Octant sensitivity for large [theta]^sub 13^ in atmospheric and long-baseline neutrino experiments

Abstract

One of the unknown parameters in neutrino oscillation studies is the octant of the atmospheric neutrino mixing angle [theta] ^sub 23^. In this paper, we discuss the possibility of determining the octant of [theta] ^sub 23^ in the long-baseline experiments T2K and NO[nu]A in conjunction with future atmospheric neutrino detectors, in the light of non-zero value of [theta] ^sub 13^ measured by reactor experiments. We consider two detector technologies for atmospheric neutrinos -- magnetized iron calorimeter and non-magnetized Liquid Argon Time Projection Chamber. We present the octant sensitivity for T2K/NO[nu]A and atmospheric neutrino experiments separately as well as the combined sensitivity. For the long-baseline experiments, a precise measurement of [theta] ^sub 13^, which can exclude degenerate solutions in the wrong octant, increases the sensitivity drastically. For [theta] ^sub 23^ = 39° and sin^sup 2^ 2[theta] ^sub 13^ = 0.1, at least ~ 2[sigma] sensitivity can be achieved by T2K + NO[nu]A for all values of δ ^sub CP^ for both normal and inverted hierarchy. For atmospheric neutrinos, the moderately large value of [theta] ^sub 13^ measured in the reactor experiments is conducive to octant sensitivity because of enhanced matter effects. A magnetized iron detector can give a 2[sigma] octant sensitivity for 500 kT yr exposure for [theta] ^sub 23^ = 39°, δ ^sub CP^ = 0 and normal hierarchy. This increases to 3[sigma] for both hierarchies by combining with T2K and NO[nu]A. This is due to a preference of different [theta] ^sub 23^ values at the minimum [chi] ^sup 2^ by T2K/NO[nu]A and atmospheric neutrino experiments. A Liquid Argon type detector for atmospheric neutrinos with the same exposure can give higher octant sensitivity, due to the interplay of muon and electron contributions and superior resolutions. We obtain a ~ 3[sigma] sensitivity for [theta] ^sub 23^ = 39° for normal hierarchy. This increases to 4[sigma] for all values of δ ^sub CP^ if combined with T2K/NO[nu]A. For inverted hierarchy the combined sensitivity is around 3[sigma].

Published for SISSA by Springer Received: February 20, 2013

Revised: May 3, 2013

Accepted: May 21, 2013

Published: June 4, 2013

Animesh Chatterjee,a Pomita Ghoshal,b Srubabati Goswamib and Sushant K. Rautb

aHarish-Chandra Research Institute, Chhatnag Road, Jhunsi,

Allahabad 211 019, India

bPhysical Research Laboratory, Navrangpura,

Ahmedabad 380 009, India

E-mail: [email protected], mailto:[email protected]

Web End [email protected] , mailto:[email protected]

Web End [email protected] , mailto:[email protected]

Web End [email protected]

Abstract: One of the unknown parameters in neutrino oscillation studies is the octant of the atmospheric neutrino mixing angle 23. In this paper, we discuss the possibility of determining the octant of 23 in the long-baseline experiments T2K and NO A in conjunction with future atmospheric neutrino detectors, in the light of non-zero value of 13

measured by reactor experiments. We consider two detector technologies for atmospheric neutrinos magnetized iron calorimeter and non-magnetized Liquid Argon Time Projection Chamber. We present the octant sensitivity for T2K/NO A and atmospheric neutrino experiments separately as well as the combined sensitivity. For the long-baseline experiments, a precise measurement of 13, which can exclude degenerate solutions in the wrong octant, increases the sensitivity drastically. For 23 = 39o and sin2 2 13 = 0.1, at least 2

sensitivity can be achieved by T2K + NO A for all values of CP for both normal and inverted hierarchy. For atmospheric neutrinos, the moderately large value of 13 measured in the reactor experiments is conducive to octant sensitivity because of enhanced matter e ects. A magnetized iron detector can give a 2 octant sensitivity for 500 kT yr exposure for 23 = 39o, CP = 0 and normal hierarchy. This increases to 3 for both hierarchies by combining with T2K and NO A. This is due to a preference of di erent 23 values at the minimum ~2 by T2K/NO A and atmospheric neutrino experiments. A Liquid Argon type detector for atmospheric neutrinos with the same exposure can give higher octant sensitivity, due to the interplay of muon and electron contributions and superior resolutions. We obtain a 3 sensitivity for 23 = 39o for normal hierarchy. This increases to >

4

for all values of CP if combined with T2K/NO A. For inverted hierarchy the combined sensitivity is around 3.

Keywords: Neutrino Physics, CP violation

ArXiv ePrint: 1302.1370

c

Octant sensitivity for large 13 in atmospheric and long-baseline neutrino experiments

JHEP06(2013)010

SISSA 2013 doi:http://dx.doi.org/10.1007/JHEP06(2013)010

Web End =10.1007/JHEP06(2013)010

Contents

1 Introduction 1

2 Analysis of octant degeneracy 42.1 Neutrino propagation in matter 52.2 Octant ambiguity in Pe and P 6

3 Analysis and results 123.1 NO A and T2K 133.2 Atmospheric neutrinos 173.3 Octant sensitivity using atmospheric muon events in a magnetized iron detector 173.4 Octant sensitivity using atmospheric events in a LArTPC 183.5 E ect of magnetization 213.6 E ect of CP 23

3.7 Octant sensitivity from combined analysis of atmospheric electron and muon events with NO A and T2K 24

4 Summary and conclusion 28

1 Introduction

The measurement of a non-zero value of the mixing angle 13 by the reactor experiments Double-Chooz [1], Daya-Bay [2] and RENO [3] heralds a major breakthrough in the advancement of neutrino physics. The best-t value of sin2 13 from latest global analysis of solar, atmospheric, reactor and accelerator data is 0.023 0.0023 [4]. which signies non

zero 13 at 10 level. Other global analyses also give similar results [5, 6]. This conrms the earlier observation of non-zero 13 in T2K [7] and MINOS [8] experiments as well the indication of non-zero best-t value of 13 from previous analyses [9, 10]. Among the other oscillation parameters the solar parameters m221 and 12 are already well measured from solar neutrino and KamLAND experiments [11, 12]. The solar matter e ect also dictates m221 > 0. The most stringent constraint on mass squared di erence m231 governing the atmospheric neutrino oscillations comes from the data from the MINOS experiment [13].

However the ordering of the third mass eigenstate with respect to the other two i.e. the sign of m231 is not yet known. There are two possible arrangements of the neutrino mass states: (i) m1 < m2 < m3 corresponding to Normal Hierarchy (NH) and (ii) m3 < m1 < m2 corresponding to Inverted Hierarchy (IH). The mixing angle sin2 23 is mainly determined by the SuperKamiokande (SK) atmospheric neutrino data. However the octant in which this mixing angle lies is not yet decisively determined by the data. A full three-avour t to the SK data gives the best-t for NH in the lower octant (LO) and IH in the higher octant

1

JHEP06(2013)010

parameter best t 3 range m221 [105 eV2] 7.54 6.998.18

| m231| [103 eV2]

0.330.640.340.66

0.0170.031

0 2

Table 1. The best-t values and 3 ranges of neutrino oscillation parameters from ref. [5]. The rst and second rows in each case denote the values for a normal and inverted neutrino mass hierarchy respectively.

(HO) keeping 13 as a free parameter in the analysis [14]. Three-avour global analysis of all available neutrino data give the best-t 23 in the lower octant. The best-t values and 3 ranges of oscillation parameters from global analysis in ref. [5] is summarized in table 1. At present there is no signicant constraint on the CP phase CP and the whole range from 0 2 is allowed at the 2 level.

There are two aspects in the measurement of 13 which is expected to play an important role in resolving the outstanding issues in neutrino oscillation physics. Firstly if 13 is non

zero and relatively large (i) CP violation in the lepton sector can be probed (ii) the earth matter e ect on the propagation of neutrinos can be sizable. The latter facilitates the determination of mass hierarchy and octant in experiments in which neutrinos travel through an appreciable path length. The second aspect is the precision measurement of 13:

which helps in increasing the sensitivity in the determination of hierarchy, octant and CP.

The octant degeneracy means impossibility of distinguishing between 23 and /2 23.

This is generic and robust for vacuum oscillation probabilities that are functions of sin2 2 23

e.g. the two avour muon survival probability in vacuum [15]. If on the other hand the leading term in the probability are functions of sin2 23 (e.g. Pe) then the inherent octant degeneracy is not there but lack of knowledge of other parameters like 13 and CP can give rise to octant degeneracy [16, 17]. These issues may a ect the octant sensitivity of the long-baseline experiments T2K and NO A where the matter e ect is not very signicant and in particular resonant matter e ects do not get a chance to develop. Although conventionally the octant degeneracy refers to the indistinguishability of 23 and /2 23, in view of the

present uncertainty in the measurement of 23 the scope of this can be generalized to any value of 23 in the wrong octant within its allowed range. In this paper by octant sensitivity we refer to this generalized denition. If in addition the hierarchy is unknown then there can also be the wrong-octant-wrong-hierarchy solutions and one needs to marginalize over the wrong hierarchy as well.

2

2.19 2.62

2.17 2.61 sin2 12 0.307 0.260.36

sin2 23

0.3860.392

0.02410.0244

2.432.42

sin2 13

JHEP06(2013)010

1.08 1.09

Atmospheric neutrinos pass through long distances in matter and they span a wide range in energy and can encounter resonant matter e ects. In this case the octant sensitivity in P ensues from the term sin4 13 sin2 2 m13 [18]. Pe in matter contains sin2 13 sin2 2 m13.

Since at resonance sin2 2 m13 1, the octant degeneracy can be removed. In this case also

one can probe the e ect of CP uncertainty on the lifting of this degeneracy.

Atmospheric neutrinos provide uxes of both neutrinos and antineutrinos as well as neutrinos of both electron and muon avour. On one hand it provides the advantage of observing both electron and muon events. However on the other hand a particular type of event gets contributions from both disappearance and appearance probabilities. This can be a problem if the matter e ects for these two channels go in opposite directions. Thus it is necessary to carefully study the various contributions and ascertain what may be the best possibility to decode the imprint of matter e ects in atmospheric neutrino propagation. Three major types of detector technologies are under consideration at the present moment as future detector of atmospheric neutrinos.

(i) Water Cerenkov detectors: Such type of detectors have already been shown to be a successful option for atmospheric neutrino detection by the SuperKamiokande collaboration. This is sensitive to both electron and muon events and the energy threshold can be relatively low. Megaton detectors of this kind under consideration for future are HK, MEMPHYS [19, 20]. These cannot be magnetized and hence provide no charge identication capability. Multi-megaton detectors with ice also fall in this category. An example of such a detector is PINGU [21, 22], which is a proposed upgrade of the DeepCore section of the IceCube detector for ultra-high energy neutrinos [23] with a lower energy threshold for atmospheric neutrino detection.

(ii) Magnetized Iron Detectors: Such a detector for atmospheric neutrinos were proposed by the MONOLITH [24] collaboration and is now actively pursued by the INO collaboration [25]. This has a relatively high threshold and is mainly sensitive to muon neutrinos. These type of detectors o er the possibility of magnetization, thus making it possible to distinguish between muon and antimuon events, which enhances the sensitivity.

(iii) Liquid Argon Time Projection Chamber (LArTPC): Examples of such detectors are ICARUS and ArgoNeuT [26, 27]. The hallmark of these detectors are their superior particle identication capability and excellent energy and angular resolution. They are sensitive to both electron and muon events with good energy and direction reconstruction capacity for both type of events [28]. Possibility of magnetization is also being discussed [29, 30].

In this paper we study in detail the possibility of removal of octant degeneracy in view of the precise measurement of a relatively large value of 13. There have been many earlier studies dealing with this subject both in the context of long-baseline and atmospheric neutrinos. The importance of combining accelerator and reactor experiments and the role of a precise measurement of 13 in abating the octant degeneracy have been considered in refs. [3133]. The possibility of resolving the octant degeneracy using long-baseline experiments has also

3

JHEP06(2013)010

been explored in refs. [3439]. Recently octant sensitivity in the T2K/NO A experiments has been investigated including the recent results on the measurement of non-zero 13 by

reactor experiments [40]. The octant sensitivity for atmospheric neutrinos in the context of magnetized iron calorimeter detectors was considered in refs. [18, 41, 42], for water Cerenkov detectors in ref. [19] and for LArTPC in ref. [43].

We examine the octant sensitivity in the long-baseline experiments T2K and NO A and in the atmospheric neutrino experiments as well as the combined sensitivity of these experiments. In particular we address whether degeneracy due to 13 can still a ect octant determination at the current level of precision of this parameter. For xed values of 13

the e ect of lack of knowledge of CP on the octant determination capability of these experiments is also studied. We take into account the uncertainty of 23 in the wrong

octant and discuss how much this can inuence the octant sensitivity. We present results for the two cases of known and unknown hierarchy.

For the study of atmospheric neutrinos we consider magnetized iron calorimeter detectors with charge sensitivity which is sensitive to the muon neutrinos. We also consider a non-magnetized LArTPC detector which can detect both electron and muon neutrinos. In particular we discuss the interplay between the muon and electron type events in the overall octant sensitivity. For our atmospheric analysis we assume a prior knowledge of hierarchy. Lastly we do a combined analysis of T2K, NO A and atmospheric neutrinos and discuss the synergistic aspects between long-baseline and atmospheric neutrino experiments.

The plan of the paper is as follows. In section 2 we discuss the octant degeneracy at the level of oscillation and survival probabilities, for baselines corresponding to both atmospheric neutrinos and those relevant to NO A and T2K. Section 3 discusses the analysis procedure and results. First we discuss the octant sensitivity in NO A and T2K. Next we describe the results obtained for octant sensitivity using atmospheric neutrino detectors. Finally we present combined octant sensitivity of long-baseline and atmospheric neutrino experiments. We end by summarizing the results.

2 Analysis of octant degeneracy

The ambiguity in the determination of the octant of 23 may appear in the oscillation and survival probabilities as

(a) the intrinsic octant degeneracy, in which the probability is a function of sin2 2 23 and

hence the measurement cannot distinguish between 23 and /2 23,

P ( tr23) = P (/2 tr23) (2.1)

(b) the degeneracy of the octant with other neutrino parameters, which confuses octant determination due to the uncertainty in these parameters. In particular, this degeneracy arises in probabilities that are functions of sin2 23 or cos2 23. For such cases P ( tr23) 6= P (/2 tr23). However for di erent values of the parameters 13 and CP

the probability functions become identical for values of 23 in opposite octants for

4

JHEP06(2013)010

di erent values of these parameters, i.e.

P ( tr23, 13, CP) = P (/2 tr23, 13, CP), (2.2)

where tr23 denotes the true value of the mixing angle and the primed and unprimed values of 13 and CP lie within the current allowed ranges of these parameters. In the case of CP, this covers the entire range from 0 to 2, while for 13 the current 3 range is given by sin2 2 13 = 0.07 0.13 . From the above equation it is evident

that even if 13 is determined very precisely, this degeneracy can still remain due to complete uncertainty in the CP phase. In fact, the scope of this degeneracy can be enlarged to dene this as

P ( tr23, 13, CP) = P ( wrong23, 13, CP) (2.3)

where wrong23 denote values of the mixing angle in the opposite octant.

The features of the octant degeneracy and the potential for its resolution in di erent neutrino energy and baseline ranges can be understood from the expressions for the oscillation and survival probabilities relevant to specic ranges. We discuss below the probability expressions in the context of the xed baseline experiments NO A/T2K and for atmospheric neutrino experiments.

2.1 Neutrino propagation in matter

Neutrinos travelling through earth encounter a potential due to matter given as,

A = 2 2 GF ne E = 2 0.76 104 Ye [bracketleftbigg]

eV2 (2.4)

where GF is the Fermi coupling constant and ne is the electron number density in matter, given by nE = NAYe (NA = Avogadros number, Ye = electron fraction 0.5, = earth

matter density.

The mass squared di erence ( m231)m and mixing angle sin2 2 m13 in matter are related to their vacuum values by

( m231)m =

q( m231 cos 2 13 A)2 + ( m231 sin 2 13)2

sin 2 m13 = m231 sin 2 13

p( m231 cos 2 13 A)2 + ( m231 sin 2 13)2

(2.5)

The MSW matter resonance [4446] occurs and the mixing angle m13 becomes maximal at neutrino energies and baselines for which the terms m231 cos 2 13 and A in the denominator of eq. (2.5) become equal. Hence the matter resonance energy Eres is given by

(2.6)

Since the corresponding expression for antineutrinos is obtained by making the replacement A A, it may be observed that the matter resonance occurs for the normal

neutrino mass hierarchy (i.e. m231 > 0) for neutrinos and for the inverted mass hierarchy(i.e. m231 < 0) for antineutrinos.

5

JHEP06(2013)010

g/cc

E

GeV

[bracketrightbigg] [bracketleftbigg]

[bracketrightbigg]

Eres = | m231| cos 2 13

2 0.76 104 Ye

2.2 Octant ambiguity in Pe and P

For NO A/T2K, the baselines are 812 and 295 Km respectively and the peak energies of the beams are in the range 0.5-2 GeV. For these values of baselines, the earth matter density is in the range 2.3 2.5 g/cc, and the corresponding matter resonance energies are above

10 GeV. Hence the neutrino energies of both experiments lie well below matter resonance, and the oscillation probabilities will only display small sub-leading matter e ects. The expressions of the relevant probabilities P and Pe in vacuum are given by the following expressions obtained in the one-mass scale dominant (OMSD) approximation,

Pv = 1 sin2 2 23 sin2 [bracketleftbigg]

1.27 m231 L

E

[bracketrightbigg]

JHEP06(2013)010

+4 sin2 13 sin2 23 cos 2 23 sin2

1.27 m231 L E[bracketrightbigg]

(2.7)

Pve = sin2 23 sin2 2 13 sin2

1.27 m231 L E

[bracketrightbigg]

(2.8)

The above probability expressions have sub-leading corrections corresponding to small matter e ect terms and the solar mass-squared di erence [4751]. We observe the following salient features from these expressions:

(a) The disappearance channel P has in its leading order a dependence on sin2 2 23, and hence is dominated by the intrinsic octant degeneracy. There is a small 13-dependent correction in the measurement of 23 which gives a minor ( 1%) resolution of the

degeneracy if 13 is known precisely.

(b) The appearance channel Pe has the combination of parameters sin2 23 sin2 2 13, and hence does not su er from the intrinsic octant degeneracy. However, the degeneracy of the octant with the parameter 13 comes into play, since the above combination may be invariant for opposite octants for di erent values of 13, and hence this degeneracy cannot get lifted with a measurement from such experiments alone [32]. This channel can be also a ected by the large uncertainty in CP when sub-leading corrections are included.

For atmospheric neutrinos, the relevant baselines and energies are in the range 1000 12500 Km and 110 GeV respectively. A large region in this L and E space exhibits strong resonant earth matter e ects, since the earth densities in this baseline range (3 8 g/cc) correspond to resonance energies Eres = 49 GeV. Hence the relevant probability

expressions Pme, Pmee and Pm can be written, in the OMSD approximation and with full matter e ects, as [48, 52]

Pme = sin2 23 sin2 2 m13 sin2

1.27 ( m231)m L E[bracketrightbigg]

(2.9)

Pm = 1 cos2 m13 sin2 2 23 sin2 [bracketleftbigg]

1.27

m231 + A + ( m231)m 2

[parenrightbigg]

L E

[bracketrightbigg]

sin2 m13 sin2 2 23 sin2 [bracketleftbigg]

1.27

m231 + A ( m231)m 2

[parenrightbigg]

L E

[bracketrightbigg]

sin4 23 sin2 2 m13 sin2 [bracketleftbigg]

1.27 ( m231)m L

E

[bracketrightbigg]

(2.10)

6

Pmee = 1 sin2 2 m13 sin2 [bracketleftbigg]

In this case, the following features are observed:

(a) The oscillation probability in matter Pme is still guided to leading order by a dependence on sin2 23. But strong resonant earth matter e ects help in resolving the degeneracy since the mixing angle 13 in matter gets amplied to maximal values (close to 45o) near resonance. The combination sin2 23 sin2 2 m13 no longer remains invariant over opposite octants, since sin2 2 m13 becomes close to 1 in both octants irrespective of the vacuum value of 13. This breaks the degeneracy of the octant with 13.

(b) The muon survival probability in matter Pm has leading terms proportional to sin2 2 23, as in the vacuum case, which could give rise to the intrinsic octant degeneracy. But the strong octant-sensitive behaviour of the term sin4 23 sin2 2 m13 near resonance can override the degeneracy present in the sin2 2 23-dependent terms.

(c) The electron survival probability Pmee is independent of 23 and hence does not contribute to the octant sensitivity.

(d) Since the Pme channel is simply the CP conjugate of Pme, the probability level discussion in this section is applicable to Pme also.

In the following discussion, we address the octant degeneracy due to 23 in the wrong

octant, 13 and unknown values of CP, at a probability level. The probability gures 14 are drawn by solving the full three avour propagation equation of the neutrinos in matter using PREM density prole [53]. In all these gures the left panels are for the NO A peak energy and baseline (2 GeV, 812 Km), while the right panels are for a typical atmospheric neutrino energy and baseline (6 GeV, 5000 Km). The top row denotes the appearance channel Pe, while the bottom row denotes the disappearance channel P.

Figure 1 depicts the probabilities Pe and P as a function of sin2 2 13 for tr23 = 39o and wrong23 = 51o. The bands show the probability range in each case when CP is varied over its full range (0 to 2). For a given xed value of sin2 2 13, the distinction between 23 in the two octants can be gauged from the separation of the two bands along the relevant vertical line. The left panels show that for Pe, the CP bands overlap and the two hierarchies cannot be distinguished till nearly sin2 2 13 = 0.1. The inset in the upper left panel shows the region of separation of the bands near sin2 2 13 = 0.1 in detail. Hence the knowledge of the parameter 13 upto its current level of precision becomes crucial, since a 13 range including lower values would wash out the octant sensitivity derivable from such experiments due to the combined degeneracy with 13 and CP. For P, the intrinsic degeneracy predominates and the e ect of CP variation is insignicant.

For the 5000 km baseline, due to the resonant matter e ects breaking the octant degeneracy at the leading order, both Pe and P show a wider separation between the opposite-octant bands, even for small values of 13. This is due to the sin2 23 sin2 2 m13 (sin4 23 sin2 2 m13) term in Pe (P). The CP bands in the right-hand panels are much

7

1.27 ( m231)m L

E

[bracketrightbigg]

(2.11)

JHEP06(2013)010

0.5

0 0.02 0.06 0.1 0.14 0.18

0.5

0 0.02 0.06 0.1 0.14 0.18

39o 51o

0.1

0.06

0.05

0.1 0.14 0.18

39o 51o

0.4

0.4

0.3

0.3

P e

P e

0.2

0.2

0.1

0.1

JHEP06(2013)010

sin2 2q13

sin2 2q13

1

0 0.02 0.06 0.1 0.14 0.18

1

0 0.02 0.06 0.1 0.14 0.18

39o 51o

39o 51o

0.8

0.8

0.6

0.6

P

P

0.4

0.4

0.2

0.2

sin2 2q13

sin2 2q13

Figure 1. Behaviour of the muon survival and oscillation probabilities as a function of sin2 2 13

showing the 23 octant degeneracy and its breaking. The left panels are for the NO A peak energy and baseline (2 GeV, 812 Km), while the right panels are for a typical atmospheric neutrino energy and baseline (6 GeV, 5000 Km). The top row denotes the appearance channels Pe and Pe, while the bottom row denotes the disappearance channel P. The values of oscillation parameters chosen are tr23 = 39o, wrong23 = 51o. The bands denote a variation over the full range of the phase CP.

The inset shows the region of separation of the bands near sin2 2 13 = 0.1.

wider because of the enhancement of the subleading terms due to matter e ects. However, the enhancement is more for the leading order term which alleviates the degeneracy with CP.

Figure 2 shows the probabilities Pe and P as a function of sin2 2 13. We have held xed, true and test CP = 0 and true tr23 = 39o, with the band denoting a variation over the full allowed range of wrong23 = 45o to 54o in the wrong octant. Thus this gure reveals the e ect of the uncertainty in the measurement of 23 in the determination of octant, for a given value of sin2 2 13. For the NO A baseline, the survival probability P shows an overlap of the test 23 band with the true curve, while in the probability Pe there is a small separation. Figures 1 and 2 thus indicate that for the NO A baseline, the

8

0.5

0 0.02 0.06 0.1 0.14 0.18

0.5

0 0.02 0.06 0.1 0.14 0.18

HO 39o

HO 39o

0.4

0.4

0.3

0.3

P e

P e

0.2

0.2

0.1

0.1

JHEP06(2013)010

sin2 2q13

sin2 2q13

1

0 0.02 0.06 0.1 0.14 0.18

1

0 0.02 0.06 0.1 0.14 0.18

HO 39o

HO 39o

0.8

0.8

0.6

0.6

P

P

0.4

0.4

0.2

0.2

sin2 2q13

sin2 2q13

Figure 2. Same as gure 1 with a xed true and test CP = 0 and true tr23 = 39o, with the band denoting a variation over the full allowed range of wrong23 = 45o to 54o in the wrong octant.

octant sensitivity from Pe is more a ected by the uncertainty in CP and less by the test 23 variation, while for P the opposite is true. The plots for the atmospheric neutrino baseline show a clear breaking of the octant degeneracy in both Pe and P even for small values of 13, indicating that the octant sensitivity from the atmospheric neutrino signal is stable against the variation of both CP and the test value of 23, even for small values of 13.

Having discussed octant sensitivity in the context of xed 13, we now come to the

question of uncertainty in this parameter. The current reactor measurements of sin2 2 13

have measured this parameter with a precision of 0.01 and hence the e ect of 13 uncertainty on octant degeneracy is largely reduced. In gure 3, the energy spectra of the probabilities Pe and P are plotted. The gure shows the variation in the probabilities in each case when sin2 2 13 is varied over three values sin2 2 13 = 0.07, 0.1 and 0.13 covering the current allowed range, and for two illustrative values of 23 39o and 51o in opposite

octants. The value of CP is xed to be 0. The gure indicates that the separation of the

9

0.2

0.5

q23 = 39o, sin2 2q13 = 0.07 q23 = 39o, sin2 2q13 = 0.10 q23 = 39o, sin2 2q13 = 0.13 q23 = 51o, sin2 2q13 = 0.07 q23 = 51o, sin2 2q13 = 0.10 q23 = 51o, sin2 2q13 = 0.13

0.4

0.15

0.3

P e

0.1

P e

0.2

0.05

0.1

JHEP06(2013)010

0 0 2 4 6 8 10

0 0 2 4 6 8 10

E (GeV)

E (GeV)

1

1

0.8

0.8

0.6

0.6

P

P

0.4

0.4

0.2

0.2

0 0 2 4 6 8 10

0 0 2 4 6 8 10

E (GeV)

E (GeV)

Figure 3. Energy spectra of the probabilities Pe and P for the NO A baseline (left panels) and for a sample atmospheric neutrino baseline 5000 Km (right panels). The gure shows the variation in the probabilities in each case when sin2 2 13 is varied over three values in the current allowed range, xing the true and test 23 values tr23 = 39o and wrong23 = 51o. CP is xed to 0.

LO and HO curves and hence the octant sensitivity depends on the value of sin2 2 13 in

opposite ways depending on whether the true 23 value lies in the higher or lower octant. In Pe, for tr23 = 39o, lower values of true sin2 13 can give a higher octant sensitivity since they are more separated from the band of variation of the probability over the whole range of test sin2 2 13, and as true sin2 2 13 increases the degeneracy with the wrong 23 band becomes more prominent. For tr23 = 51o, the opposite is true, i.e. higher values of sin2 2 tr13 have a better separation with the wrong 23 band. For example, for the NO A baseline, if tr23 = 39o, the Pe curve for sin2 2 tr13 = 0.07 is well-separated from the band for wrong23 = 51, while the curve for sin2 2 tr13 = 0.1 is seen to be just separated from it, and the sin2 2 tr13 = 0.13 curve lies entirely within the band of test sin2 2 13 variation with the wrong octant. But if tr23 = 51o, the sin2 2 tr13 = 0.07 curve su ers from the degeneracy while the curves for sin2 2 tr13 = 0.1 and upwards lie clearly outside the wrong23 band. For

10

0.5

0.5

51o

HO 39o

51o

HO 39o

0.4

0.4

0.3

0.3

P e

P e

0.2

0.2

0.1

0.1

JHEP06(2013)010

0 1 2 3 4 5 6 7 8 9 10

0 1 2 3 4 5 6 7 8 9 10

E (GeV)

E (GeV)

1

1

51o

HO 39o

51o

HO 39o

0.8

0.8

0.6

0.6

P

P

0.4

0.4

0.2

0.2

0 1 2 3 4 5 6 7 8 9 10

0 1 2 3 4 5 6 7 8 9 10

E (GeV)

E (GeV)

Figure 4. Energy spectra of the probabilities Pe and P for the NO A baseline (left panels) and for a sample atmospheric neutrino baseline 5000 Km (right panels). The gure shows the variation in the probabilities in each case when wrong23 is varied over the entire allowed range in the wrong

octant, as well as varying the test CP, xing the true values tr23 = 39o and trCP = 0 in the solid curve. The spread due to variation of both test parameters is denoted by the blue band. The black band shows the variation with test CP for a xed wrong23 = 51o.

P, the e ect of 13 on the separation between the opposite octant bands is less, since the behaviour is governed by the intrinsic octant degeneracy.

For the 5000 km baseline, due to strong matter e ects, the separation of the true and wrong 23 bands is much better, and only the highest (lowest) values of sin2 2 tr13 su er from a degeneracy with the wrong octant for Pe if the true octant is lower (higher). For P, the behaviour is reversed.

Figure 4 again depicts the energy spectra of the probabilities Pe and P. This gure shows the variation in the probabilities in each case when wrong23 is varied over the entire allowed range in the wrong octant, as well as varying the test CP, xing tr23 = 39o and trCP = 0. The solid black band denotes the variation with test CP for a xed wrong23 = 51o.

11

For the NO A baseline, the test probability bands show an almost complete overlap with the tr23 = 39o, trCP = 0 curve. However, the octant sensitivity may still be retained due to spectral information. So there always exist specic energy regions and bins from which the octant sensitivity can be derived.

At 5000 km, the minimum separation between octants does not occur at or near wrong23 = 90o tr23 = 51o as can be seen from the solid black shaded region. The edge of the striped blue band corresponding to some other value of 23 is closest to the true curve and well-separated from it. This shows that there is octant sensitivity for this baseline even after including the uncertainty in CP and 23. The wrong23 for which the minimum separation is likely to occur will be further discussed in the context of gure 9.

3 Analysis and results

In this section we present the results of our analysis for T2K, NO A and atmospheric experiments. We also give results for octant sensitivity when the results from both type of experiments are combined.

In refs. [54, 55], it has been shown that the atmospheric parameters m2atm and measured in MINOS are related to the oscillation parameters in nature, m231 and 23 using the following non-trivial transformations:

sin 23 = sin cos 13 , (3.1)

m231 = m2atm + (cos2 12 cos sin 13 sin 2 12 tan 23) m221 . (3.2) These transformations become signicant in light of the moderately large measured value of 13. Therefore, in order to avoid getting an erroneous estimate of octant sensitivity, we take these corrected denitions into account. Thus, in calculating oscillation probabilities, we use the corrected parameters m231 and 23, after allocating the measured values to m2atm and .

Our analysis procedure consists of simulating the experimental data for some specic values of the known oscillation parameters known as the true values. The experimental data is generated for a xed hierarchy and for the following xed values of the parameters:

( m221)tr = 7.6 105 eV2 (sin2 12)tr = 0.31

(sin2 2 13)tr = 0.1 (3.3)

( m2atm)tr = 2.4 103 eV2 ,and specic values of tr and trCP. In the theoretical predictions which are tted to the simulated experimental data, the test parameters are marginalized over the following ranges:

CP [0, 2)

((35o, 45o) (true higher octant) (45o, 55o) (true lower octant)

sin2 2 13 (0.07, 0.13) . (3.4)

12

JHEP06(2013)010

25

25

NOvA + T2K, octant sensitivity with priors

(sin2 2q13)tr = 0.10, NH

3s sensitivity

2s sensitivity

(dCP)tr = 0

(dCP)tr = p/2

(dCP)tr = p

(dCP)tr = -p/2

NOvA + T2K, octant sensitivity with priors

(sin2 2q13)tr = 0.10, IH

3s sensitivity

2s sensitivity

(dCP)tr = 0

(dCP)tr = p/2

(dCP)tr = p

(dCP)tr = -p/2

20

20

15

15

prior

prior

c2 tot

c2 tot

10

10

5

5

JHEP06(2013)010

0 37 39 41 43 45 47 49 51 53

0 37 39 41 43 45 47 49 51 53

true q23

true q23

Figure 5. Marginalized octant sensitivity from a combination of NO A and T2K, for the case of normal and inverted mass hierarchy. The test hierarchy has been xed to be the same as the true hierarchy in this case. In this gure priors have been added.

m221 and sin2 12 are xed to their true values since their e ect is negligible. Also, after verifying that the e ect of a marginalization over m231 is minimal, we have xed m2atm to its true value for computational convenience.

In our calculation, the hierarchy is assumed to be known in all the atmospheric neutrino experiments, since the time-scale involved would ensure that the hierarchy is determined before any signicant octant sensitivity is achievable. For NO A/T2K, results are given both with and without prior knowledge of hierarchy, i.e. marginalizing over the test hierarchy.

Priors are taken in terms of the measured quantities sin2 2 13 and sin2 2 as follows:

~2prior =

sin2 2 true sin2 2

(sin2 2 )

!2+

sin2 2 true13 sin2 2 13 (sin2 2 13)

2(3.5)

with the 1 error ranges as sin2 2 = 5% and sin2 2 13 = 0.01 unless otherwise stated. The latter is the error on 13 quoted recently by Double Chooz, Daya Bay and RENO [13].

3.1 NO A and T2K

We simulate the current generation of long-baseline experiments NO A and T2K, using the GLoBES package [56, 57] and its associated data les [58, 59]. For T2K, we assume a 3 year run with neutrinos alone, running with beam power of 0.77 MW throughout. (We choose this low running time for T2K to compensate for the fact that their beam power will be increased to its proposed value over a period of a few years [60].) The energy resolutions and backgrounds are taken from refs. [6165]. The detector mass is taken to be 22.5 kT. For NO A, we consider the set-up as described in refs. [66, 67], which is re-optimized for the moderately large measured value of 13. The 14 kT detector receives a neutrino and antineutrino beam for 3 years each, from the NuMI beam.

13

25

25

NOvA + T2K, octant sensitivity with priors

(sin2 2q13)tr = 0.10, NH

3s sensitivity

2s sensitivity

(dCP)tr = 0

(dCP)tr = p/2

(dCP)tr = p

(dCP)tr = -p/2

NOvA + T2K, octant sensitivity with priors

(sin2 2q13)tr = 0.10, IH

3s sensitivity

2s sensitivity

(dCP)tr = 0

(dCP)tr = p/2

(dCP)tr = p

(dCP)tr = -p/2

20

20

15

15

prior

prior

c2 tot

c2 tot

10

10

JHEP06(2013)010

5

5

0 37 39 41 43 45 47 49 51 53

0 37 39 41 43 45 47 49 51 53

true q23

true q23

Figure 6. Marginalized octant sensitivity from a combination of NO A and T2K, for the case of normal and inverted mass hierarchy. The test hierarchy has been left free in this case. In this gure priors have been added.

Figures 5 and 6 depict the octant sensitivity from a combination of NO A and T2K marginalized over the test parameters and with added priors. The ~2 is dened as

(~2tot)prior = min(~2NOvA + ~2T2K + ~2prior) (3.6)

Here (and elsewhere), min denotes a marginalization over the test parameters as outlined above. In gure 5, the neutrino mass hierarchy is assumed to be known in each case, and in gure 6 the mass hierarchy is taken to be unknown and therefore marginalized over. These plots are done for four specic true values of the CP phase, CP = 0, /2, and -/2.

Table 2 lists the values of the octant sensitivity from NO A and T2K individually and from the combination for a specic value trCP = 0, and a set of true 23 values from both octants, without and with added priors, to depict the relative contributions from the two experiments. Figure 7 shows how the octant ~2 for tr23 = 36o varies with the test values of 23 and CP for the appearance and disappearance channels of NO A and for T2K. In the gure, 13 and CP are marginalized in the left panel and 13 and 23 are marginalized in the right panel. Normal hierarchy is assumed in the gure. The following features are observed in the sensitivity behaviour of the two experiments and the appearance/disappearance channels in each case:

1. Figure 7 (left panel) shows that the ~2 minima for the NO A disappearance channel occur near test23 = /2 tr23, because of the predominant dependence on sin2 2 23,

while for the appearance channel the minima occur near test23 = 45o, because of the sin2 23 dependence. In the combination of NO A appearance and disappearance channels (red solid curve in the gure), the ~2 minima are near test23 = /2 tr23,

following the behaviour of the disappearance channel ~2, but the values are enhanced due to the contribution from the appearance ~2 values at that point.

14

tr23 ~2 (NO A) ~2 (T2K) ~2 (NO A ~2 (NO A ~2 (NO A+T2K) +T2K+prior) +T2K+priorn)

36 1.5 (4.1) 0.0 (0.8) 1.7 (5.8) 9.6 (14.8) 17.5 (26.7) 39 0.2 (0.4) 0.0 (0.1) 0.3 (0.6) 3.9 (7.3) 6.3 (12.0) 41 0.1 (0.1) 0.0 (0.0) 0.1 (0.1) 1.9 (3.6) 2.4 (5.4) 43 0.1 (0.1) 0.0 (0.0) 0.1 (0.1) 1.0 (0.8) 1.3 (1.1) 47 0.0 (0.1) 0.0 (0.0) 0.1 (0.1) 0.8 (1.0) 1.0 (1.3) 49 0.2 (0.3) 0.0 (0.0) 0.3 (0.5) 3.8 (2.3) 5.4 (3.1) 51 2.3 (1.1) 0.2 (0.1) 2.9 (1.5) 8.5 (6.0) 13.0 (8.2) 54 11.0 (6.8) 2.8 (0.5) 14.7 (9.4) 21.5 (16.1) 32.4 (22.6)

Table 2. Marginalized octant sensitivity from NO A, T2K and a combination of the two experiments for trCP = 0 and sin2 2 tr13 = 0.1 without added priors (rst three columns) and with added priors (fourth and fth columns). prior denotes the present prior of sin2 2 13 = 0.01 and

priorn denotes a projected prior of sin2 2 13 = 0.005. Here normal hierarchy (inverted hierarchy) is assumed.

5

10

JHEP06(2013)010

NOvA, T2K octant sensitivity q13 and dCP marginalized

NH, sin2 2q13 = 0.1

(q23)tr = 36o, (dCP)tr = 0

NOvA app NOvA disapp NOvA app+disapp

T2K app+disapp

NOvA, T2K octant sensitivity q13 and q23 marginalized

NH, sin2 2q13 = 0.1

(q23)tr = 36o, (dCP)tr = 0

NOvA app NOvA disapp NOvA app+disapp

T2K app+disapp

4

8

3

c2 NOvA,T2K

6

c2 NOvA,T2K

2

4

1

2

0 46 48 50 52 54

0 0 90 180 270 360

test q23

test dCP

Figure 7. Octant sensitivity from NO A appearance and disappearance channels and their combination and from T2K as a function of test 23 (left panel) and test CP (right panel). 13 and CP are marginalized in the left panel and 13 and 23 are marginalized in the right panel.

2. The ~2 values are asymmetric across the lower and higher octants, as can be seen in table 2. For example, ~2min is about 1.5 for NO A (appearance + disappearance) at tr23 = 36o with sin2 2 tr13 = 0.1, trCP = 0. For tr23 = 54o, ~2min goes up to about 11 for

NO A (app + disapp) for the same value of trCP.

3. The ~2 values for NO A and T2K strongly depends on the true value of CP . We nd for trCP = /2, ~2min for NO A (app + disapp) is 5.6 for tr23 = 36o and 7.5 for tr23 = 54o. This point will be illustrated in more detail later in the context of gures 12 and 13.

15

4. From gure 7 (right panel) , we see that the ~2 for the disappearance channel is weakly dependent on the test value of CP, and remains small for all values of test CP. On the other hand, the ~2 for the appearance channel has a strong dependence on test CP, which is consistent with the behaviour of the respective probabilities seen in section 2.2. In terms of test CP, the minima of the combination occur at test CP values close to those for the appearance channel, which is the principal contributor to the CP dependence of the sensitivity. The increased values of the combined NO A ~2 minima at each test CP, can be attributed to the tension between the two channels with respect to test23. Thus marginalization over CP reduces the sensitivity to some extent because of the e ect of CP uncertainty in the appearance channel.

5. The ~2 minima for both appearance and disappearance channels are very low for all values of tr23, indicating negligible octant sensitivity from the channels separately.

This is apparent from the left panel of gure 7, where the minimum values of ~2 for individual channels are quite small when marginalized over the entire 23 range.

6. There is no major tension between NO A appearance + disappearance and T2K appearance + disappearance. The ~2 minima occur at the same values of test sin2 2 13 and test 23, and for somewhat displaced values of test CP. This is because both T2K and NO A roughly follow the octant behaviour dictated by the vacuum probabilities with subleading contributions of the CP-dependent terms. The slightly increased matter e ect contribution for NO A does not seem to have a signicant e ect. The combined NO A+T2K ~2 values are nearly equal to the sum of the corresponding individual NO A and T2K values, as seen in table 2.1 For example, ~2min for T2K appearance + disappearance is about 3 for tr23 = 54o. The corresponding NO A value is about 11. For NO A+T2K, ~2min is about 15 for the same tr23.

7. The addition of priors to NO A+T2K enhances the sensitivity drastically, making it (for example) (~2min)prior = 21 for tr23 = 54o with the present value of the 13 prior. This underscores the importance of precision measurement of 13 on octant

sensitivity. With more precise measurements of sin2 2 13 expected from the reactor experiments, the octant sensitivity is expected to get better. If we take a stronger projected prior of sin2 2 13 = 0.005 instead of the present value of sin2 2 13 = 0.01, the results improve further, as seen in column 5 of the table, where priorn denotes the projected prior. Here, for example, the ~2 goes up from 3.9 to 6.3 for tr23 = 39, CPtr = 0 and normal hierarchy. In the limit of innite precision, i.e. if 13 is held xed, the ~2 goes up further to 7.7 for the same case.

8. We see from the gures 5 and 6 that the ~2 is asymmetric between the lower and higher octants. The nature of this asymmetry depends on the true CP value. For instance for trCP = 0, the ~2 values on the LO side are much lower than on the

HO side, but this is reversed for other trCP values. Note that the addition of priors

1In this table and some subsequent gures and tables, the ~2 values without priors are given only for comparison of the relative weightage of the contributions from di erent channels and di erent experiments.

16

JHEP06(2013)010

makes the asymmetry less pronounced since the prior contributions for the lower and higher octants are roughly symmetrical. This can be seen by comparing the with and without prior values of ~2 in table 2.

3.2 Atmospheric neutrinos

For our study of octant sensitivity in atmospheric neutrino experiments, we look at the following set-ups:

1. A large magnetized iron detector with an exposure of 500 kT yr, capable of detecting muon events with charge identication, using the following neutrino energy and angular resolution: E = 0.1E , = 10o.

Note that such a detector will be constructed by the India-based Neutrino Observatory (INO) collaboration [25]. The energy and angular resolutions of muons are available from INO simulation code [68, 69]. But the work on reconstruction of neutrino energy and angle requiring the resolutions for both muons and hadrons are in progress. In our neutrino analysis therefore we use xed resolutions in terms of neutrino energy and angle as described above. Determination of the octant sensitivity of INO using the resolutions obtained from INO simulations is in progress.

2. A LArTPC with an exposure of 500 kT yr (unless otherwise stated) capable of detecting muon and electron events. No charge identication is assumed here. The angular resolutions are taken to be [43]:

e = 2.8o,

= 3.2o (3.7)

For the neutrino energy resolutions, we use the estimated value E = 0.1E . A

LArTPC has a very good angular resolution since ionization tracks can be transported undistorted over distances of several metres in highly puried LAr, allowing for excellent direction reconstruction by recording several projective views of the same event using wire planes with di erent orientations [28].

3.3 Octant sensitivity using atmospheric muon events in a magnetized iron detector

The ~2 is dened as,

(~2tot)prior = min(~2Atm + ~2prior) , (3.8)

where,

where ~2Atm = ~2 + ~2

For the atmospheric analysis, the ux and detector systematic uncertainties are included using the method of ~2 pulls as outlined in [52, 7072].

It is well known that the possibility of magnetization gives the iron detectors an excellent sensitivity to hierarchy [52, 68, 7376]. Therefore it is plausible to assume that

17

JHEP06(2013)010

Magnetized iron detector (500 kT yr)

octant sensitivity with priors

(sin2 2q13)tr = 0.10, (dCP)tr = 0, NH

3s sensitivity

2s sensitivity

Magnetized iron detector (500 kT yr)

octant sensitivity with priors

(sin2 2q13)tr = 0.10, (dCP)tr = 0, IH

3s sensitivity

2s sensitivity

15

15

10

10

prior

prior

c2 tot

c2 tot

5

5

JHEP06(2013)010

0 37 39 41 43 45 47 49 51 53

0 37 39 41 43 45 47 49 51 53

true q23

true q23

Figure 8. Marginalized octant sensitivity from muon events with a magnetized iron detector (500 kT yr exposure), for the case of normal and inverted mass hierarchy. In this gure priors have been added.

hierarchy would be determined before octant in these detectors. Thus in our analysis of atmospheric neutrinos, we assume the neutrino mass hierarchy xed to be either normal or inverted, and do not marginalize over the hierarchy. This is tantamount to the assumption that the wrong-octant-wrong hierarchy solutions are excluded. In gure 8, we present the octant sensitivity of a magnetized iron calorimeter detector with an exposure of 500 kT yr. The second column of table 4 displays the ~2 values for di erent values of 23 in the LO. The ~2 in this case is symmetric about /4, and therefore the values in the higher octant are similar. Assuming an inverted hierarchy gives worse results because in this case, matter resonance and hence octant sensitivity occurs in the antineutrino component of the event spectrum, for which the ux and detection cross-sections are lower. A 2 sensitivity is obtained at 23 = 39o if NH is the true hierarchy.

3.4 Octant sensitivity using atmospheric events in a LArTPC

A LArTPC is sensitive to both muon and electron type events and one can study the interplay of both type of events in octant sensitivity using atmospheric neutrinos. We give the results separately for the atmospheric muon and electron signals as well as for the combined analysis.

In the following analysis we assume that the hierarchy will be determined by the combination of reactor, long-baseline and INO experiments [68] before a LArTPC can give an octant measurement. Therefore we do not marginalize over hierarchy in the wrong octant.

The muon and electron event spectra are related to the oscillation probabilities as follows:

N (P + ePe) (CC cross section, exposure, e ciency)

Ne (Pe + ePee) (CC cross section, exposure, e ciency) (3.9)

18

tr23 ~2 ~2e ~2+e

NH(IH) NH(IH) NH(IH) 36 8.5 (1.5) 3.5 (1.4) 15.4 (5.8) 37 6.7 (1.3) 2.8 (1.1) 11.5 (4.8) 38 4.6 (1.0) 2.5 (0.8) 9.0 (3.7) 39 3.0 (0.7) 1.7 (0.6) 7.1 (2.8) 40 1.9 (0.6) 1.4 (0.5) 4.8 (1.7) 41 1.0 (0.3) 1.0 (0.3) 3.0 (0.9) 42 0.6 (0.2) 0.6 (0.2) 1.9 (0.5) 43 0.3 (0.1) 0.4 (0.1) 1.0 (0.3) 44 0.1 (0.1) 0.2 (0.1) 0.4 (0.2)

Table 3. Marginalized octant sensitivity from atmospheric muon, electron and muon + electron events with a LArTPC (500 kT yr exposure), for the case of normal (inverted) mass hierarchy, with sin2 2 tr13 = 0.1 and CPtr = 0. Priors have not been included here.

The antineutrino event rates are given by the same expressions with the ux and probabilities replaced by their antineutrino counterparts.

The ~2 in this case is given by

(~2tot)prior = min(~2Atm + ~2prior) , (3.10)

where,

where ~2Atm = ~2+ + ~2e+

The atmospheric muon ux is approximately twice that of the electron ux. Hence the behaviour of the muon events is dictated by the muon survival probability and to a lesser extent by the Pe oscillation probability. The sensitivity derivable from muon events is somewhat compromised by the fact that Pe and P shift in opposite directions for a transition from one octant to another, as observed in gure 3. On the other hand, for electron events the only source of the octant sensitivity is from Pe, since the electron survival probability is independent of 23. Therefore both muon and electron events individually give comparable values of octant sensitivity. The sensitivity from muon events is more strongly dependent on the value of tr23, and is therefore higher than the sensitivity from electron events for values further away from maximal, getting closer to the latter as tr23 approaches 45o. This can be seen from table 3 where we list the values of octant sensitivity from atmospheric muon and electron events in a LArTPC with an exposure of 500 kT yr, marginalized over the allowed ranges of the oscillation parameters. The neutrino mass hierarchy is xed to be either normal or inverted. The results presented are for true values of 23 lying in the lower octant. The behaviour for tr23 in the upper octant is similar and symmetrical about tr23 = 45o.

Figure 9 shows the behaviour of the octant sensitivity with the atmospheric neutrino signal in a LArTPC for a specic true value ( 23)tr = 39o, as a function of the test values of 23, for both muon (left panel) and electron (right panel) events. For the latter the only

19

JHEP06(2013)010

12

0 35 40 45 50

20

0 35 40 45 50

LArTPC (500 kT yr) muon events

fixed-parameter octant sensitivity

(dCP)tr = 0, NH

3s sensitivity

2s sensitivity

(sin2 2q13)tr = 0.0

(sin2 2q13)tr = 0.1

LArTPC (500 kT yr) electron events

fixed-parameter octant sensitivity

(dCP)tr = 0, NH

(sin2 2q13)tr = 0.1

3s sensitivity

2s sensitivity

10

15

8

c2

6

c2 e

10

4

5

2

JHEP06(2013)010

test q23

test q23

Figure 9. Fixed-parameter octant sensitivity from atmospheric neutrinos with a LArTPC (500 kT yr exposure) as a function of test 23 for (sin2 2 13)tr = 0.1 and ( 23)tr = 39o. The left panel is for muon events and the right panel is for electron events.

octant-sensitive contribution is from Pe, which does not su er from the intrinsic octant degeneracy at the leading order and the octant sensitivity is due to the sin2 23 sin2 2 m13

term. Since sin2 2 m13 becomes close to 1 near matter resonance, the octant sensitivity increases proportionally with the test value of sin2 23. Hence the minimum sensitivity is seen in the region near test23 45o in the wrong octant. The solid red curve in the left panel is for sin2 2 13 = 0 for which the contribution comes from P only. The curve exhibits no octant sensitivity due to the intrinsic degeneracy coming from the sin2 2 23 term in P. This degeneracy is broken for higher values of sin2 2 13 where both P and Pe can contribute. As a combined e ect of all these factors the octant sensitivity does not have a clean proportionality with test23, but can have a minimum anywhere within the range 45o < test23 < (90o tr23) depending on the relative weightage of the two terms for specic

energies, baselines and values of the neutrino parameters. This is reected by the blue dot-dashed curve in the left panel.

We now study whether combining muon and electron events will give an enhanced octant sensitivity compared to that from the muon and electron event spectra individually. The last column of table 3 lists the ~2+e values for NH (and IH). These values are obtained by marginalizing over all test parameters, but without adding priors. In gure 10 the sensitivity is presented with the inclusion of priors. The following points may be noted from the listed results:

1. The values of the octant sensitivity that can be derived from the atmospheric muon and electron events separately are relatively low. A combined analysis of muon and electron events gives improved sensitivities which are better than the sum of the marginalized ~2 sensitivities from the two kinds of signals. This is because the muon and electron event spectra behave di erently as functions of 23 and hence their ~2 minima occur at di erent parameter values. Utilizing this fact, a marginalization

20

25

25

LArTPC (500 kT yr)

octant sensitivity with priors

(sin2 2q13)tr = 0.10, (dCP)tr = 0, NH

3s sensitivity

2s sensitivity

with charge-id

without charge-id

LArTPC (500 kT yr)

octant sensitivity with priors

(sin2 2q13)tr = 0.10, (dCP)tr = 0, IH

3s sensitivity

2s sensitivity

with charge-id

without charge-id

20

20

15

15

prior

prior

c2 tot

c2 tot

10

10

5

5

JHEP06(2013)010

0 37 39 41 43 45 47 49 51 53

0 37 39 41 43 45 47 49 51 53

true q23

true q23

Figure 10. Marginalized octant sensitivity from both muon and electron events with a LArTPC (500 kT yr exposure), for the case of normal and inverted mass hierarchy. In this gure priors have been added.

over the sum of ~2 values gives an improved result compared to the individual contributions. The enhancement in the sensitivity due to this synergy can be anywhere between 20% and 50%, depending on the true value of 23, as can be seen in table 3.

2. The addition of prior information further improves the sensitivity by about 20 -40%. The most signicant contribution comes from the reduced error range of the parameter 13 from recent reactor results. For an assumed normal hierarchy, a 3 signal of the octant may be achieved for tr23 = 39o(51o) for a true lower octant (higher octant) with this exposure, as seen in gure 10.

3. Assuming an inverted hierarchy gives worse results because in this case, matter resonance and hence octant sensitivity occurs in the antineutrino component of the event spectrum, for which the detection cross-sections are lower.

In gure 11, the marginalized octant sensitivity from a LArTPC is plotted as a function of detector exposure for two true values of 23. The gure shows that it is possible to achieve a 2 sensitivity for tr23 = 39o and a 3 sensitivity for tr23 = 36o from a LArTPC alone for an exposure as low as 120 kT yr, in the case of a normal hierarchy.

3.5 E ect of magnetization

Figure 10 shows the values of octant sensitivity derivable from a LArTPC with and without magnetization. The magnetization o ers the possibility of charge identication. In the case of a LArTPC with magnetization, charge identication details are incorporated as given in refs. [29, 30, 43], assuming a 100% charge identication capability for muon events and a 20% charge identication capability in the energy range 1-5 GeV (none for higher energies) for electron events.

21

40

LArTPC (no charge-id)

octant sensitivity with priors

(sin2 2q13)tr = 0.10, (dCP)tr = 0, NH

(q23)tr = 39o

(q23)tr = 36o

5s sensitivity

3s sensitivity

2s sensitivity

30

prior

20

c2 tot

10

JHEP06(2013)010

0

200 400 600 800 1000

Detector exposure (kT yr)

Figure 11. Octant sensitivity for a non-magnetized LArTPC as a function of exposure. ~2 has been plotted for normal hierarchy for two values of 23 (true) 36 and 39.

The octant sensitivity without charge identication is seen to be about 80% (60%) of that with charge identication capability with a similar exposure, in the case of a normal (inverted) mass hierarchy. This di erence in behaviour is explained as follows.

If the true hierarchy is normal, neutrino events have octant sensitivity due to resonant matter e ects, while antineutrino events do not. Therefore the antineutrino events for both octants are almost the same, say k. In the absence of charge-identication, we add these events, and

~2 = ([NHO + k] [NLO + k])2

NHO + k .

On the other hand, if we do have charge-identication, then the chisq is simply

~2 = ([NHO] [NLO])2

NHO +

([k] [k])2

k .

In both cases, the numerator is same, but the denominator is more in the former case. Therefore charge-identication gives us higher sensitivity.

Note that when the hierarchy is normal, k comes from the antineutrino events. Because of the ux and cross-section being small, k is a relatively small number. But if the hierarchy is inverted, then k will be because of neutrino events, whose higher ux and cross-section will make the denominator quite large. Therefore, the reduction in sensitivity due to loss of charge-identication will be more apparent for the inverted hierarchy. Charge identication capability has been shown to play a very crucial role in determination of mass hierarchy in such detectors [43]. However this does not seem to play such an important role for octant determination if we already assume a prior knowledge of the hierarchy. For a LArTPC without charge indentication, if we assume that the hierarchy is not known then the octant sensitivity is una ected for | tr23 45o| < 7o, i.e. for 39o tr23 51o, but for smaller

22

(larger) values of tr23 in the lower (higher) octant, there is a drop of 20-30% in the sensitivity. For a magnetized iron detector, we have checked that the e ect of marginalizing over the hierarchy is negligible since the wrong hierarchy is excluded with a reliable condence level for the exposure considered (500 kT yr). The same is true for a LArTPC with charge identication capability.

When we compare the octant sensitivity from a magnetized iron detector with the LArTPC results without charge identication, the iron detector sensitivities are about 40% of those with a LArTPC if the hierarchy is normal and about 50% of the LArTPC sensitivities if the hierarchy is inverted. The sensitivities from a LArTPC are higher than those from a magnetized iron detector . This is because of the possibility of realizing very high angular resolutions in the former type of detector and the signicant contributions from muon as well as electron events.

3.6 E ect of CP

The dependence of the octant sensitivity on the CP phase CP is di erent for atmospheric neutrino experiments and the long-baseline experiments considered. Because of the strong earth matter e ects over a large range of atmospheric neutrino baselines, the behaviour of the corresponding oscillation probabilities is governed by the enhanced resonant features and their dependence on CP is suppressed. On the other hand, for NO A/T2K baselines, since the matter e ects are smaller, CP plays a greater role in the probability behaviour and hence in the octant sensitivity, because of the degeneracy of the octant with 13 and

CP as explained previously.

These features are reected in gure 12, in which the marginalized octant sensitivity for a LArTPC with atmospheric neutrinos, NO A, T2K and their combinations are plotted as a function of the true CP for tr23 = 39o (LO) and 51o (HO) for both normal and inverted mass hierarchies. The CP behaviour of the NO A and T2K sensitivities are seen to be similar, and they follow an opposite behaviour with respect to CP for tr23 lying in the lower and higher octants, i.e. for tr23 = 39o they are higher in the range 0o < CPtr < 180o and for tr23 = 51o they are higher in the range 180o < CPtr < 0o [40].

For tr23 = 39o (LO) and NH (the top left panel) the contribution from a LArTPC is higher than that from combined NO A+T2K excepting for a narrow range CPtr = 90o

to 135o. For tr23 = 51o (HO) and NH (bottom left panel) the same trend is observed, except that in this case the combined NO A+T2K has a higher sensitivity for the range CPtr = 15o to 90o.

For the top (bottom) right panels which are for tr23 = 39o (51o) and IH, the NO A + T2K as well as the standalone NO A contribution to the sensitivity are higher than the atmospheric contribution over almost all values of true CP. This is because the sensitivity from atmospheric neutrinos is less than half for an inverted hierarchy compared to normal hierarchy, while for NO A and T2K the values are similar.

The T2K sensitivity is lower than NO A in all cases, and lower than the atmospheric contribution for most values of true CP, besides certain small ranges in the inverted hierarchy case where it is higher. The combined sensitivity from atmospheric neutrinos and NO A + T2K follows the true CP dependence of the NO A + T2K sensitivity.

23

JHEP06(2013)010

LAr(no charge-id) NOvA+T2K

NOvA

T2K LAr+NOvA+T2K

35

0 -180 -135 -90 -45 0 45 90 135 180

(q23)tr = 39o

NH

LAr(no charge-id) NOvA+T2K

NOvA

T2K LAr+NOvA+T2K

(q23)tr = 39o

IH

35

0 -180 -135 -90 -45 0 45 90 135 180

30

30

25

25

prior

20

prior

20

c2 tot

c2 tot

15

15

10

10

5

5

JHEP06(2013)010

true dCP

true dCP

LAr(no charge-id) NOvA+T2K

NOvA

T2K LAr+NOvA+T2K

35

0 -180 -135 -90 -45 0 45 90 135 180

(q23)tr = 51o

NH

LAr(no charge-id)

NOvA+T2K

NOvA

T2K LAr+NOvA+T2K

(q23)tr = 51o

IH

35

0 -180 -135 -90 -45 0 45 90 135 180

30

30

25

25

prior

20

prior

20

c2 tot

c2 tot

15

15

10

10

5

5

true dCP

true dCP

Figure 12. Marginalized octant sensitivity with priors as a function of true CP from NO A, T2K, NO A + T2K and for an atmospheric neutrino experiment with a LArTPC for the case of normal and inverted mass hierarchy, for 2 values of tr23 in the lower and higher octants.

Finally, in gure 13, we show the wrong octant exclusion sensitivity for NO A+T2K in the true 23 - true CP plane. Contours are shown in this plane for 1, 2, 3 and 4 octant exclusion. In the part of the parameter space that is enclosed within a certain contour, it is possible to exclude the wrong octant with the corresponding condence level. As expected, the ability of the experiments to exclude the wrong octant is small around true 23 45.

As 23 becomes more non-maximal, the exclusion ability becomes better. The e ect of CP on octant sensitivity for any given true value of 23 can also be read from these plots. Since the results using atmospheric neutrinos are almost independent of CP, the behaviour of the ~2 is similar to the plots in gures 8 and 10 drawn for CP = 0.

3.7 Octant sensitivity from combined analysis of atmospheric electron and muon events with NO A and T2K

In this section we present the octant sensitivity from a combined analysis of simulated long-baseline and atmospheric data. We add ~2prior to the combination to take into account the

24

180

180

150

150

120

120

90

90

60

60

30

30

d CP(true)

0

d CP(true)

0

-30

-30

-60

-60

-90

-90

-120

-120

JHEP06(2013)010

-150

-150

-180

-180

37 39 41 43 45 47 49 51 53

37 39 41 43 45 47 49 51 53

q23 (true)

Figure 13. Wrong octant exclusion for NO A+T2K in the true 23 true CP plane. The left(right) panel is for NH(IH) as the true hierarchy. The brown(dense-dotted)/red(sparse-dotted)/gold(dashed)/green(solid) contours denote 1/2/3/4 exclusion, respectively.

q23 (true)

30

30

25

Magnetized iron detector (500 kT yr)

+ NOvA + T2K,

octant sensitivity with priors

(sin2 2q13)tr = 0.10, (dCP)tr = 0, NH

3s sensitivity

2s sensitivity

25

Magnetized iron detector (500 kT yr)

+ NOvA + T2K,

octant sensitivity with priors

(sin2 2q13)tr = 0.10, (dCP)tr = 0, IH

3s sensitivity

2s sensitivity

20

20

prior

prior

15

15

c2 tot

c2 tot

10

10

5

5

0 37 39 41 43 45 47 49 51 53

0 37 39 41 43 45 47 49 51 53

true q23

true q23

Figure 14. Marginalized octant sensitivity from a combination of the atmospheric muon neutrino signal in a magnetized iron calorimeter detector (500 kT yr) + NO A + T2K, for the case of normal and inverted mass hierarchy. In this gure priors have been added.

future precision measurements on 13 and and minimize the (~2tot)prior given as,

(~2tot)prior = min(~2NOvA + ~2T2K + ~2Atm + ~2prior) (3.11)

gure 14 shows the combined octant sensitivity using the atmospheric muon neutrino signal in a magnetized iron detector with NO A and T2K. In gure 15 the octant sensitivity computed from a combination of the atmospheric electron and muon neutrino signal in a LArTPC without charge identication capability with NO A and T2K is plotted. In in table 4 we list the marginalized octant sensitivity with priors for a LArTPC (500 kT yr exposure), a magnetized iron detector (500 kT yr exposure), and a combination of each of

25

30

30

25

LArTPC (500 kT yr, no charge ID)

+ NOvA + T2K,

octant sensitivity with priors

(sin2 2q13)tr = 0.10, (dCP)tr = 0, NH

3s sensitivity

2s sensitivity

25

LArTPC (500 kT yr, no charge ID)

+ NOvA + T2K,

octant sensitivity with priors

(sin2 2q13)tr = 0.10, (dCP)tr = 0, IH

3s sensitivity

2s sensitivity

20

20

prior

prior

15

15

c2 tot

c2 tot

10

10

5

JHEP06(2013)010

5

0 37 39 41 43 45 47 49 51 53

0 37 39 41 43 45 47 49 51 53

true q23

true q23

Figure 15. Marginalized octant sensitivity from a combination of the atmospheric muon + electron neutrino signal in a LArTPC (500 kT yr, without charge ID) + NO A + T2K, for the case of normal and inverted mass hierarchy. In this gure priors have been added.

tr23 LArTPC Mag.Iron LArTPC+NO A+T2K Mag.Iron+NO A+T2K 36 19.8 (11.5) 8.5 (3.9) 29.9 (21.9) 21.1 (19.9)

37 15.6 (9.5) 6.8 (3.2) 24.6 (18.0) 17.0 (16.3) 38 12.4 (7.0) 5.3 (2.5) 19.7 (14.3) 13.2 (12.9) 39 8.9 (5.5) 3.9 (1.9) 15.5 (10.9) 9.1 (9.8) 40 5.9 (3.5) 2.7 (1.3) 11.6 (8.0) 7.1 (7.1) 41 4.0 (2.5) 1.5 (0.9) 7.7 (5.3) 4.9 (4.8) 42 2.5 (1.6) 0.6 (0.5) 4.6 (3.0) 3.2 (2.6) 43 1.5 (0.8) 0.2 (0.2) 1.6 (1.1) 1.4 (1.0) 44 0.6 (0.6) 0.1 (0.1) 0.7 (0.5) 0.2 (0.2)

Table 4. Marginalized octant sensitivity with a LArTPC (500 kT yr exposure), a magnetized iron detector (500 kT yr exposure), and a combination of either of them with NO A + T2K, for the case of normal (inverted) mass hierarchy, with sin2 2 tr13 = 0.1 and CPtr = 0. Priors have been included in this table.

them with NO A + T2K, for the case of both NH and IH. All of the above results are for CPtr = 0. For a magnetized iron detector, the combination with NO A + T2K gives a 3

sensitivity at 23 = 39o for NH. A non-magnetized LArTPC + NO A + T2K gives a 4 sensitivity in the same case. There is a tension between the behaviour of the NO A/T2K octant sensitivity and the octant sensitivity from an atmospheric neutrino experiment as a function of test 23, which can be seen by comparing gures 7 and 9. For NO A/T2K, the ~2 minima occur at or close to test23 = /2 tr23, while for an atmospheric experiment

the muon events may have ~2 minima anywhere between test23 = 45o and /2 tr23 and the

electron events have minima close to test23 = 45o. This synergy leads to an enhancement of the octant sensitivity when the NO A + T2K and atmospheric neutrino experiments are combined.

26

tr23 Mag.Iron+ LArTPC Mag.Iron+LArTPC+NO A+T2K 36 29.1 (15.6) 41.2 (27.0)

37 22.8 (12.9) 33.9 (22.3) 38 18.5 (9.7) 27.1 (17.7) 39 13.8 (7.6) 21.0 (13.5) 40 9.1 (5.0) 15.4 (9.8) 41 6.4 (3.5) 10.1 (6.5) 42 3.1 (2.1) 5.9 (3.7) 43 1.7 (1.0) 1.9 (1.4) 44 0.7 (0.7) 0.9 (0.7)

Table 5. Marginalized octant sensitivity with a a combination of a LArTPC (500 kT yr exposure) and a magnetized iron detector (500 kT yr exposure), as well as a combination of both of them with NO A + T2K, for the case of normal (inverted) mass hierarchy, with sin2 2 tr13 = 0.1 and CPtr = 0.

Priors have been included in this table.

The combined ~2 values depend strongly on the true value of CP following the behaviour of the NO A/T2K ~2, as can be seen from the green (dot-dashed) curve in gure 12. The LArTPC+NO A+T2K combination is seen to reach a sensitivity of > 4 for all values of CP for NH for the sample values of 23 of 39o and 51o considered (the top and bottom left panels). For IH and 39o (51o) one achieves close to 3 (4) sensitivity. The combination of the magnetized iron detector with NO A+T2K is also expected to have a similar behaviour with CP albeit with a lower sensitivity. The NO A and T2K contribution play a greater role in this case than that for a LArTPC. The sensitivity for NO A+T2K is higher for IH than for NH for CPtr = 0 and tr23 lying in the LO (as seen in table 2). Therefore for these parameter values, the octant sensitivity for a magnetized iron detector+NO A+T2K combination has comparable values for NH and IH, even though the sensitivity from a magnetized iron detector alone is less for IH than for NH. In the case of a LArTPC+NO A+T2K combination, because of a greater contribution from LArTPC, the sensitivity is less for IH than for NH, reecting the behaviour of the sensitivity from LArTPC. This feature can be observed in table 4.

Finally, we present the results of a combined analysis of an unmagnetized LArTPC with a magnetized iron detector in table 5, which lists the octant sensitivities for a LArTPC+iron detector combination as well as a LArTPC+iron detector+NO A+T2K combination. The results are seen to improve further in this case. The synergy between these experiments helps in completely removing the e ect of marginalizing over the hierarchy, since a magnetized iron detector itself gives good hierarchy discrimination for the detector exposure considered, as discussed in section 3.5. A combination of a magnetized iron detector with a LArTPC (500 kT yr) and NO A+ T2K gives a sensitivity of 4.5 for 23 = 39o and nearly

6 for 23 = 37o for NH, and nearly 5 for 23 = 37o for IH. These results are una ected by a marginalization over the hierarchy.

27

JHEP06(2013)010

4 Summary and conclusion

In this paper we have studied the possibility of determining the octant of the atmospheric mixing angle 23 in the long-baseline experiments T2K and NO A as well as by atmospheric neutrino experiments. While the octant degeneracy conventionally refers to the indistinguishability between 23 and /2 23, this can be generalized to include the whole range

of allowed value of 23 in the wrong octant, and we consider this generalized denition in our analysis.

We present a probability level discussion on the e ect of uncertainty in 13, CP and

values of 23 in the wrong octant for baselines relevant to long-baseline and atmospheric experiments. Below we summarize the salient features that emerge from our study at the probability level:

For baselines where matter e ects are small, the appearance channel probability

Pe displays a degeneracy of the 23 octant with the values of 13 and CP due to its dependence on the combination sin2 23 sin2 2 13 at leading order as well as its subleading CP dependence. The disappearance channel probability P su ers from an intrinsic octant degeneracy between 23 and /2 23 due to being a function of

sin2 2 23 at leading order.

For NO A/T2K baselines, there is a strong e ect of the uncertainty in CP in the appearance channel, and of the 23 uncertainty in the disappearance channel. For instance, for the NO A baseline the degeneracy between 23 = 39o and 51o in Pe

is lifted only for sin2 2 13 > 0.12 if a variation over the entire range of CP is taken

into account.

We nd that after including the improved precision in 13 from the recent reactor

results, the octant degeneracy with respect to 13 is largely reduced. Some amount of degeneracy with respect to 13 still remains for higher (lower) values of 13 in the allowed range for a true lower (higher) octant. Also, in general, information from the energy spectrum helps in reducing the degeneracy since for two di erent energies the degeneracy exists for di erent sets of parameter values.

For a sample baseline of 5000 km traversed by the atmospheric neutrinos strong

resonant matter e ects help in lifting both the intrinsic octant degeneracy in P and

the octant degeneracy with 13 and CP in Pe. This is because the term sin2 2 m13 becomes close to 1 at or near matter resonance, and this makes the leading-order term proportional to sin2 23 (sin4 23) in Pe (P) predominate and give distinct values in the two octants irrespective of the vacuum value of 13.

We perform a ~2 analysis of the octant sensitivity for T2K/NO A and atmospheric neutrinos as well as a combined study. For atmospheric neutrinos we consider two types of detectors magnetized iron calorimeter detectors capable of detecting muons and identifying their charge and a LArTPC (non-magnetized) which can detect both muons and electrons with superior energy and angular resolutions. For NO A/T2K we present the

28

JHEP06(2013)010

results for both cases of known and unknown hierarchy while the atmospheric results are assuming hierarchy to be known. The main results are summarized below:

The ~2 minima for the NO A/T2K disappearance channel occur near test23 = /2

tr23, because of the predominant dependence on sin2 2 23, while for the appearance channel the minima occur near test23 = 45o, because of the sin2 23 dependence. This leads to a tension between the ~2 behaviour of the two spectra as a function of test23, so that the combination of appearance and disappearance channels enhances octant sensitivity, but even then the ~2 is not very high. Combining the NO A and T2K data leads to a higher octant sensitivity due to the addition of sensitivities from the two experiments. What plays a major role in enhancing the octant sensitivity in these experiments is the addition of priors, especially on 13, which helps in ruling out the degenerate solutions in the wrong octant. After adding priors one can achieve a 2 sensitivity at 23 = 39o for sin2 2 13 = 0.1 and CP = 0 for both normal and

inverted hierarchies.

A magnetized iron calorimeter gives a 2 sensitivity to the octant for 23 = 39o and sin2 2 13 = 0.1 for a true normal hierarchy. A non-magnetized LArTPC can give a 3

sensitivity for the same parameter values. The enhanced sensitivity of the LArTPC is due to the contribution of the electron events as well as superior energy and angular resolutions compared to an iron calorimeter detector. In a LArTPC, combining the muon and electron events gives improved sensitivities due to the di erent behaviour of the muon and electron event spectra with respect to 23. If a LArTPC can have charge identication capability there will be a 20-40% increase in sensitivity, the enhancement being more in the case of an inverted hierarchy than for a normal hierarchy. Since we assume hierarchy to be already known, the magnetization of LArTPC (which is technically challenging) does not play a signicant role. A marginalization over the hierarchy does not a ect the results for a magnetized iron detector, since it already excludes the wrong hierarchy with a good condence level for the same exposure. For a LArTPC, the results are unchanged by a hierarchy marginalization over the range 39o 23 51o, but su er a drop of 20-30% for values of 23 above

and below this.

Combining long-baseline and atmospheric results can give a signicant enhancement

in the octant sensitivity because of the tension in the behaviour of the NO A/T2K and atmospheric ~2 as functions of test 23, arising due to the di erent energy and baseline ranges involved and the fact that strong matter e ects dictate the probability behaviour for atmospheric baselines. Since the ~2 minima occur at di erent parameter values, there is a synergy between the experiments which gives an increased octant sensitivity. A combination of NO A, T2K and LArTPC (500 kT yr) can give a nearly 3 sensitivity for 23 = 41o, a 4 sensitivity for 23 = 39o and a 5 sensitivity for 23 = 37o for sin2 2 13 = 0.1 and CP = 0 in the case of a normal hierarchy. The corresponding sensitivities for inverted hierarchy are somewhat less. A magnetized iron calorimeter combined with NO A and T2K can give 3 sensi-

29

JHEP06(2013)010

tivity for 23 = 39o for both NH and IH. Finally, a combination of a magnetized iron detector with a LArTPC (500 kT yr) and NO A+ T2K gives a further improved sensitivity of 4.5 for 23 = 39o and nearly 6 for 23 = 37o for NH, and nearly 5 for 23 = 37o for IH. These results hold good with a marginalization over the hierarchy.

The octant sensitivity from an atmospheric neutrino experiment is nearly indepen

dent of the true value of CP, while the NO A and T2K sensitivities are seen to be strongly CP-dependent and follow a denite shape as a function of CP. The shape gets ipped for a true lower or higher octant. For a normal mass hierarchy, the contribution of NO A + T2K to the octant sensitivity is lower than that from a LArTPC measurement for almost all values of CP, while for an inverted hierarchy it is higher, due to the worse sensitivity from an atmospheric experiment in the inverted hierarchy case.

In conclusion, we nd that the improved precision of 13 and the di erent dependence on 23 in the disappearance and appearance channels and in vacuum and matter probabilities leads to an enhanced octant sensitivity when long-baseline and atmospheric neutrino experiments are combined.

References

[1] DOUBLE-CHOOZ collaboration, Y. Abe et al., Indication for the disappearance of reactor electron antineutrinos in the Double CHOOZ experiment,http://dx.doi.org/10.1103/PhysRevLett.108.131801

Web End =Phys. Rev. Lett. 108 (2012) 131801 [arXiv:1112.6353] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1112.6353

Web End =INSPIRE ].

[2] DAYA-BAY collaboration, F. An et al., Observation of electron-antineutrino disappearance at Daya Bay, http://dx.doi.org/10.1103/PhysRevLett.108.171803

Web End =Phys. Rev. Lett. 108 (2012) 171803 [arXiv:1203.1669] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1203.1669

Web End =INSPIRE ].

[3] RENO collaboration, J. Ahn et al., Observation of reactor electron antineutrino disappearance in the RENO experiment, http://dx.doi.org/10.1103/PhysRevLett.108.191802

Web End =Phys. Rev. Lett. 108 (2012) 191802 [arXiv:1204.0626] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1204.0626

Web End =INSPIRE ].

[4] M. Gonzalez-Garcia, M. Maltoni, J. Salvado and T. Schwetz, Global t to three neutrino mixing: critical look at present precision, http://dx.doi.org/10.1007/JHEP12(2012)123

Web End =JHEP 12 (2012) 123 [arXiv:1209.3023] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1209.3023

Web End =INSPIRE ].

[5] G. Fogli et al., Global analysis of neutrino masses, mixings and phases: entering the era of leptonic CP-violation searches, http://dx.doi.org/10.1103/PhysRevD.86.013012

Web End =Phys. Rev. D 86 (2012) 013012 [arXiv:1205.5254] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1205.5254

Web End =INSPIRE ].

[6] D. Forero, M. Tortola and J. Valle, Global status of neutrino oscillation parameters after Neutrino-2012, http://dx.doi.org/10.1103/PhysRevD.86.073012

Web End =Phys. Rev. D 86 (2012) 073012 [arXiv:1205.4018] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1205.4018

Web End =INSPIRE ].

[7] T2K collaboration, K. Abe et al., Indication of electron neutrino appearance from an accelerator-produced o -axis muon neutrino beam, http://dx.doi.org/10.1103/PhysRevLett.107.041801

Web End =Phys. Rev. Lett. 107 (2011) 041801 [arXiv:1106.2822] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1106.2822

Web End =INSPIRE ].

[8] MINOS collaboration, P. Adamson et al., Improved search for muon-neutrino to electron-neutrino oscillations in MINOS, http://dx.doi.org/10.1103/PhysRevLett.107.181802

Web End =Phys. Rev. Lett. 107 (2011) 181802 [arXiv:1108.0015] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1108.0015

Web End =INSPIRE ].

[9] G. Fogli, E. Lisi, A. Marrone, A. Palazzo and A. Rotunno, Hints of 13 > 0 from global

neutrino data analysis, http://dx.doi.org/10.1103/PhysRevLett.101.141801

Web End =Phys. Rev. Lett. 101 (2008) 141801 [arXiv:0806.2649] [http://inspirehep.net/search?p=find+EPRINT+arXiv:0806.2649

Web End =INSPIRE ].

30

JHEP06(2013)010

[10] S. Goswami and A.Y. Smirnov, Solar neutrinos and 1-3 leptonic mixing, http://dx.doi.org/10.1103/PhysRevD.72.053011

Web End =Phys. Rev. D 72 (2005) 053011 [http://arxiv.org/abs/hep-ph/0411359

Web End =hep-ph/0411359 ] [http://inspirehep.net/search?p=find+EPRINT+hep-ph/0411359

Web End =INSPIRE ].

[11] SNO collaboration, B. Aharmim et al., Combined analysis of all three phases of solar neutrino data from the Sudbury Neutrino Observatory, arXiv:1109.0763 [http://inspirehep.net/search?p=find+EPRINT+arXiv:1109.0763

Web End =INSPIRE ].

[12] KamLAND collaboration, S. Abe et al., Precision measurement of neutrino oscillation parameters with KamLAND, http://dx.doi.org/10.1103/PhysRevLett.100.221803

Web End =Phys. Rev. Lett. 100 (2008) 221803 [arXiv:0801.4589] [http://inspirehep.net/search?p=find+EPRINT+arXiv:0801.4589

Web End =INSPIRE ].

[13] MINOS collaboration, P. Adamson et al., Measurements of atmospheric neutrinos and antineutrinos in the MINOS far detector, http://dx.doi.org/10.1103/PhysRevD.86.052007

Web End =Phys. Rev. D 86 (2012) 052007 [arXiv:1208.2915] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1208.2915

Web End =INSPIRE ].

[14] Super-Kamiokande collaboration, R. Wendell et al., Atmospheric neutrino oscillation analysis with sub-leading e ects in Super-Kamiokande I, II and III,http://dx.doi.org/10.1103/PhysRevD.81.092004

Web End =Phys. Rev. D 81 (2010) 092004 [arXiv:1002.3471] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1002.3471

Web End =INSPIRE ].

[15] G.L. Fogli and E. Lisi, Tests of three avor mixing in long baseline neutrino oscillation experiments, http://dx.doi.org/10.1103/PhysRevD.54.3667

Web End =Phys. Rev. D 54 (1996) 3667 [http://arxiv.org/abs/hep-ph/9604415

Web End =hep-ph/9604415 ] [http://inspirehep.net/search?p=find+EPRINT+hep-ph/9604415

Web End =INSPIRE ].

[16] V. Barger, D. Marfatia and K. Whisnant, Breaking eight fold degeneracies in neutrino CP-violation, mixing and mass hierarchy, http://dx.doi.org/10.1103/PhysRevD.65.073023

Web End =Phys. Rev. D 65 (2002) 073023 [http://arxiv.org/abs/hep-ph/0112119

Web End =hep-ph/0112119 ] [http://inspirehep.net/search?p=find+EPRINT+hep-ph/0112119

Web End =INSPIRE ].

[17] R. Gandhi, P. Ghoshal, S. Goswami, P. Mehta and S.U. Sankar, Earth matter e ects at very long baselines and the neutrino mass hierarchy, http://dx.doi.org/10.1103/PhysRevD.73.053001

Web End =Phys. Rev. D 73 (2006) 053001 [http://arxiv.org/abs/hep-ph/0411252

Web End =hep-ph/0411252 ] [http://inspirehep.net/search?p=find+EPRINT+hep-ph/0411252

Web End =INSPIRE ].

[18] S. Choubey and P. Roy, Probing the deviation from maximal mixing of atmospheric neutrinos, http://dx.doi.org/10.1103/PhysRevD.73.013006

Web End =Phys. Rev. D 73 (2006) 013006 [http://arxiv.org/abs/hep-ph/0509197

Web End =hep-ph/0509197 ] [http://inspirehep.net/search?p=find+EPRINT+hep-ph/0509197

Web End =INSPIRE ].

[19] K. Abe et al., Letter of intent: the Hyper-Kamiokande experiment Detector design and physics potential, arXiv:1109.3262 [http://inspirehep.net/search?p=find+EPRINT+arXiv:1109.3262

Web End =INSPIRE ].

[20] A. de Bellefon et al., MEMPHYS: a large scale water Cerenkov detector at Frejus, http://arxiv.org/abs/hep-ex/0607026

Web End =hep-ex/0607026 [http://inspirehep.net/search?p=find+EPRINT+hep-ex/0607026

Web End =INSPIRE ].

[21] D.J. Koskinen, IceCube-DeepCore-PINGU: fundamental neutrino and dark matter physics at the South Pole, http://dx.doi.org/10.1142/S021773231103725X

Web End =Mod. Phys. Lett. A 26 (2011) 2899 [http://inspirehep.net/search?p=find+J+Mod.Phys.Lett.,A26,2899

Web End =INSPIRE ].

[22] E.K. Akhmedov, S. Razzaque and A.Y. Smirnov, Mass hierarchy, 2-3 mixing and CP-phase with huge atmospheric neutrino detectors, http://dx.doi.org/10.1007/JHEP02(2013)082

Web End =JHEP 02 (2013) 082 [arXiv:1205.7071] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1205.7071

Web End =INSPIRE ].

[23] IceCube collaboration, R. Abbasi et al., The design and performance of IceCube DeepCore, http://dx.doi.org/10.1016/j.astropartphys.2012.01.004

Web End =Astropart. Phys. 35 (2012) 615 [arXiv:1109.6096] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1109.6096

Web End =INSPIRE ].

[24] MONOLITH collaboration, N. Agafonova et al., MONOLITH: a massive magnetized iron detector for neutrino oscillation studies, http://cds.cern.ch/record/494266

Web End =CERN-SPSC-2000-031 (2000) [http://inspirehep.net/search?p=find+R+CERN-SPSC-2000-031

Web End =INSPIRE ].

[25] INO collaboration, M.S. Athar et al., India-based Neutrino Observatory: project report. Volume I, INO-2006-01 (2006) [http://inspirehep.net/search?p=find+R+INO-2006-01

Web End =INSPIRE ].

[26] C. Rubbia et al., Underground operation of the ICARUS T600 LAr-TPC: rst results, http://dx.doi.org/10.1088/1748-0221/6/07/P07011

Web End =2011 JINST 6 P07011 [arXiv:1106.0975] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1106.0975

Web End =INSPIRE ].

[27] ArgoNeuT collaboration, O. Palamara, Neutrino detection in the ArgoNeuT LAr TPC,http://dx.doi.org/10.1088/1742-6596/408/1/012039

Web End =J. Phys. Conf. Ser. 408 (2013) 012039 [arXiv:1110.3070] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1110.3070

Web End =INSPIRE ].

31

JHEP06(2013)010

[28] A. Ereditato and A. Rubbia, Ideas for future liquid Argon detectors,

http://dx.doi.org/10.1016/j.nuclphysBPS.2004.11.236

Web End =Nucl. Phys. Proc. Suppl. 139 (2005) 301 [http://arxiv.org/abs/hep-ph/0409143

Web End =hep-ph/0409143 ] [http://inspirehep.net/search?p=find+EPRINT+hep-ph/0409143

Web End =INSPIRE ].

[29] A. Ereditato and A. Rubbia, Conceptual design of a scalable multi-kton superconducting magnetized liquid Argon TPC, http://dx.doi.org/10.1016/j.nuclphysBPS.2006.02.059

Web End =Nucl. Phys. Proc. Suppl. 155 (2006) 233 [http://arxiv.org/abs/hep-ph/0510131

Web End =hep-ph/0510131 ] [http://inspirehep.net/search?p=find+EPRINT+hep-ph/0510131

Web End =INSPIRE ].

[30] R. Gandhi, P. Ghoshal, S. Goswami and S.U. Sankar, Resolving the mass hierarchy with atmospheric neutrinos using a liquid argon detector, http://dx.doi.org/10.1103/PhysRevD.78.073001

Web End =Phys. Rev. D 78 (2008) 073001 [arXiv:0807.2759] [http://inspirehep.net/search?p=find+EPRINT+arXiv:0807.2759

Web End =INSPIRE ].

[31] P. Huber, M. Lindner, T. Schwetz and W. Winter, Reactor neutrino experiments compared to superbeams, http://dx.doi.org/10.1016/S0550-3213(03)00493-0

Web End =Nucl. Phys. B 665 (2003) 487 [http://arxiv.org/abs/hep-ph/0303232

Web End =hep-ph/0303232 ] [http://inspirehep.net/search?p=find+EPRINT+hep-ph/0303232

Web End =INSPIRE ].

[32] K. Hiraide et al., Resolving 23 degeneracy by accelerator and reactor neutrino oscillation experiments, http://dx.doi.org/10.1103/PhysRevD.73.093008

Web End =Phys. Rev. D 73 (2006) 093008 [http://arxiv.org/abs/hep-ph/0601258

Web End =hep-ph/0601258 ] [http://inspirehep.net/search?p=find+EPRINT+hep-ph/0601258

Web End =INSPIRE ].

[33] H. Minakata, H. Sugiyama, O. Yasuda, K. Inoue and F. Suekane, Reactor measurement of 13 and its complementarity to long baseline experiments, http://dx.doi.org/10.1103/PhysRevD.70.059901

Web End =Phys. Rev. D 68 (2003) 033017 [Erratum ibid. D 70 (2004) 059901] [http://arxiv.org/abs/hep-ph/0211111

Web End =hep-ph/0211111 ] [http://inspirehep.net/search?p=find+EPRINT+hep-ph/0211111

Web End =INSPIRE ].

[34] S. Antusch, P. Huber, J. Kersten, T. Schwetz and W. Winter, Is there maximal mixing in the lepton sector?, http://dx.doi.org/10.1103/PhysRevD.70.097302

Web End =Phys. Rev. D 70 (2004) 097302 [http://arxiv.org/abs/hep-ph/0404268

Web End =hep-ph/0404268 ] [http://inspirehep.net/search?p=find+EPRINT+hep-ph/0404268

Web End =INSPIRE ].

[35] D. Choudhury and A. Datta, Detecting matter e ects in long baseline experiments, http://dx.doi.org/10.1088/1126-6708/2005/07/058

Web End =JHEP 07 (2005) 058 [http://arxiv.org/abs/hep-ph/0410266

Web End =hep-ph/0410266 ] [http://inspirehep.net/search?p=find+EPRINT+hep-ph/0410266

Web End =INSPIRE ].

[36] M. Gonzalez-Garcia, M. Maltoni and A.Y. Smirnov, Measuring the deviation of the 2-3 lepton mixing from maximal with atmospheric neutrinos, http://dx.doi.org/10.1103/PhysRevD.70.093005

Web End =Phys. Rev. D 70 (2004) 093005 [http://arxiv.org/abs/hep-ph/0408170

Web End =hep-ph/0408170 ] [http://inspirehep.net/search?p=find+EPRINT+hep-ph/0408170

Web End =INSPIRE ].

[37] H. Minakata, M. Sonoyama and H. Sugiyama, Determination of 23 in long-baseline neutrino oscillation experiments with three-avor mixing e ects, http://dx.doi.org/10.1103/PhysRevD.70.113012

Web End =Phys. Rev. D 70 (2004) 113012 [http://arxiv.org/abs/hep-ph/0406073

Web End =hep-ph/0406073 ] [http://inspirehep.net/search?p=find+EPRINT+hep-ph/0406073

Web End =INSPIRE ].

[38] K. Hagiwara and N. Okamura, Solving the degeneracy of the lepton-avor mixing angle ATM

by the T2KK two detector neutrino oscillation experiment, http://dx.doi.org/10.1088/1126-6708/2008/01/022

Web End =JHEP 01 (2008) 022 [http://arxiv.org/abs/hep-ph/0611058

Web End =hep-ph/0611058 ] [http://inspirehep.net/search?p=find+EPRINT+hep-ph/0611058

Web End =INSPIRE ].

[39] D. Meloni, Solving the octant degeneracy with the Silver channel,

http://dx.doi.org/10.1016/j.physletb.2008.05.031

Web End =Phys. Lett. B 664 (2008) 279 [arXiv:0802.0086] [http://inspirehep.net/search?p=find+EPRINT+arXiv:0802.0086

Web End =INSPIRE ].

[40] S.K. Agarwalla, S. Prakash and S.U. Sankar, Resolving the octant of 23 with T2K and NOvA, arXiv:1301.2574 [http://inspirehep.net/search?p=find+EPRINT+arXiv:1301.2574

Web End =INSPIRE ].

[41] D. Indumathi, M. Murthy, G. Rajasekaran and N. Sinha, Neutrino oscillation probabilities: Sensitivity to parameters, http://dx.doi.org/10.1103/PhysRevD.74.053004

Web End =Phys. Rev. D 74 (2006) 053004 [http://arxiv.org/abs/hep-ph/0603264

Web End =hep-ph/0603264 ] [http://inspirehep.net/search?p=find+EPRINT+hep-ph/0603264

Web End =INSPIRE ].

[42] A. Samanta and A.Y. Smirnov, The 2-3 mixing and mass split: atmospheric neutrinos and magnetized spectrometers, http://dx.doi.org/10.1007/JHEP07(2011)048

Web End =JHEP 07 (2011) 048 [arXiv:1012.0360] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1012.0360

Web End =INSPIRE ].

[43] V. Barger et al., Neutrino mass hierarchy and octant determination with atmospheric neutrinos, http://dx.doi.org/10.1103/PhysRevLett.109.091801

Web End =Phys. Rev. Lett. 109 (2012) 091801 [arXiv:1203.6012] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1203.6012

Web End =INSPIRE ].

[44] L. Wolfenstein, Neutrino oscillations in matter, http://dx.doi.org/10.1103/PhysRevD.17.2369

Web End =Phys. Rev. D 17 (1978) 2369 [http://inspirehep.net/search?p=find+J+Phys.Rev.,D17,2369

Web End =INSPIRE ].

[45] S.P. Mikheev and A.Y. Smirnov, Resonance amplication of oscillations in matter and spectroscopy of solar neutrinos, Sov. J. Nucl. Phys. 42 (1985) 913 [http://inspirehep.net/search?p=find+J+Sov.J.Nucl.Phys.,42,913

Web End =INSPIRE ].

32

JHEP06(2013)010

[46] S.P. Mikheev and A.Y. Smirnov, Resonant amplication of neutrino oscillations in matter and solar neutrino spectroscopy, http://dx.doi.org/10.1007/BF02508049

Web End =Nuovo Cim. C 9 (1986) 17 [http://inspirehep.net/search?p=find+J+NuovoCim.,C9,17

Web End =INSPIRE ].

[47] J. Burguet-Castell, M. Gavela, J. Gomez-Cadenas, P. Hernndez and O. Mena, On the measurement of leptonic CP-violation, http://dx.doi.org/10.1016/S0550-3213(01)00248-6

Web End =Nucl. Phys. B 608 (2001) 301 [http://arxiv.org/abs/hep-ph/0103258

Web End =hep-ph/0103258 ] [http://inspirehep.net/search?p=find+EPRINT+hep-ph/0103258

Web End =INSPIRE ].

[48] E.K. Akhmedov, R. Johansson, M. Lindner, T. Ohlsson and T. Schwetz, Series expansions for three avor neutrino oscillation probabilities in matter, http://dx.doi.org/10.1088/1126-6708/2004/04/078

Web End =JHEP 04 (2004) 078 [http://arxiv.org/abs/hep-ph/0402175

Web End =hep-ph/0402175 ] [http://inspirehep.net/search?p=find+EPRINT+hep-ph/0402175

Web End =INSPIRE ].

[49] A. Cervera et al., Golden measurements at a neutrino factory, http://dx.doi.org/10.1016/S0550-3213(00)00221-2

Web End =Nucl. Phys. B 579 (2000) 17 [Erratum ibid. B 593 (2001) 731-732] [http://arxiv.org/abs/hep-ph/0002108

Web End =hep-ph/0002108 ] [http://inspirehep.net/search?p=find+EPRINT+hep-ph/0002108

Web End =INSPIRE ].

[50] M. Freund, Analytic approximations for three neutrino oscillation parameters and probabilities in matter, http://dx.doi.org/10.1103/PhysRevD.64.053003

Web End =Phys. Rev. D 64 (2001) 053003 [http://arxiv.org/abs/hep-ph/0103300

Web End =hep-ph/0103300 ] [http://inspirehep.net/search?p=find+EPRINT+hep-ph/0103300

Web End =INSPIRE ].

[51] K. Kimura, A. Takamura and H. Yokomakura, Exact formula of probability and CP-violation for neutrino oscillations in matter, http://dx.doi.org/10.1016/S0370-2693(02)01907-X

Web End =Phys. Lett. B 537 (2002) 86 [http://arxiv.org/abs/hep-ph/0203099

Web End =hep-ph/0203099 ] [http://inspirehep.net/search?p=find+EPRINT+hep-ph/0203099

Web End =INSPIRE ].

[52] R. Gandhi et al., Mass hierarchy determination via future atmospheric neutrino detectors, http://dx.doi.org/10.1103/PhysRevD.76.073012

Web End =Phys. Rev. D 76 (2007) 073012 [arXiv:0707.1723] [http://inspirehep.net/search?p=find+EPRINT+arXiv:0707.1723

Web End =INSPIRE ].

[53] A. Dziewonski and D. Anderson, Preliminary reference Earth model, Phys. Earth Planet. Interiors 25 (1981) 297.

[54] A. de Gouva, J. Jenkins and B. Kayser, Neutrino mass hierarchy, vacuum oscillations and vanishing |U(e3), http://dx.doi.org/10.1103/PhysRevD.71.113009

Web End =Phys. Rev. D 71 (2005) 113009 [http://arxiv.org/abs/hep-ph/0503079

Web End =hep-ph/0503079 ] [

http://inspirehep.net/search?p=find+EPRINT+hep-ph/0503079

Web End =INSPIRE ].

[55] S.K. Raut, E ect of non-zero 13 on the measurement of 23, arXiv:1209.5658 [http://inspirehep.net/search?p=find+EPRINT+arXiv:1209.5658

Web End =INSPIRE ].

[56] P. Huber, M. Lindner and W. Winter, Simulation of long-baseline neutrino oscillation experiments with GLoBES (General Long Baseline Experiment Simulator),http://dx.doi.org/10.1016/j.cpc.2005.01.003

Web End =Comput. Phys. Commun. 167 (2005) 195 [http://arxiv.org/abs/hep-ph/0407333

Web End =hep-ph/0407333 ] [http://inspirehep.net/search?p=find+EPRINT+hep-ph/0407333

Web End =INSPIRE ].

[57] P. Huber, J. Kopp, M. Lindner, M. Rolinec and W. Winter, New features in the simulation of neutrino oscillation experiments with GLoBES 3.0: General Long Baseline Experiment Simulator, http://dx.doi.org/10.1016/j.cpc.2007.05.004

Web End =Comput. Phys. Commun. 177 (2007) 432 [http://arxiv.org/abs/hep-ph/0701187

Web End =hep-ph/0701187 ] [http://inspirehep.net/search?p=find+EPRINT+hep-ph/0701187

Web End =INSPIRE ].

[58] M.D. Messier, Evidence for neutrino mass from observations of atmospheric neutrinos with Super-Kamiokande, UMI-99-23965 (1999) [http://inspirehep.net/search?p=find+R+UMI-99-23965

Web End =INSPIRE ].

[59] E. Paschos and J. Yu, Neutrino interactions in oscillation experiments, http://dx.doi.org/10.1103/PhysRevD.65.033002

Web End =Phys. Rev. D 65 (2002) 033002 [http://arxiv.org/abs/hep-ph/0107261

Web End =hep-ph/0107261 ] [http://inspirehep.net/search?p=find+EPRINT+hep-ph/0107261

Web End =INSPIRE ].

[60] T2K collaboration, T. Nakaya, New results from T2K, talk given at the http://neu2012.kek.jp/

Web End =Neutrino 2012 Conference , June 39, Kyoto, Japan (2012).

[61] T2K collaboration, Y. Itow et al., The JHF-Kamioka neutrino project, http://arxiv.org/abs/hep-ex/0106019

Web End =hep-ex/0106019 [ http://inspirehep.net/search?p=find+EPRINT+hep-ex/0106019

Web End =INSPIRE ].

[62] M. Ishitsuka, T. Kajita, H. Minakata and H. Nunokawa, Resolving neutrino mass hierarchy and CP degeneracy by two identical detectors with di erent baselines,http://dx.doi.org/10.1103/PhysRevD.72.033003

Web End =Phys. Rev. D 72 (2005) 033003 [http://arxiv.org/abs/hep-ph/0504026

Web End =hep-ph/0504026 ] [http://inspirehep.net/search?p=find+EPRINT+hep-ph/0504026

Web End =INSPIRE ].

[63] P. Huber, M. Lindner and W. Winter, Superbeams versus neutrino factories, http://dx.doi.org/10.1016/S0550-3213(02)00825-8

Web End =Nucl. Phys. B 645 (2002) 3 [http://arxiv.org/abs/hep-ph/0204352

Web End =hep-ph/0204352 ] [http://inspirehep.net/search?p=find+EPRINT+hep-ph/0204352

Web End =INSPIRE ].

33

JHEP06(2013)010

[64] M. Fechner, Study of the expected performance of the T2K experiment on /- /e oscillation using data from the K2K experiment, Ph.D. thesis, Universit Paris VI, Paris, France (2006).

[65] T2K collaboration, I. Kato, Status of the T2K experiment,http://dx.doi.org/10.1088/1742-6596/136/2/022018

Web End =J. Phys. Conf. Ser. 136 (2008) 022018 [http://inspirehep.net/search?p=find+J+J.Phys.Conf.Ser.,136,022018

Web End =INSPIRE ].

[66] NO A collaboration, R. Patterson, The no a experiment: status and outlook, talk given at the http://neu2012.kek.jp/

Web End =Neutrino 2012 Conference , June 39, Kyoto, Japan (2012).

[67] S.K. Agarwalla, S. Prakash, S.K. Raut and S.U. Sankar, Potential of optimized NOvA for large (13) and combined performance with a LArTPC and T2K, http://dx.doi.org/10.1007/JHEP12(2012)075

Web End =JHEP 12 (2012) 075 [arXiv:1208.3644] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1208.3644

Web End =INSPIRE ].

[68] A. Ghosh, T. Thakore and S. Choubey, Determining the neutrino mass hierarchy with INO, T2K, NOvA and reactor experiments, http://dx.doi.org/10.1007/JHEP04(2013)009

Web End =JHEP 04 (2013) 009 [arXiv:1212.1305] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1212.1305

Web End =INSPIRE ].

[69] INO collaboration, S. Choubey, Future of atmospheric neutrino measurements, talk given at the http://neu2012.kek.jp/

Web End =Neutrino 2012 Conference , June 39, Kyoto, Japan (2012).

[70] M. Gonzalez-Garcia and M. Maltoni, Atmospheric neutrino oscillations and new physics, http://dx.doi.org/10.1103/PhysRevD.70.033010

Web End =Phys. Rev. D 70 (2004) 033010 [http://arxiv.org/abs/hep-ph/0404085

Web End =hep-ph/0404085 ] [http://inspirehep.net/search?p=find+EPRINT+hep-ph/0404085

Web End =INSPIRE ].

[71] G. Fogli, E. Lisi, A. Marrone, D. Montanino and A. Palazzo, Getting the most from the statistical analysis of solar neutrino oscillations, http://dx.doi.org/10.1103/PhysRevD.66.053010

Web End =Phys. Rev. D 66 (2002) 053010 [http://arxiv.org/abs/hep-ph/0206162

Web End =hep-ph/0206162 ] [http://inspirehep.net/search?p=find+EPRINT+hep-ph/0206162

Web End =INSPIRE ].

[72] G. Fogli, E. Lisi, A. Marrone and D. Montanino, Status of atmospheric () ()

oscillations and decoherence after the rst K2K spectral data,

http://dx.doi.org/10.1103/PhysRevD.67.093006

Web End =Phys. Rev. D 67 (2003) 093006 [http://arxiv.org/abs/hep-ph/0303064

Web End =hep-ph/0303064 ] [http://inspirehep.net/search?p=find+EPRINT+hep-ph/0303064

Web End =INSPIRE ].

[73] D. Indumathi and M. Murthy, A question of hierarchy: matter e ects with atmospheric neutrinos and anti-neutrinos, http://dx.doi.org/10.1103/PhysRevD.71.013001

Web End =Phys. Rev. D 71 (2005) 013001 [http://arxiv.org/abs/hep-ph/0407336

Web End =hep-ph/0407336 ] [http://inspirehep.net/search?p=find+EPRINT+hep-ph/0407336

Web End =INSPIRE ].

[74] S. Petcov and T. Schwetz, Determining the neutrino mass hierarchy with atmospheric neutrinos, http://dx.doi.org/10.1016/j.nuclphysb.2006.01.020

Web End =Nucl. Phys. B 740 (2006) 1 [http://arxiv.org/abs/hep-ph/0511277

Web End =hep-ph/0511277 ] [http://inspirehep.net/search?p=find+EPRINT+hep-ph/0511277

Web End =INSPIRE ].

[75] A. Samanta, Discrimination of mass hierarchy with atmospheric neutrinos at a magnetized muon detector, http://dx.doi.org/10.1103/PhysRevD.81.037302

Web End =Phys. Rev. D 81 (2010) 037302 [arXiv:0907.3540] [http://inspirehep.net/search?p=find+EPRINT+arXiv:0907.3540

Web End =INSPIRE ].

[76] M. Blennow and T. Schwetz, Identifying the neutrino mass ordering with INO and NOvA, http://dx.doi.org/10.1007/JHEP08(2012)058

Web End =JHEP 08 (2012) 058 [Erratum ibid. 1211 (2012) 098] [arXiv:1203.3388] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1203.3388

Web End =INSPIRE ].

34

JHEP06(2013)010