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arXiv:hep-ph/0609286v1 27 Sep 2006

hep-ph/0609286

Resolving Eight-Fold Neutrino Parameter Degeneracy by

Two Identical Detectors with Different Baselines

Takaaki Kajita1,∗Hisakazu Minakata2,†Shoei Nakayama1,‡and Hiroshi Nunokawa3§

1Research Center for Cosmic Neutrinos,

Institute for Cosmic Ray Research,

University of Tokyo, Kashiwa, Chiba 277-8582, Japan

2Department of Physics, Tokyo Metropolitan University, Hachioji, Tokyo 192-0397, Japan

3Departamento de F´ ısica, Pontif´ ıcia Universidade Cat´ olica do Rio de Janeiro,

C. P. 38071, 22452-970, Rio de Janeiro, Brazil

(Dated: September 27, 2006)

Abstract

We have shown in a previous paper that two identical detectors with each fiducial mass of 0.27

megaton water, one in Kamioka and the other in Korea, which receive the (anti-) muon neutrino

beam of 4 MW power from J-PARC facility have potential of determining the neutrino mass

hierarchy and discovering CP violation by resolving the degeneracies associated with them. In this

paper, we point out that the same setting has capability of resolving the θ23octant degeneracy in

region where sin22θ23<∼0.97 at 2 standard deviation confidence level even for very small values

of θ13. Altogether, it is demonstrated that one can solve all the eight-fold neutrino parameter

degeneracies in situ by using the Tokai-to-Kamioka-Korea setting if θ13is within reach by the next

generation superbeam experiments. We also prove the property called “decoupling between the

degeneracies”, which is valid to first order in perturbation theory of the earth matter effect, that

guarantees approximate independence between analyses to solve any one of the three different type

of degeneracies.

PACS numbers: 14.60.Pq,14.60.Lm,13.15.+g

∗Electronic address: kajita@icrr.u-tokyo.ac.jp

†Electronic address: minakata@phys.metro-u.ac.jp

‡Electronic address: shoei@suketto.icrr.u-tokyo.ac.jp

§Electronic address: nunokawa@fis.puc-rio.br

Typeset by REVTEX1

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I.INTRODUCTION

Physics of neutrinos has entered into a new stage after establishment of the mass-induced

neutrino oscillation due to the atmospheric [1], the accelerator

neutrino [4] experiments, confirming the earlier discovery [5, 6, 7] and identifying the nature

of the phenomenon. In the new era, the experimental endeavors will be focused on search

for the unknowns in neutrino masses and the lepton flavor mixing, θ13, the neutrino mass

hierarchy, and CP violation. On the theory side, various approaches toward understanding

physics of lepton mixing and the quark-lepton relations are extensively pursuit [8], which

then further motivate precision measurement of the lepton mixing parameters. We will use

the standard notation [9] of the lepton mixing matrix, the Maki-Nakagawa-Sakata (MNS)

matrix [10], throughout this paper.

It was recognized sometime ago that there exists problem of parameter degeneracy which

would act as an obstacle against precision measurement of the lepton mixing parameters.

The nature of the degeneracy can be understood as the intrinsic degeneracy [11], which is

duplicated by the unknown sign of atmospheric ∆m2[12] (hereafter, “sign-∆m2degeneracy”

for simplicity) and by the possible octant ambiguity of θ23 [13] that exists if θ23 is not

maximal. For an overview of the resultant eight-fold degeneracy, see e.g., [14, 15].

In a previous paper [16], we have shown that the identical two detector setting in Kamioka

and in Korea with each fiducial mass of 0.27 Mton water, which receives the identical

neutrino beam from the J-PARC facility can be sensitive to the neutrino mass hierarchy

and CP violation in a wide range of the lepton mixing parameters, θ13and the CP phase δ.

It is the purpose of this paper to point out that the same setting has capability of resolving

the θ23octant degeneracy to a value of θ23which is rather close to the maximal, sin22θ23<

0.97(0.94) at 2 (3) standard deviation confidence level (CL). It is achieved by detecting

solar-∆m2scale oscillation effect in the Korean detector. Together with the sensitivities to

resolution of the degeneracy related to the mass hierarchy and the CP phase discussed in the

previous paper, we demonstrate that the Kamioka-Korea two detector setting is capable of

solving the total eight-fold parameter degeneracy. We stress that resolving the degeneracy

is crucial to precision measurement of the lepton mixing parameters on which we make

further comments at appropriate points in the subsequent discussions. We also emphasize

that it is highly nontrivial that one can formulate such a global strategy for resolving all

the known degeneracies (though in a limited range of the mixing parameters) only with the

experimental apparatus using conventional muon neutrino superbeam.1

In some of the previous analyses including ours [16, 18], people often tried to resolve the

degeneracy of a particular type without knowing (or addressing) the solutions of the other

types of degeneracies. But, then, the question of consistency of the procedure immediately

arises; Can one solve the degeneracy of type A without knowing the solutions of the other

degeneracies B and C? Does the obtained solution remain unchanged when the assumed

solutions for the other type of degeneracies are changed to the alternative ones?, etc. We

answer to these questions in the positive in experimental settings where the earth matter

effect can be treated as perturbation. We do so by showing that the resolution of the

degeneracy of a particular type decouples from the remaining degeneracies, the property

[2, 3], and the reactor

1It may be contrasted to the method for resolving the degeneracy based on neutrino factory examined

in [17]; It uses a 40 kton magnetized iron calorimeter and a 4 kton emulsion chamber, and conventional

νµbeam watched by a 400 kton water Cherenkov detector.

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called the “decoupling between the degeneracies” in this paper.

In Sec. II, we present a pedagogical discussion of how the eight-fold degeneracy can be

lifted by measurement with the Kamioka-Korea two detector setting. In Sec. III, we prove

the “decoupling” and make a brief comment on its significance. In Sec. IV, we discuss some

characteristic features of the νeand ¯ νe appearance probabilities that allow the Kamioka-

Korea identical two detector setting to resolve the θ23 octant degeneracy. In Sec. V, the

actual analysis procedure and the obtained sensitivities for solving the θ23degeneracy are

described in detail. In Sec. VI, we reexamine the sensitivities to the mass hierarchy and

CP violating phase by using our new code with disappearance channels and additional

systematic errors. In Sec. VII, we give a summary and discussions.

II.

FOLD DEGENERACY?

HOW THE IDENTICAL TWO DETECTOR SYSTEM SOLVES THE EIGHT-

We describe in this section how the eight-fold parameter degeneracy can be resolved by

using two identical detectors, one placed at a medium baseline distance of a few times 100

km, and the other at ∼1000 km or so. We denote them as the intermediate and the far

detectors, respectively, in this paper. Whenever necessary we refer the particular setting

of Kamioka-Korea two detector system, but most of the discussions in this and the next

sections are valid without the specific setting.

To give the readers a level-one understanding we quote here, ignoring complications,

which effect is most important for solving which degeneracy:

• The intrinsic degeneracy; Spectrum information solves the intrinsic degeneracy.

• The sign-∆m2degeneracy; Difference in the earth matter effect between the interme-

diate and the far detectors solves the sign-∆m2degeneracy.

• The θ23 octant degeneracy; Difference in solar ∆m2oscillation effect (which is pro-

portional to c2

degeneracy.

23) between the intermediate and the far detectors solves the θ23octant

To show how the eight-fold parameter degeneracy can be resolved, we present in Fig 1 a

comparison between the sensitivities achieved by the Kamioka only setting and the Kamioka-

Korea setting by taking a particular set of true values of the mixing parameters which are

quoted in caption of Fig 1. The left four panels of Fig 1 show the expected allowed regions of

oscillation parameters in the Tokai-to-Kamioka phase-II (T2K II) setting, while the right four

panels show the allowed regions by the Tokai-to-Kamioka-Korea setting. For both settings

we assume 4 years of neutrino plus 4 years of anti-neutrino running2and the total fiducial

volume is kept to be the same, 0.54 Mton. Some more information of the experimental

setting and the details of the analysis procedure are described in the caption of Fig 1 and

in Sec. V.

2It was shown in the previous study [16] that the sensitivity obtained with 2 years of neutrino and 6 years

of anti-neutrino running in the T2K II setting [19] is very similar to that of 4 years of neutrino and 4

years of anti-neutrino running.

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Kamioka 0.54Mton detector, ν 4yr + ν

– 4yr 4MW beams

10

-2

10

-1

normal

(aN)

normal

(bN)

10

-2

10

-1

0246

δCP

sin22θ13

inverted

(aI)

0.40.50.6

sin2θ23

inverted

(bI)

Kamioka 0.27Mton + Korea 0.27Mton detectors, ν 4yr + ν

-1

– 4yr 4MW beams

10

-2

10

normal

(cN)

normal

(dN)

10

-2

10

-1

0246

δCP

sin22θ13

inverted

(cI)

0.40.50.6

sin2θ23

inverted

(dI)

FIG. 1: The region allowed in δ − sin22θ13 and sin2θ23− sin22θ13 spaces by T2K II (left four

panels) and by the Kamioka-Korea two detector setting (right four panels) in both of which 4

years of neutrino plus 4 years of anti-neutrino running are assumed. The upper (lower) four panels

show the allowed region for the positive (negative) sign of ∆m2

T2K II and Kamioka-Korea settings are assumed to be 0.54 Mton and each 0.27 Mton, respectively,

and the beam power of J-PARC is assumed to be 4 MW. The baseline to the Kamioka and Korea

detectors are, 295 km and 1050 km, respectively. The true solution is assumed to be located at

sin22θ13=0.01, sin2θ23=0.60 and δ=π/4 with positive sign of ∆m2

indicated by the green star. The solar mixing parameters are fixed as ∆m2

sin2θ12=0.31. Three contours in each figure correspond to the 68% (blue line), 90% (black line)

and 99% (red line) C.L. sensitivities, which are defined as the difference of the χ2being 2.30, 4.61

and 9.21, respectively.

31. The detector fiducial volumes of

31(= +2.5 × 10−3eV2), which is

21= 8 × 10−5eV2and

Let us first focus on the left four panels of Fig 1. In the left-most two panels labeled as

(aN) and (aI), one observes some left-over degeneracies of the total eight-fold degeneracy; If

we plot the result of a rate only analysis without spectrum information we would have seen

8 separate (or overlapped) allowed parameter regions. The θ23octant degeneracy remains

unresolved as seen in panels (bN) and (bI). Note that the overlapping two regions in (aN) and

(aI) are nothing but the consequence of unresolved θ23degeneracy. The intrinsic degeneracy,

horizontal pair seen in (aN), is almost resolved apart from 99% CL region at the particular

set of values of the mixing parameters indicated above. The corresponding pair in (aI) is

missing because the intrinsic degeneracy is completely lifted. Since the matter effect plays

minor role in the T2K II setting it is likely that the spectral information is mainly responsible

for lifting the intrinsic degeneracy. See Sec. IIIC for more about it.

Here is a brief comment on the property of the intrinsic and the sign-∆m2degeneracies.

Because the degenerate solutions of CP phase δ satisfy approximately the same relationship

δ2= π − δ1in both the intrinsic and the sign-∆m2degeneracies [11, 12] (see Eqs. (5) and

(6) in Sec. III), the would-be four (one missing) regions in the panels (aN) and (aI) in Fig. 1

forms a cross (or X) shape, with crossing connection between a pair of solutions of the

sign-∆m2degeneracy.

In the right four panels of Fig. 1 it is exhibited that the intrinsic degeneracy as well as θ23

octant degeneracy are completely resolved by the Kamioka-Korea two-detector setting at

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the same values of the mixing parameters, indicating power of the two detector method [20].

Namely, the comparison between the spectral shapes in Kamioka and in Korea located at

the first and nearly the second oscillation maxima, respectively, supersedes a single detector

measurement in Kamioka with the same total volume despite much less statistics in the

Korean detector. We will give a detailed discussion on how θ23octant degeneracy can be

resolved by the Kamioka-Korea setting in Sec. IV, and present the details of the analysis in

Sec. V.

It should be noted that the sign-∆m2degeneracy is also lifted though incompletely at

the particular set of values of the mixing parameters as indicated in the panels (cI) of Fig. 1

where only the 99% CL regions remain. In fact, we have shown in our previous paper

that the Kamioka-Korea identical two detector setting is powerful in resolving the sign-∆m2

degeneracy in a wide range of the mixing parameters [16]. We note that resolution of the

degeneracy in turn leads to an enhanced sensitivity to CP violation than that of T2K II

setting in a region of relatively large θ13. See [16] for comparison with T2K II sensitivity.

Altogether, we verify that the identical two detector setting in Kamioka-Korea with neutrino

beam from J-PARC solves all the eight-fold parameter degeneracy in situ if θ13 is within

reach by the next generation superbeam experiments such as T2K [19] and NOνA [21].

III.DECOUPLING BETWEEN DEGENERACIES

In this section we discuss the property called the “decoupling between degeneracies”

which arises due to the special setting of baselines shorter than ∼1000 km. The content of

this section is somewhat independent of the main line of the discussion in this paper, and

the readers can skip it to go directly to the analysis of θ23octant degeneracy in Secs. IV

and V. Nonetheless, the property makes the structure of analysis for resolving the eight-fold

degeneracy transparent, and therefore it may worth to report.

The problem of decoupling came to our attention via the following path. In most part of

the previous paper [16], we have discussed how to solve the sign-∆m2degeneracy without

worrying about the θ23octant degeneracy. Conversely, the authors of [18] analyzed the latter

degeneracy without resolving the former one. Are these correct procedure? The answer is

yes if the analysis procedure and the results for the θ23degeneracy is independent of which

solutions we take for the sign-∆m2degeneracy, and vice versa. We call this property the

“decoupling between the degeneracies”.3Though discussion on this point was partially given

in [18], we present here a complete discussion of the decoupling.

Under the approximation of lowest nontrivial order in matter effect, we prove that the

decoupling holds between the above two degeneracies, and furthermore that it can be gen-

eralized, though approximately, to the relation between any two pair of degeneracies among

the three types of degeneracies. To our knowledge, leading order in matter perturbation

theory appears to be the only known circumstance that the argument goes through. For-

tunately, the approximation is valid for the setting used in this paper with baseline up to

∼1000 km, in particular in the Kamioka-Korea setting. In the following treatment we make

a further approximation that the degenerate solutions are determined primarily by the mea-

3Here is a concrete example for which the decoupling does not work; In the method of comparison between

νµ and ¯ νµ disappearance measurement for lifting θ23 octant degeneracy [22] one in fact determines the

combined sign of cos2θ23× ∆m2

31as noticed in [18], and hence no decoupling.

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surement at the intermediate detector. It is a sensible approximation because the statistics

is about 10 times higher at the intermediate detector, and its validity is explicitly verified

in the analysis performed in [16].

A.Approximate analytic treatment of the parameter degeneracy

To make the discussion self-contained, we start from the derivation of the degenerate

solutions by using the matter perturbation theory [23], in which the matter effect is kept

to its lowest nontrivial order. Namely, the matter effect can be ignored in leading order

in the disappearance channel whose oscillation probability is order of unity. Then, the

disappearance probability P(νµ→ νµ) can be given by the vacuum oscillation approximation

with leading order in s2

13and the solar ∆m2

21corrections as

1 − P(νµ→ νµ) =

?sin22θ23+ 4s2

− c2

13s2

23

?2s2

21L

4E

23− 1??sin2

?

?∆m2

31L

2E

31L

4E

?

12sin22θ23

?∆m2

sin

?∆m2

?

.(1)

The probability for anti-neutrino channel is the same as that for neutrino one in this approx-

imation. One can show [23] that the other solar ∆m2

by either a small sin22θ13<∼0.1, or the Jarlskog factor J ≡ c12s12c2

In fact, the validity of the approximation is explicitly verified in [18] where the matter ef-

fect terms are shown to be of the order of 10−3even at L = 1000 km. A disappearance

measurement, therefore, determines s2

21corrections are suppressed further

13s13c23s23sinδ<∼0.04.

23to first order in s2

13as

(s2

23)(1)= (s2

23)(0)(1 + s2

13),(2)

where (s2

the two solutions of (s2

form of the θ23 octant degeneracy. For example, (s2

sin22θ23= 0.96(0.99).

For the appearance channel, we use the νµ(¯ νµ) → νe(¯ νe) oscillation probability with

first-order matter effect [23]

23)(0)is the solution obtained by ignoring s2

23)(0)is determined as (s2

13. From the first term in Eq. (1),

23)(0)=1

2

1 ±

23)(0)= 0.4 or 0.6 (0.45 or 0.55) for

?

?

1 − sin22θ23

?

, the simplest

P[νµ(¯ νµ) → νe(¯ νe)] = c2

23sin22θ12

?∆m2

31L

4E

?

21L

4E

?

sin2

?2

2s2

?∆m2

31L

2E

+ sin22θ13s2

23

?

sin2

?∆m2

?4Ea

??

?2

−1

12

?∆m2

31L

4E

?

21L

2E

?

?

sin

?∆m2

?∆m2

?∆m2

31L

2E

?

??

??

±

∆m2

31

∓aL

2

sin

31L

2E

+ 2Jr

?∆m2

21L

2E

cosδsin

?∆m2

∓ 2sinδsin2

31L

4E

, (3)

where the terms of order s13

√2GFNe[24] where GF is the Fermi constant, Nedenotes the averaged electron number

?

∆m2

∆m2

21

31

and aLs13

?∆m2

21

∆m2

31

?

are neglected. In Eq. (3), a ≡

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density along the neutrino trajectory in the earth, Jr (≡ c12s12c2

reduced Jarlskog factor, and the upper and the lower sign ± refer to the neutrino and

anti-neutrino channels, respectively. We take constant matter density approximation in this

paper. The first term of Eq. (3) is due to the oscillation driven by the solar ∆m2

essentially negligible in the intermediate detector but not at the far detector and is of key

importance to resolve the θ23octant degeneracy.

We make an approximation of ignoring terms of order (∆m2

Note that keeping only the leading order in this quantity is reasonable because Jr<∼0.04,

|∆m2

solutions obey an approximate relationship

13s13c23s23) denotes the

21, which is

21/∆m2

31)Jrcos2θ23in Eq. (3).

21/∆m2

31| ≃ 1/30, and cos2θ23= ±0.2 for sin22θ23= 0.96. Then, the two degenerate

?sin22θ13s2

23

?1st=?sin22θ13s2

23

?2nd, (4)

or, s1st

correction in s2

Analytic treatment of the intrinsic and the sign-∆m2degeneracies is given in [15]. In an

environment where the vacuum oscillation approximation applies the solutions corresponding

to the intrinsic degeneracy are given by [11]

13s1st

23= s2nd

13s2nd

13to s2

23 ignoring higher order terms in s13. We can neglect the leading order

23in these relations because it gives O(s4

13) terms.

θ(2)

13= θ(1)

13,δ(2)= π − δ(1),(5)

where the superscripts (1) and (2) label the solutions due to the intrinsic degeneracy. Under

the same approximation the solutions corresponding to the sign-∆m2degeneracy are given

by [12]

θnorm

13

= θinv

13,δnorm= π − δinv,(∆m2

31)norm= −(∆m2

31)inv,(6)

where the superscripts “norm” and “inv” label the solutions with the positive and the

negative sign of ∆m2

exchange of these two solutions through which the degeneracy is uncovered [12]. The va-

lidity of these approximate relationships in the actual experimental setup in the T2K II

measurement is explicitly verified in [16]. It should be noticed that even if sizable matter

effect is present the relation (5) holds at the energy corresponding to the vacuum oscillation

maximum, or more precisely, the shrunk ellipse limit [25].

31. The degeneracy stems from the approximate symmetry under the

B.Decoupling between degeneracies

Resolution of the degeneracy can be done when a measurement distinguishes between

the values of the oscillation probabilities with the two different solutions corresponding to a

degeneracy. Therefore, we define the probability difference

∆Pab(να→ νβ)

≡ P

?

να→ νβ;θ(a)

23,θ(a)

13,δ(a),(∆m2

31)(a)?

− P

?

να→ νβ;θ(b)

23,θ(b)

13,δ(b),(∆m2

31)(b)?

(7)

where the superscripts a and b label the degenerate solutions. Suppose that we are discussing

the degeneracy A. The decoupling between the degeneracies A and B holds if ∆Pabdefined

in (7) for the degeneracy A is invariant under the replacement of the mixing parameters

corresponding to the degeneracy B, and vice versa.

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The best example of the decoupling is given by the one between the θ23 octant and

the sign-∆m2degeneracies. By noting that J1st

cos2θ23, the difference between probabilities with the first and the second octant solutions

can be given by

r

− J2nd

r

= cos2θ1st

23J1st

r

in leading order in

∆P1st 2nd(νµ→ νe) = cos2θ1st

?∆m2

The remarkable feature of (8) is that the leading-order matter effect terms drops out com-

pletely. Therefore, our approximated treatment remains valid until the second order matter

effect starts to become sizable in the appearance oscillation probability. More importantly,

∆P1st 2nd, being composed only of the vacuum oscillation terms, is obviously invariant under

the replacement normal ↔ inverted solutions with different signs of ∆m2

Therefore, the resolution of the θ23octant degeneracy can be carried out without worrying

about the presence of the sign-∆m2

Next, we examine the inverse problem; Does the determination of mass hierarchy decouple

with the resolution of the θ23degeneracy? One can show, by using Eq. (3), that the similar

probability difference between the solutions in Eq. (6) with the normal and the inverted

hierarchies is given by

23sin22θ12

?∆m2

31L

2E

21L

4E

?

?2

+ 2J1st

r

cos2θ1st

23

21L

2E

??

cosδ sin

?∆m2

∓ 2sinδsin2

?∆m2

31L

4E

??

.(8)

31given in Eq. (6).

31degeneracy.

∆Pnorm inv(νµ→ νe)

= sin22θnorm

13

(snorm

23

)2

?

−s2

12

?∆m2

sin2

21L

2E

?(∆m2

?

sin

?(∆m2

31)normL

4E

31)normL

2E

?

?

?(∆m2

± 2(aL)

??

4E

31)normL (∆m2

?

−1

2sin

31)normL

2E

???

(9)

where the superscripts “norm” and “inv” can be exchanged if one want to start from the

inverted hierarchy. We notice that most of the vacuum oscillation terms, including the solar

term, drop out because of the invariance under δ → π − δ and ∆m2

observe that ∆Pnorm invis invariant under the transformation θ1st

because ∆Pnorm invdepends upon θ13 and θ23 only through the combination sin22θ13s2

within our approximation. Therefore, the sign-∆m2

each other.

In our previous paper, we have shown that the sign-∆m2

Kamioka-Korea two detector setting. The above argument for decoupling guarantees that

our treatment is valid irrespective of the solutions assumed for θ23degeneracy.4

31→ −∆m2

23↔ θ2nd

31. Now, we

and θ1st

2313↔ θ2nd

13,

23

31and the θ23degeneracies decouple with

31degeneracy can be lifted by the

4We remark that in most part of [16], we have assumed that θ23= π/4 so that this problem itself does

not exist. The above discussion implies that even in the case of non-maximal value of θ23 the similar

analysis as in [16] must go through without knowing in which octant θ23lives. The resultant sensitivity

for resolving the mass hierarchy will change as θ23goes away from π/4 but only slightly as will be shown

in Sec. V.

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C.Including the intrinsic degeneracy

Now we turn to the intrinsic degeneracy for which the situation is somewhat different.

First of all, in our setting, the intrinsic degeneracy is already resolved by spectrum infor-

mations at the intermediate detector if θ13is relatively large, sin22θ13>∼0.02 as illustrated

in Fig. 1 before the information from the far detector is utilized. It means that there is no

intrinsic degeneracy from the beginning in the analysis with spectrum informations. Because

of this feature, the intrinsic degeneracy decouple from the beginning from the task of resolv-

ing the eight-fold degeneracy in our setting for the relatively large values of θ13. Because of

a further enhanced sensitivity, the intrinsic degeneracy may be resolved to a smaller values

of θ13in the Kamioka-Korea setting.

In fact, powerfulness of the spectral information for resolving the intrinsic degeneracy

can be understood easily by noting that ∆Pabdefined in (7) is given by using the intrinsic

degeneracy solution (5) as

∆P12(νµ→ νe) = 4Jr

?∆m2

21L

2E

?

cosδ(1)sin

?∆m2

31L

2E

?

,(10)

with notable feature that the matter effect cancels out. Notice that even if the matter effect

cannot be negligible the solution (5) holds for measurement at energies around the vacuum

oscillation maximum. The right-hand side of Eq. (10) is proportional to E−2at energies

near the vacuum oscillation maximum,

2E

used to lift the degeneracy. Hence, the spectrum analysis is a powerful tool for resolving the

intrinsic degeneracy.

∆m2

21L

= π, and the steep energy dependence can be

D. The case that the intrinsic degeneracy is not solved

Even if θ13is too small, or if the energy resolution is too poor for the spectrum analysis

to resolve the intrinsic degeneracy, we can show that the intrinsic degeneracy approximately

decouples from the other degeneracies. ∆P12in Eq. (10) is not exactly but approximately

invariant under the transformation first-octant ↔ second-octant solutions. The difference

between ∆P12(1st) and ∆P12(2nd) is of order cos2θ23Jr∆m2

0.4 and sin22θ13 = 0.1 apart from the further suppression by sin

oscillation maximum. Being the vacuum oscillation term ∆P12is obviously invariant under

the replacement normal ↔ inverted solutions with different signs of ∆m2

resolution of the intrinsic degeneracy can be done, to a good approximation, independent of

the presence of the sign-∆m2

The remaining problem we need to address is the inverse problem, whether the resolution

of the sign-∆m2

lutions of the intrinsic degeneracy. The sign-∆m2

one because ∆Pnorm invin (9) is invariant under the exchange of two intrinsic degeneracy

solutions. The θ23octant degeneracy also approximately decouples from the intrinsic one.

∆P1st 2ndin (8) changes under the interchange of two intrinsic degeneracy solutions only by

the same amount as the difference between ∆P12of the first and the octant θ23solutions,

cos2θ23Jr∆m2

Here is a clarifying comment on what the decoupling really means; Because of the cross-

shaped structure of the degenerate solutions of the intrinsic and the sign-∆m2

21/∆m2

31≃ 3 × 10−4for s2

?

31. Therefore,

23=

∆m2

2E

31L

?

at around the

31and the θ23octant degeneracies.

31and the θ23octant degeneracies can be carried out without knowing so-

31degeneracy decouples from the intrinsic

21/∆m2

31≃ 3 × 10−4(for s2

23= 0.4 and sin22θ13= 0.1).

31degeneracies

9

Page 10

(as was shown in Sec. II) the decoupling of the former from the latter does not imply that the

correct value of δ can be extracted from the measurement without knowing the correct sign

of ∆m2

related by δ ↔ π − δ for a given sign of ∆m2

hierarchy, the true sign of ∆m2

always resolved by the spectrum analysis in region of not too small θ13, as is the case in our

setting, is particularly transparent one from this viewpoint.

To sum up, we have shown that to leading order in the matter effect the intrinsic, the

sign-∆m2

except for between the intrinsic and the θ23octant degeneracies for which the decoupling

is approximate but sufficiently good to allow one-by-one resolution of all the three types of

degeneracies. The decoupling implies that in analysis for lifting the eight-fold degeneracy

the structure of the χ2minimum is very simple in multi-dimensional parameter space, and

it may be of use in discussions of how to solve the degeneracy in much wider context than

that discussed in this paper.

31.5It means that the elimination of one of the “intrinsic” degenerate pair solutions

31can be done without knowing the mass

31. Therefore, the situation that the intrinsic degeneracy is

31, and the θ23octant degeneracies decouples with each other. They do so exactly

IV.

GENERACY?

HOW IDENTICAL TWO DETECTOR SETTING SOLVES θ23OCTANT DE-

Now, we turn to the problem of how the identical two detector setting can resolve the θ23

degeneracy, the unique missing link in a program of resolving eight-fold parameter degen-

eracy in the Kamioka-Korea two detector setting. The solar ∆m2oscillation term, the first

term in Eq. (3) with the coefficient of c2

was argued on very general ground [18] that the θ23degeneracy is hard to resolve only by ac-

celerator experiments with baseline of <∼1000 km or so, the argument can be circumvented

if the solar term can be isolated. We emphasize that the accuracy of the determination of

θ23is severely limited by the octant degeneracy, as discussed in detail in [26].

Therefore, the question we must address first is the relative importance of the solar

term to the remaining terms in ∆P1st 2ndin Eq. (8). We note that the ratio of the so-

lar term to the δ-dependent solar-atmospheric interference term in ∆P1st 2ndis given by

sin22θ12(∆m2

tio is roughly given by ≃ 3(1/30)(π/2)0.86(1/4Jr) ≃ 0.9 (0.16/s13) with beam energy having

the first oscillation maximum in Kamioka. Therefore, the solar term is indeed comparable

or lager for smaller θ13in size with the interference terms in ∆P1st 2ndat the far detector.

Obviously, the solar term is independent of θ13, which suggests that the sensitivity to resolve

the θ23degeneracy is almost independent of θ13, as will be demonstrated in Sec. V. We note

that while the solar term is the key to resolve the θ23degeneracy, the interference terms also

contributes to lift the degeneracy. In particular, as shown in (8), the sinδ term has opposite

sign when the polarity of the beam is switched from the neutrino to the anti-neutrino runs.

The next question we must address is how the solar term can be separated from the

other terms to have enhanced sensitivity to the θ23degeneracy. To understand the behavior

of the solar term and its difference from that of the atmospheric terms in the oscillation

probability, we plot in Fig. 2 a comparison between them in Kamioka (left panels) and in

23, may be of key importance to do the job. While it

21L/4E)/4Jr, assuming the square parenthesis in (8) is of order unity. The ra-

5Notice, however, that it does not obscure the CP violation, because the ambiguity is only two-fold;

δ ↔ π − δ.

10

Page 11

0.4

8

0.6

0.81 1.2

-2

0

2

4

6

8

Patm or Psolar [%]

δ = 0

δ = π/2

δ=π

δ=3π/2

Kamioka

0.4

0.6

0.81 1.2

Psolar

Korea

0.4

0.6

Neutrino Energy (GeV)

0.81 1.2

-2

0

2

4

6

Patm or Psolar [%]

0.4

0.6

Neutrino Energy (GeV)

0.811.2

ν

ν

Normal Hierarchy, sin22θ13 = 0.05, sin2θ23 = 0.5

ν

ν

}Patm

FIG. 2:

of atmospheric plus interference terms in the νeappearance oscillation probabilities with various

values of CP phase δ; δ = 0 (dotted line), δ = π/2 (dashed line), δ = π (dash-dotted line), and

δ = 3π/2 (double-dash-dotted line). For this plot, we used analytic expression in Eq. (3); Psolaris

defined to be the first term in Eq. (3) whereas Patmis defined to be the rest in Eq. (3).¯Psolarand

¯Patmrefer to the corresponding terms for anti-neutrinos.

The energy dependence of the solar term (red solid line) is contrasted with the ones

Korea (right panels) for various values of δ. As one can observe in the right panels, the

energy dependence of the solar oscillation term, a monotonically decreasing (approximately

1/E2) behavior with increasing energy, is quite different from the oscillating behavior of the

atmospheric ones. It is also notable that the ratio of the solar term to the atmospheric-

solar interference term is quite different between the intermediate and the far detectors.

Due to the differing relative importance of the solar term in the two detectors and the

clear difference in the energy dependences between the solar and the atmospheric terms,

the spectrum analysis, the powerful method for resolving the intrinsic degeneracy, must be

able to isolate the solar term from the remaining ones. This will be demonstrated in the

quantitative analysis in the next section.

We note that several alternative methods are proposed to resolve the θ23 degeneracy.

11

Page 12

They include: the atmospheric neutrino method [27, 28, 29], and the reactor accelerator

combined method [18, 30], the atmospheric accelerator combined method [31]. The atmo-

spheric neutrino method discussed in [27, 28] is closest to ours in physics principle of utilizing

the solar mass scale oscillation effect. Possible advantage of the present method may be in

a clean detection of the solar term by the intermediate-versus-far two detector comparison.

V.SENSITIVITY FOR RESOLVING θ23OCTANT DEGENERACY

In this section, we describe details of our analysis for resolving the θ23octant degeneracy.

They include treatment of experimental errors, treatment of background, and the statistical

procedure which is used to investigate the sensitivity of the experiment. Then, the results

of our analysis are presented.

A. Assumptions and the definition of χ2

In order to understand the sensitivity of the experiment with the two detector system at

295 km (Kamioka) and 1050 km (Korea), we carry out a detailed χ2analysis. To address

the θ23 octant degeneracy, it is of course necessary to include νµ and ¯ νµ disappearance

channels in addition to the appearance ones in our treatment. In short, the definition of

the statistical procedure is similar to the one used in Ref. [16] with necessary extension for

including muon events. The assumption on the experimental setting is also identical to that

of the best performance setting identified in Ref. [16]. Namely, 0.27 Mton fiducial masses for

the intermediate site (Kamioka, 295 km) and the far site (Korea, 1050 km). The neutrino

beam is assumed to be 2.5 degree off-axis one produced by the upgraded J-PARC 4 MW

proton beam. It is assumed that the experiment will continue for 8 years with 4 years of

neutrino and 4 years of anti-neutrino runs.

We use various numbers and distributions available from references related to T2K [32], in

which many of the numbers are updated after the original proposal [19]. Here, we summarize

the main assumptions and the methods used in the χ2analysis. We use the reconstructed

neutrino energy for single-Cherenkov-ring electron and muon events. The resolution in the

reconstructed neutrino energy is 80 MeV for quasi-elastic events. We assume that |∆m2

should be known precisely by the time when the experiment we consider in this report will be

carried out. We take ∆m2

of the beam is the one expected by the 2.5 degree off-axis-beam in T2K. The shape of the

energy spectrum for the anti-neutrino beam is assumed to be identical to that of the neutrino

beam. The event rate for the anti-neutrino beam in the absence of neutrino oscillations is

smaller by a factor of 3.4 due mostly to the lower neutrino interaction cross sections and

partly to the slightly lower flux. The signal to noise ratio is worse for the anti-neutrino beam

than that for the neutrino beam by a factor of about 2.

28 background electron events are expected for the reconstructed neutrino energies be-

tween 350 and 850 MeV for (0.75×0.0225×5)MW·Mton·yr measurement with the neutrino

beam. The energy dependence of the background rate and the rate itself are taken from [32].

The background rate is expected to be higher in the lower neutrino energies. The expected

number of electron events is assumed to be 122 for sin22θ13=0.1 with the same detector

exposure and beam, assuming the normal mass hierarchy and δ = 0.

We assume that the experiment is equipped with a near detector which measures the

31|

31= ±2.5×10−3eV2. Hence, we assume that the energy spectrum

12

Page 13

rate and the energy dependence of the background for electron events, un-oscillated muon

spectrum, and the signal detection efficiency. These measurements are assumed to be carried

out within the uncertainty of 5%. We already demonstrated that the dependence on the

assumed value of the experimental systematic errors is rather weak [16]. We stress that in

the present setting the detectors located in Kamioka and in Korea are not only identical but

also receive neutrino beams with essentially the same energy distribution (due to the same

off-axis angle of 2.5 degree) in the absence of oscillations. However, it was realized recently

that, due to a non-circular shape of the decay pipe of the J-PARC neutrino beam line, the

flux energy spectra viewed at detectors in Kamioka and in Korea are expected to be slightly

different even at the same off-axis angle, especially in the high-energy tail of the spectrum

[33]. The possible difference between fluxes in the intermediate and the far detectors is

newly taken into account as a systematic error in the present analysis.

We compute neutrino oscillation probabilities by numerically integrating neutrino evolu-

tion equation under the constant density approximation. The average density is assumed

to be 2.3 and 2.8 g/cm3for the matter along the beam line between the production target

and Kamioka and between the target and Korea, respectively [16]. We assume that the

number of electron with respect to that of nucleons to be 0.5 to convert the matter density

to the electron number density. In our χ2analysis, we fix the absolute value of |∆m2

be 2.5 × 10−3eV2, and fix solar parameters as ∆m2

Fig. 3 shows an example of the energy spectrum of electron and muon events to be

observed in Kamioka and Korea for 4 years of neutrino beam plus 4 years of anti-neutrino

beam. The two sets of parameters give very similar spectrum for both the electron and muon

events at the Kamioka detector and the muon events at the Korean detector. However, due

to the long baseline distance, the solar term plays some role in the(ν)

probability at the Korean detector. Therefore, the two sets of parameters give slightly

different oscillation probabilities in Korea. Since the solar term is proportional to c2

this feature to obtain information on sin2θ23.

The statistical significance of the measurement considered in this paper was estimated

by using the following definition of χ2:

31| to

21= 8 × 10−5eV2and sin2θ12=0.31.

µ→

(ν)

eoscillation

23we use

χ2=

4

?

k=1

?

5

?

i=1

?N(e)obs

i

− N(e)exp

σ2

i

i

?2

+

20

?

i=1

?N(µ)obs

i

− N(µ)exp

σ2

i

i

?2

?

+

7

?

j=1

?ǫj

˜ σj

?2

,(11)

where

N(e)exp

i

= NBG

i

· (1 +

?

?

j=1,2,7

f(e)i

j· ǫj) + Nsignal

i

· (1 +

?

?

j=3,7

f(e)i

j· ǫj) , (12)

N(µ)exp

i

= Nnon−QE

i

· (1 +

j=4,6,7

f(µ)i

j· ǫj) + NQE

i

· (1 +

j=4,5,7

f(µ)i

j· ǫj) .(13)

The first and second terms in Eq. (11) are for the number of observed single-ring electron

and muon events, respectively. N(e or µ)obs

i

is the number of events to be observed for the

given oscillation parameter set, and N(e or µ)exp

assumed oscillation parameters in the χ2analysis. k = 1,2,3 and 4 correspond to the four

combinations of the detectors in Kamioka and in Korea with the neutrino and anti-neutrino

beams, respectively. The index i represents the reconstructed neutrino energy bin for both

electrons and muons. For electron events, both N(e)obs

i

is the expected number of events for the

i

and N(e)exp

i

include background

13

Page 14

0

200

400

600

800

1000

00.511.5

Number of electron events/bin

Kamioka

0

20

40

60

80

100

0 0.511.5

Korea

0

1000

2000

3000

4000

5000

00.511.5

Reconstructed Eν (GeV)

Number of muon events/bin

Kamioka

0

500

1000

1500

00.511.5

Korea

FIG. 3: Examples of electron and muon events to be observed in Kamioka and Korea for 4 years of

neutrino plus 4 years of anti-neutrino running are presented as a function of reconstructed neutrino

energy. The fiducial masses are taken to be 0.27 Mton for both the detectors in Kamioka and Korea.

The dashed histograms for electron events show the background events. The open circles show the

expected energy spectrum of signal events with sin2θ23=0.40 and sin22θ13=0.01. The solid circles

show the expected energy spectrum of signal events with sin2θ23=0.60 and sin22θ13=0.0067. In

both cases, δ = 3π/4 and normal mass hierarchy are assumed in simulating the events.

events. The energy ranges of the five energy bins for electron events are respectively 400-

500 MeV, 500-600 MeV, 600-700 MeV, 700-800 MeV and 800-1200 MeV. The energy range

for the muon events covers from 200 to 1200 MeV. Each energy bin has 50 MeV width. σi

denotes the statistical uncertainties in the expected data. The third term in the χ2definition

collects the contributions from variables which parameterize the systematic uncertainties in

the expected number of signal and background events.

NBG

i

is the number of background events for the ithbin for electrons. Nsignal

number of electron appearance events that are observed, and depends on neutrino oscillation

parameters. The uncertainties in NBG

i

and Nsignal

i

to 3 and 7).Similarly, Nnon−QE

i

are the number of non-quasi-elastic events for the ith

i

is the

are represented by 4 parameters ǫj(j = 1

14

Page 15

bin for muons.

quasi-elastic and quasi-elastic muon events separately, since the neutrino energy cannot be

properly reconstructed for non-quasi-elastic events. Both Nnon−QE

neutrino oscillation parameters. The uncertainties in Nnon−QE

4 parameters ǫj(j = 4 to 7).

During the fit, the values of N(e or µ)exp

i

are recalculated for each choice of the oscillation

parameters which are varied freely to minimize χ2, and so are the systematic error parame-

ters ǫj. The parameter f(e or µ)i

in the ithbin due to a variation of the parameter ǫj. The overall background normalization

for electron events is assumed to be uncertain by ±5% (˜ σ1=0.05). It is also assumed that the

background events for electron events have an energy dependent uncertainty with the func-

tional form of f(e)i

in ǫ2(˜ σ2=0.05). The functional form of f(µ)i

define the uncertainty in the spectrum shape for muon events (˜ σ4=0.05). The uncertainties

in the signal detection efficiency are assumed to be 5% for both electron and muon events

(˜ σ3 = ˜ σ5=0.05). The uncertainty in the separation of quasi-elastic and non-quasi-elastic

interactions in the muon events is assumed to be 20% (˜ σ6=0.20). These systematic errors

are assumed to be not correlated between the electron and muon events. In addition, for

the number of events in Korea, the possible flux difference between Kamioka and Korea is

taken into account in f(e or µ)i

the 1 σ uncertainty in the flux difference (˜ σ7).

NQE

i

are the number of quasi-elastic muon events.We treat the non-

i

and NQE

are represented by

i

depend on

i

and NQE

i

jrepresents the fractional change in the predicted event rate

2= ((Eν(rec)−800 MeV)/400 MeV). 5% is assumed to be the uncertainty

4= (Eν(rec) − 800 MeV)/800 MeV is used to

7. The predicted flux difference [33] is simply assumed to be

B.Sensitivity with two-detector complex

Now we present the results of the sensitivity analysis for the θ23octant degeneracy. The

results for the mass hierarchy as well as CP violation sensitivities will be discussed in the next

section. Fig. 4 shows the sensitivity to the θ23octant determination as a function of sin22θ13

and sin2θ23. The areas shaded with light (dark) gray of this figure indicate the regions of

parameters where the octant of θ23can be determined at 2 (3) standard deviation confidence

level, which is determined by the condition χ2

(9). The upper (lower) panels correspond to the case where the true hierarchy is normal

(inverted). Note, however, that the fit was performed without assuming the mass hierarchy.

Since the sensitivity mildly depends on the CP phase δ, we define the sensitivity to resolving

the octant degeneracy in two ways: the left (right) panels correspond to the case where the

sensitivity is defined such that the octant is determined for any value of delta (half of the δ

space). From this figure, we conclude that the experiment we consider here is able to solve

the octant ambiguity, if sin2θ23< 0.38(0.42) or > 0.62(0.58) at 3 (2) standard deviation

confidence level. This conclusion depends weakly on the value of sin22θ13, as well as the

value of the CP phase δ and the mass hierarchy.

The sensitivity of lifting the octant degeneracy by this setting is quite high even for rather

small values of θ13to sin22θ13∼ 10−3where the mass hierarchy is not determined, a possible

consequence of the decoupling. See Figs. 5 in the next section. The sensitivity depends very

weakly on θ13in relatively small values of sin22θ13where the dominant atmospheric terms

are small. The feature of almost independence of the sensitivity to θ13should be contrasted

with that of the accelerator-reactor combined method in which a strong dependence on θ13

is expected [18]. Very roughly speaking the sensitivity by the present method is better than

min(wrong octant) − χ2

min(true octant) > 4

15

Page 16

0.40.50.6

10

-2

10

-1

(a)

normal

0.40.50.6

10

-2

10

-1

(b)

normal

sin2θ23

sin22θ13

0.40.5 0.6

10

-2

10

-1

inverted

sin2θ23

sin22θ13

0.40.50.6

10

-2

10

-1

inverted

FIG. 4: 2 (light gray area) and 3 (dark gray area) standard deviation sensitivities to the θ23octant

degeneracy for 0.27 Mton detectors both in Kamioka and Korea. 4 years running with neutrino

beam and another 4 years with anti-neutrino beam are assumed. In (a), the sensitivity is defined

so that the experiment is able to identify the octant of θ23for any values of the CP phase δ. In

(b), it is defined so that the experiment is able to identify the octant of θ23for half of the CP δ

phase space.

the latter method in a region sin22θ13<∼0.05 − 0.06 according to the result given in Fig. 8

of [18]. The sensitivity of our method is also at least comparable to that could be achieved

by the high statistics observation of atmospheric neutrinos [27, 28, 29].

VI.

CHY AND CP VIOLATION

REEXAMINATION OF SENSITIVITIES TO NEUTRINO MASS HIERAR-

In this section we reexamine the problem of sensitivities to the neutrino mass hierarchy

and CP violation achievable by the Kamioka-Korea identical two detector complex. We

want to verify that the sensitivities do not depend on which octant θ23lives, as indicated

by our discussion of the decoupling given in Sec. III. It is also interesting to examine how

the sensitivities depend upon sin22θ23. Furthermore, the inclusion of the new systematic

error which accounts for difference in the spectral shapes of the neutrino beam between the

intermediate and the far detectors makes the reexamination worth to do.

16

Page 17

0123456

10

-2

10

-1

normal

δ

sin22θ13

2(thin lines) and 3(thick lines) standard deviation sensitivities to the mass hierarchy

determination for several values of sin22θ23 (red, yellow, black, green and blue lines show the

results for sin2θ23= 0.40, 0.45, 0.50, 0.55 and 0.60, respectively). The sensitivity is defined in the

plane of sin22θ13versus CP phase δ. The top and bottom panels show the cases for positive and

negative mass hierarchies, respectively. The experimental setting is identical to that in Fig.4.

0123456

sin2θ23 = 0.40

sin2θ23 = 0.45

sin2θ23 = 0.50

sin2θ23 = 0.55

sin2θ23 = 0.60

10

-2

10

-1

inverted

FIG. 5:

In Figs. 5 and 6 the regions sensitive to the mass hierarchy and CP violation, respectively,

are presented. In both figures, the thin-lines and the thick-lines indicate the sensitivity

region at 2 and 3 standard deviations, respectively. As in the previous work [16], 2 (3)

standard deviation sensitivity regions are defined by the conditions, χ2

χ2

mass hierarchy and CP violation, respectively.

The sensitivities to the mass hierarchy and CP violation at sin2θ23 = 0.5 are almost

identical to those obtained in [16]. It is evident that the sensitivities do not depend strongly

on sin2θ23 as far as the value is between 0.40 and 0.60. In fact, the mass hierarchy can

be determined even if the θ23 octant degeneracy is not resolved. But, the sensitivity to

mass hierarchy resolution gradually improves as sin2θ23becomes larger, as seen in Fig. 5.

It is natural because ∆Pnorm invin (9), or the appearance probability itself is proportional

min(wrong hierarchy)−

min(true hierarchy) > 4 (9) and χ2

min(δ = 0 or π) − χ2

min(true value ofδ) > 4 (9) for the

17

Page 18

0123456

10

-2

10

-1

normal

δ

sin22θ13

Sensitivities to the CP violation, sinδ ?= 0. The meaning of the lines and colors are

identical to that in Fig. 5.

0123456

10

-2

10

-1

inverted

FIG. 6:

to sin2θ23. An alternative way of presenting the same result is to use s2

ordinate. An approximate scaling behavior is observed as expected by ∆Pnorm invin (9).

23sin22θ13for the

VII.SUMMARY AND DISCUSSION

In this paper, we have shown that a setting with two identical water Cherenkov detectors

of 0.27 Mton fiducial mass, one in Kamioka and the other in Korea, which receive almost

the same neutrino beam from J-PARC has capability of resolving the θ23octant degeneracy

in situ by observing difference of the solar oscillation term between both detectors. The

feature of the sensitivity region indicates that the present method is quite complementary

to the reactor-accelerator combined method explored in [18]. Together with the potential for

resolution of the intrinsic and the sign-∆m2

confirmation in Sec. VI by an improved treatment), we have demonstrated that the Kamioka-

Korea two detector complex can resolve all the eight-fold neutrino parameter degeneracy

31degeneracies previously reported in [16] (with

18

Page 19

under the assumption that θ13is within reach by the next generation accelerator experiments

and θ23is not too close to π/4.

As an outcome of these studies, the strategy toward determination of the remaining

unknowns in the lepton flavor mixing can be discussed. It is nice to see that such program can

be defined only with the single experiment based on the conventional superbeam technology

which does not require long-term R&D efforts, and the well established detector technology.

It opens the possibility of accurate determination of the neutrino mixing parameters, θ23,

θ13, δ, as well as the neutrino mass hierarchy, by lifting all the eight-fold degeneracy which

should merit our understanding of physics of lepton sector.

Our treatment in this paper includes a new systematic error which accounts for possible

difference in spectral shape of the neutrino beam received by the two detectors in Kamioka

and in Korea. We have shown that, despite the existence of such new uncertainty which

might hurt the principle of near-far cancellation of the systematic errors, the capability of

determining neutrino mass hierarchy and sensitivity to CP violation are kept intact.

We have also reported a progress in understanding the theoretical aspect of the problem

of how to solve the parameter degeneracy. Because of the property phrased as “decoupling

between degeneracies” which is shown to hold in a setting that allows perturbative treat-

ment of matter effect, one can try to solve a particular degeneracy without worrying about

the presence of other degeneracies. This feature may be contrasted to those of the very

long baseline approaches, such as the neutrino factory, in which one would not expect the

discussion in this paper to hold.

An alternative but closely related approach toward determination of the global structure

of lepton flavor mixing in a single experiment is to utilize an on-axis wide band neutrino

beam to explore the multiple oscillation maxima, which may be called the “BNL strategy”

[34, 35]. This strategy can be applied to the far detector in Korea, as examined by several

authors [36, 37, 38].6In this case, however, one needs to understand the energy dependence

of the background and the signal efficiency as well as the neutrino interaction cross section

precisely for both the intermediate and the far detectors. In particular, since the low energy

bins are enriched with neutral current background contamination that comes from events

with higher neutrino energies [37] the cancellation of the systematic errors between the

two detectors, which is the key ingredient in our analysis, does not hold. Nonetheless, we

emphasize that the potentially powerful method is worth to examine further with realistic

estimate of the detector performance.

Finally, we remark that the J-PARC 2.5 degree off-axis beam with the baseline length of

1,000 to 1,250 km should be available in the Korean Peninsula. Therefore, it may be possible

to further enhance the sensitivity to the θ23octant by taking a longer baseline length for

the Korean detector. The best baseline length and the detector location should be decided

so that the experiment has the best sensitivities to the oscillation parameters, especially to

the CP phase δ, mass hierarchy and the octant of θ23.

6Very roughly speaking ignoring the issue of backgrounds and assuming the same baseline length, one

would expect that wide band beam option is better in sensitivity to the neutrino mass hierarchy, while

the same off-axis angle option studied in this paper is advantageous to resolve the θ23octant degeneracy

for which low energy bins are essential.

19

Page 20

Acknowledgments

We would like to thank M. Ishitsuka and K. Okumura for the assistance in the analysis

code. H.N. thanks Stephen Parke and Olga Mena for useful discussion. This work was

supported in part by the Grant-in-Aid for Scientific Research, Nos. 15204016 and 16340078,

Japan Society for the Promotion of Science, Funda¸ c˜ ao de Amparo ` a Pesquisa do Estado de

Rio de Janeiro (FAPERJ) and by Conselho Nacional de Ciˆ encia e Tecnologia (CNPq).

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