(2)Pμμv=1-sin2⁡2θ23sin2⁡1.27Δm312LE+4sin2⁡θ13sin2⁡θ23cos⁡2θ23sin2⁡1.27Δm312LE,Pμev=sin2⁡θ23sin2⁡2θ13sin2⁡1.27Δm312LE.The leading order term in the νμ survival probability (Pμμv) depends on sin2⁡2θ23 and one cannot distinguish between Pμμv(θ23) and Pμμv(π/2-θ23). This kind of degeneracy that comes from the inherent structure of neutrino oscillation probability is called intrinsic octant degeneracy, whereas in the case of Pμev the degeneracy of the octant with the parameter θ13 comes into play, since it depends on the parameter combination sin2⁡θ23sin2⁡2θ13. The values of θ23 in opposite octant for different values of θ13 and δCP can have the same probabilities; that is, Pμev(θ23,θ13,δCP)=Pμev(π/2-θ23,θ13′,δCP′). This also gives rise to octant degeneracy.Before presenting the main results, we would like to discuss what one can expect about the determination of mass hierarchy and octant ofθ23 from the biprobability plots, that is, neutrino-antineutrino appearance event rates. Figure 2 shows ν versus ν¯ events for all octant-hierarchy combinations. The blue curves are obtained by considering inverted hierarchy mass ordering and both of the values of θ23; that is, sin2⁡θ23=0.41 (LO) and 0.59 (HO). The red curves are obtained by considering normal hierarchy mass ordering and LO/HO values for sin2⁡θ23. These ellipses are plotted by obtaining event spectra for (3+3) yrs, (5+5) yrs, and (7+3) yrs in ν and ν¯ mode for all values of δCP for NOνA, T2K, and (3+7) yrs for T2HK. Each point on x-axis (y-axis) represents the number of events measured by the respective experiments in neutrino (antineutrino) mode. The top panel represents the ellipses for (3+2), (5+5), and (7+3) years of running in neutrino and antineutrino modes for T2K, the second panel represents the NOνA event rates for (3+3), (5+5), and (7+3) years of run period, and the bottom panel represents the T2HK event rates for (3+7) years of run period. For T2K and T2HK experiments the ellipses of both normal and inverted mass orderings overlap with each other for both the octants whereas for NOνA the overlap region is less (marginal) for LO (HO). Thus, it is very likely that the mass hierarchy and octant degeneracy could be probed better with the NOνA experiment.Figure 2
Neutrino and antineutrino appearance events for theνμ→νe versus ν¯μ→ν¯e channels by assuming both IH and NH and for lower and higher octants of θ23.Before doing the simulation, here we would like to emphasize that the relation between atmospheric parameters(Δmatm2) and θμμ, measured in MINOS, and the standard oscillation parameters in nature are given as [35, 36] (3)sin⁡θ23=sin⁡θμμcos⁡θ13,Δm312=Δmatm2+cos2⁡θ12-cos⁡δCPsin⁡θ13sin⁡2θ12tan⁡θ23Δm212. It is clear from the above relations that the observed value of moderately large θ13 significantly affects the oscillation parameters. So here we use corrected definitions of these parameters to analyze octant sensitivity. We allocate measured values Δmatm2 and θμμ and calculate oscillation probabilities in terms of Δm312 and θ23.We consider the true values of oscillation parameters given in Table3 and vary the test values of sin2⁡θ23 in LO (HO) for true higher octant (lower octant). We also marginalize over sin22θ13 in the range [0.07:0.13], δCP in its full range, and Δmatm2 in the range [2.05:2.75]×10-3eV2 for NH. The parameters θ12 and Δm212 have been kept fixed in the analysis and priors for sin2⁡2θ13 and sin2⁡θ23 with σ(sin2⁡2θ13)=0.01 and σ(sin2⁡θ23)=0.05 are also added.We simulate the long-baseline experiments T2K and NOνA using the GLoBES package. For T2K, we assume 3 years of running in neutrino mode and 2 years in antineutrino mode and for NOνA, we consider 3 years of neutrino running followed by 3 years of antineutrino running. Furthermore, we also consider the case if NOνA continues the data taking for ten years beyond its scheduled (3+3) years and perform the analysis for two possible combinations (5+5) and (7+3) years of running.In Figure3, we illustrate the ability of NOνA experiment to determine the octant as a function of the true value of θ23. The values of χ2 are evaluated using the standard rules as described in GLoBES. The green, red, and blue curves (in the bottom panel) represent the octant resolution of NOνA with (3+3), (5+5), and (7+3) yrs of runs in ν and ν¯ modes, respectively. From Figure 3, it can be seen that, with only T2K data of (3+2) years of run, it is possible to resolve the octant degeneracy with 2σ significance if the true sin2θ23 will lie around 0.41 (LO) or 0.59 (HO) and one can have a better sensitivity for NOνA experiment with (3+3) yrs of run period. The significance increases significantly if we combine the data from both T2K and NOνA as seen from the top panels. For ten years of NOνA run, although we get a better sensitivity than that of (3+3) yrs of run, there is no significant difference between (5+5) yrs and (7+3) years of running.Figure 3
Octant sensitivity for a combination of T2K and NOνA for the case of normal (left panel) and inverted (right panel) hierarchy.
(a)
(b)


## 4. Mass Hierarchy Determination

Determination of neutrino mass hierarchy is one of the outstanding issues in neutrino oscillation physics. The conventional method to achieve this is by using matter effects in very long-baseline neutrino oscillation experiments, as the matter effects enhance the separation between oscillation spectra and, therefore, the event spectra between the normal and inverted hierarchy. In this section we describe the capabilities of T2K, NOνA, and T2HK experiments for the determination of mass hierarchy.The value ofχ2 has been obtained by using the true parameters as listed in Table 3, except that of sin2⁡θ23, which is taken to be 0.5. The true value of δCP is varied within its full range, that is, in [-π,π], and test value of Δmatm2 is varied in IH (NH) range for true NH (IH). We also marginalize over sin2⁡2θ13 and sin2⁡θ23 in their 3σ ranges and add prior to sin2⁡2θ13 with σ(sin2⁡2θ13)=0.01.In Figure4, we present the hierarchy determination sensitivity of T2K, NOνA, and T2HK as a function of true value of δCP. We assume NH (IH) to be the true hierarchy in the left (right) panel. It can be seen that the wrong hierarchy can be ruled out quite effectively in the LHP (UHP) for NH (IH), which is basically the favorable half plane and in the other half plane the mass hierarchy cannot be determined effectively for T2K and NOνA experiments. However, the combined data from these two experiments (T2K (3+2) and NOνA (3+3)) improves the situation significantly and the sensitivity increases to more than 1σ for all values of δCP. The mass hierarchy significance above 3σ has a δCP coverage of 75% for T2HK experiment alone and 90% for combined data of T2K, NOνA, and T2HK experiments.Figure 4
Mass hierarchy significance as a function of trueδCP. In the left panel normal hierarchy is considered as true hierarchy and inverted is taken as test hierarchy and in the right panel inverted hierarchy is considered true hierarchy and normal is taken as test hierarchy.
(a)
(b)Next, we would like to study the effect ofθ23 octant on the MH sensitivity. We obtain the MH sensitivity by varying the true value of sin2⁡θ23 in LO (HO) which has been shown in Figure 5 where the red (blue) band in the top (bottom) panel corresponds to HO (LO). It is clear from the figure that the MH sensitivity is significantly large if the value of sin2⁡θ23 is in higher octant.Figure 5
Mass hierarchy significance with the octant ofθ23 for the scheduled run of NOνA experiment.


## 5. CP Violation Discovery Potential

Accelerator based long-baseline neutrino oscillation experiments can address CP violation problem through the appearance channels ofνμ→νe and ν¯μ→ν¯e. From (1) we can see that the CP violating effects due to δCP are modified by all the three mixing angles and their combinations, thus resulting in an eightfold parameter degeneracy. In order to obtain the significance of CP violation sensitivity, we simulate the true event spectrum by keeping the true values of oscillation parameters as in Table 3 except for sin2⁡θ23=0.5 and vary the true value of δCP in the range [-π,π]. We then compare those with test event spectrum for δCP=0 or π and, thus, obtain the minimum χ2. We consider the sign degeneracy of Δm312 by marginalizing over it, in both NH and IH 3σ ranges. We also do marginalization over sin2⁡2θ13 and sin2⁡θ23 in their 3σ and added prior for sin2⁡2θ13.In Figure6, we plot the sensitivity to rule out the CP conserving scenarios, as a function of true δCP assuming NH (IH) to be the true hierarchy in the left panel (right panel). From the figure one can notice that T2K by itself has no CP violation sensitivity at 2σ CL. For NOνA with (3+3) years of running, there will be CP violation sensitivity above 1.5σ level for about one-third of the CP violating phase δCP space. Furthermore, the synergistic combination of NOνA and T2K leads to much better CP violation sensitivity compared to the individual capabilities. Even the combination of NOνA (3+3) and T2K (3+2) has comparable sensitivity as for 10-year running of NOνA. Owing to the fact that main goal of T2HK experiment is to determine CP violation, one can see that it has a significance of above 5σ CL for a fraction of two-fifths values of the CP violating phase δCP space. This in turn boosts up the sensitivity when its data is added to NOνA (3+3) yrs and T2K (3+2) yrs. From the plots in the lower panel, one can observe that the sensitivity of NOνA increases slightly for 10 years of run time, with (5ν+5ν¯) combination having better sensitivity than that of (7ν+3ν¯) combination. From the figure, we can see that there is drop in the χ2 values in the half planes of δCP, that is, in the region [0,180]∘ ([-180,0]∘) for NH (IH). Marginalization over both the hierarchies causes this drop in the CPV sensitivity for unfavorable values of δCP.Figure 6
CP violation sensitivity for different combinations of run time of T2K, NOνA, and T2HK experiment for NH (IH) in the left (right) panel.
(a)
(b)In Figure7, the left panel shows the 1σ uncertainty of δCP as a function of running time (in years) for true value of δCP=0 and the right panel shows the CP violation sensitivity as a function of running time. In both cases, the ratio of neutrino and antineutrino modes is fixed to 1 : 1 for T2K and NOνA and 3 : 7 for T2HK. In this analysis, mass hierarchy is assumed to be unknown. Therefore, we have marginalized over both the hierarchies, and the result shown in Figure 7 is for the true hierarchy as normal hierarchy. From the left panel of the figure, we can see that the values of δCP can be determined to be better than 35∘ (21∘) for all values of δCP for T2K (NOνA). In the case of T2HK the values of δCP can be determined to be better than 9∘ for all values of δCP. From the right panel, we can see that CP violation can be observed with more than 1σ significance for 40 (75)% of the possible values of δCP for T2K (NOνA), whereas, for T2HK, CP violation can be observed with more than 1σ significance for 80% of the possible values of δCP.Figure 7
Sensitivity versus running time:1σ error in δCP as a function of running time in years for true value of δCP=0 (left panel). The fraction of δCP for which δCP=0∘, 180∘ is excluded with 1σ as a function of running time.
(a)
(b)


### 5.1. Correlation betweenδCP and θ13

The knowledge of reactor mixing angleθ13 plays a crucial role in the discovery potential of δCP. The recent discovery of large value of θ13 has established the need to study and understand the dependency between δCP and θ13. In this subsection, we discuss the correlation between the oscillation parameters θ13 and δCP. To obtain the confidence region, we have fixed the true values as in Table 3 and considered true sin2⁡θ23=0.59 for higher octant and true sin2⁡θ23=0.41 for lower octant, since the octant of θ23 is not known. We have varied the test value of sin2⁡2θ13 in its 3σ range. In this analysis we have kept both true and test hierarchy as normal hierarchy.Figure8 shows the confidence regions in the sin22θ13-δCP plane for different combinations of T2K and NOνA experiments. One can see from these figures that at 2σ confidence level, the uncertainty in the knowledge of θ23 octant has a noticeable effect on the correlation between δCP and θ13.Figure 8
Confidence region insin2⁡2θ13-δCP plane for δCP=0 and for different run combinations of T2K and NOνA experiments, where the red, blue, and black contours represent the 1σ (68.3% CL), 1.64σ (90% CL), and 2σ (95.45% CL) values, respectively, for two degrees of freedom.


### 5.2. Correlation betweenδCP and θ23

From the previous subsection, we can see that the uncertainty inθ23 has a very large impact on determination of neutrino oscillation parameters. Thus, it is important to understand the exclusive correlation between δCP and θ23 while keeping the true values of rest of the oscillation parameters fixed. In this subsection, we discuss the correlation between the oscillation parameters θ23 and δCP. For our analysis, we have kept true values of oscillation parameters as in Table 3. We vary the test values of sin2θ23 and δCP in their 3σ ranges. The obtained results of the confidence regions in sin2⁡θ23-δCP plane are shown in Figures 9 and 10 for different combinations of T2K and NOA experiments.Figure 9
Confidence region insin2⁡θ23-δCP plane for true δCP=0, where red, blue, and black contours represent the 1σ (68.3% CL), 1.64σ (90% CL), and 2σ (95.45% CL) values, respectively, for two degrees of freedom. Here hierarchy is assumed to be IH.Figure 10
Confidence region insin2⁡θ23-δCP plane for true δCP=0, where red, blue, and black contours represent the 1σ, 1.64σ, and 2σ values, respectively, for two degrees of freedom. Here hierarchy is assumed to be NH.


## 5.1. Correlation betweenδCP and θ13

The knowledge of reactor mixing angleθ13 plays a crucial role in the discovery potential of δCP. The recent discovery of large value of θ13 has established the need to study and understand the dependency between δCP and θ13. In this subsection, we discuss the correlation between the oscillation parameters θ13 and δCP. To obtain the confidence region, we have fixed the true values as in Table 3 and considered true sin2⁡θ23=0.59 for higher octant and true sin2⁡θ23=0.41 for lower octant, since the octant of θ23 is not known. We have varied the test value of sin2⁡2θ13 in its 3σ range. In this analysis we have kept both true and test hierarchy as normal hierarchy.Figure8 shows the confidence regions in the sin22θ13-δCP plane for different combinations of T2K and NOνA experiments. One can see from these figures that at 2σ confidence level, the uncertainty in the knowledge of θ23 octant has a noticeable effect on the correlation between δCP and θ13.Figure 8
Confidence region insin2⁡2θ13-δCP plane for δCP=0 and for different run combinations of T2K and NOνA experiments, where the red, blue, and black contours represent the 1σ (68.3% CL), 1.64σ (90% CL), and 2σ (95.45% CL) values, respectively, for two degrees of freedom.


## 5.2. Correlation betweenδCP and θ23

From the previous subsection, we can see that the uncertainty inθ23 has a very large impact on determination of neutrino oscillation parameters. Thus, it is important to understand the exclusive correlation between δCP and θ23 while keeping the true values of rest of the oscillation parameters fixed. In this subsection, we discuss the correlation between the oscillation parameters θ23 and δCP. For our analysis, we have kept true values of oscillation parameters as in Table 3. We vary the test values of sin2θ23 and δCP in their 3σ ranges. The obtained results of the confidence regions in sin2⁡θ23-δCP plane are shown in Figures 9 and 10 for different combinations of T2K and NOA experiments.Figure 9
Confidence region insin2⁡θ23-δCP plane for true δCP=0, where red, blue, and black contours represent the 1σ (68.3% CL), 1.64σ (90% CL), and 2σ (95.45% CL) values, respectively, for two degrees of freedom. Here hierarchy is assumed to be IH.Figure 10
Confidence region insin2⁡θ23-δCP plane for true δCP=0, where red, blue, and black contours represent the 1σ, 1.64σ, and 2σ values, respectively, for two degrees of freedom. Here hierarchy is assumed to be NH.


## 6. Summary and Conclusion

With the recent discovery of the last unknown reactor mixing angleθ13, the mechanism of three-flavor neutrino mixing pattern is now well established. But still there are several issues related to neutrino oscillation parameters that remain open, namely, the absolute mass scale of neutrinos, determination of the mass hierarchy, octant of the atmospheric mixing angle θ23, the magnitude of the CP violating phase δCP, and the observation of CP violation in the neutrino sector. Therefore, the main focus of the current and future oscillation experiments is to provide answers to some of these unsolved questions.In this paper, we have investigated the prospects of the determination of mass hierarchy, the octant ofθ23, and the observation of CP violation in the neutrino sector due to δCP with the currently running accelerator based neutrino experiments NOνA and T2K and the forthcoming T2HK experiment. As the reactor mixing angle θ13 is now known to be significantly large, the oscillation probability P(νμ→νe) and its corresponding antineutrino counterpart are sensitive for the determination of mass hierarchy and θ23 octant. We found that T2K experiment with (3ν+2ν¯) years of running can resolve the octant degeneracy with nearly 2σ CL if the true value of θ23 is around sin2θ23=0.41 (LO) or sin2⁡θ23=0.59 (HO). The sensitivity increases to nearly 3σ with (3ν+3ν¯) years of running of NOνA. However, if we combine the data from these two experiments the sensitivity increases significantly than the sensitivities of individual experiments. Furthermore, if we assume that NOνA continues data taking for 10 years then octant degeneracy can be resolved with NOνA experiment alone with more than 3σ significance. For the determination of mass hierarchy, it is also possible to rule out nearly one-third of the δCP space at 3σ CL if we use the synergy between NOνA and T2K experiments. In this case the sensitivity increases significantly for ten years of running of NOνA with (5 + 5) combination that is found to be more suitable than the combination of (7+3) years.Measuring CP violation in the lepton sector is another important challenging problem today. We have also performed a systematic study of the CP sensitivity of the current long-baseline experiments T2K and NOνA. Although these experiments are not planned to study leptonic CP violation, we analyze the synergies between these setups which may aid in CP violation discovery by constraining the value of δCP. Although dedicated long-baseline experiments like DUNE, T2HK are planned to study CP violation in neutrino sector, we may have the first hand information on δCP from these experiments much before those dedicated facilities are operational. We found that T2K by itself has marginal CP violation sensitivity at 1σ CL. For NOνA with (3+3) years of running there will be CP violation sensitivity above 1.5σ level for about one-third of the CP violating phase δCP space. The sensitivity increases slightly for 10 years of run time, with (5ν+5ν¯) combination having sensitivity compared to that of (7ν+3ν¯) combination. The data from T2HK experiment will improve the CPV sensitivity significantly. We have also found that the CP violating phase δCP can be determined to be better than 35∘, 21∘, and 9∘ for all values of δCP for T2K, NOνA, and T2HK experiments. We also obtained the confidence regions in the δCP-θ13 (θ23) plane for both T2K and NOνA experiments.



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*Source: 9139402-2016-02-29.xml*