review article physics potential of long-baseline experiments

Review ArticlePhysics Potential of Long-Baseline Experiments

Sanjib Kumar Agarwalla

Institute of Physics Sachivalaya Marg Sainik School Post Bhubaneswar 751005 Orissa India

Correspondence should be addressed to Sanjib Kumar Agarwalla sanjibiopbresin

Received 15 August 2013 Revised 6 November 2013 Accepted 8 November 2013 Published 20 January 2014

Academic Editor Srubabati Goswami

Copyright copy 2014 Sanjib Kumar Agarwalla This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited The publication of this article was funded by SCOAP3

The discovery of neutrinomixing and oscillations over the past decade provides firm evidence for new physics beyond the StandardModel Recently 120579

13has been determined to be moderately large quite close to its previous upper bound This represents a

significant milestone in establishing the three-flavor oscillation picture of neutrinos It has opened up exciting prospects for currentand future long-baseline neutrino oscillation experiments towards addressing the remaining fundamental questions in particularthe type of the neutrinomass hierarchy and the possible presence of aCP-violating phase Another recent and crucial development isthe indication of non-maximal 2-3mixing angle causing the octant ambiguity of 120579

23 In this paper I will review the phenomenology

of long-baseline neutrino oscillations with a special emphasis on sub-leading three-flavor effects which will play a crucial role inresolving these unknowns First I will give a brief description of neutrino oscillation phenomenonThen I will discuss our presentglobal understanding of the neutrinomass-mixing parameters and will identify the major unknowns in this sector After that I willpresent the physics reach of current generation long-baseline experiments Finally I will conclude with a discussion on the physicscapabilities of accelerator-driven possible future long-baseline precision oscillation facilities

1 Introduction and Motivation

We are going through an exciting phase when the light ofnew findings is breaking apart our long-held understandingof the Standard Model of particle physics This revolutionstarted in part with thewidely confirmed claim that neutrinoshave mass and it will continue to be waged by currentlyrunning and upcoming neutrino experiments Over the lastfifteen years or so fantastic data from world-class exper-iments involving neutrinos from the sun [1ndash7] the Earthatmosphere [8 9] nuclear reactors [10ndash16] and accelerators[17ndash22] have firmly established the phenomenon of neutrinoflavor oscillations [23 24] This implies that neutrinos havemass and they mix with each other providing an exclusiveexample of experimental evidence for physics beyond theStandard Model

The most recent development in the field of neutrinos isthe discovery of the smallest lepton mixing angle 120579

13 Finally

it has been measured to be nonzero with utmost confidenceby the reactor neutrino experimentsDaya Bay [13] andRENO[14] They have found a moderately large value of 120579

13

sin2212057913|Daya Bay (rate-only) = 0089 plusmn 0010 (stat) plusmn

0005 (syst) [13]sin22120579

13|RENO (rate-only) = 0113 plusmn 0013 (stat) plusmn

0019 (syst) [14]which is in perfect agreement with the data provided bythe another reactor experiment Double Chooz [15 16] andthe accelerator experiments MINOS [20] and T2K [22]All the three global fits [25ndash27] of all the world neutrinooscillation data available indicate a nonzero value of 120579

13at

more than 10120590 and suggest a best-fit value of sin212057913≃ 0023

with a relative 1120590 precision of 10 Daya Bay experiment isexpected to reduce this uncertainty to a level of 5 by 2016when they will finish collecting all the data [28] This recenthigh-precision measurement of a moderately large value of12057913

signifies an important breakthrough in validating thestandard three-flavor oscillation picture of neutrinos [29]It has created exciting opportunities for current and futureneutrino oscillation experiments to address the remainingfundamental unknowns This fairly large value of 120579

13has

provided a ldquogoldenrdquo avenue to directly probe the neutrino

Hindawi Publishing CorporationAdvances in High Energy PhysicsVolume 2014 Article ID 457803 29 pageshttpdxdoiorg1011552014457803

2 Advances in High Energy Physics

Mass

Atmosph

eric

1

1

2

23

3

Normalhierarchy hierarchy

Inverted

solarΔm2

solarΔm2

Δm2

e 120583 120591

Figure 1The sign of Δ119898231equiv 1198982

3minus1198982

1is unknownThe hierarchy of

the neutrino mass spectrum can be normal or inverted

mass hierarchy (two possibilities are there it can be eithernormal (NH) if Δ1198982

31equiv 1198982

3minus 1198982

1gt 0 or inverted (IH) if

Δ1198982

31lt 0 as described in Figure 1) using the Earth matter

effects and to search for leptonic CP violation (if the Dirac CPphase 120575CP differs from 0

∘ or 180∘) in accelerator-based long-baseline neutrino oscillation experiments [30 31] Anotherrecent and important development related to neutrino mix-ing parameters is the hint of nonmaximal 2-3 mixing bythe MINOS accelerator experiment [32 33] However themaximal value of 120579

23is still favored by the atmospheric neu-

trino data dominated by Super-Kamiokande [34] Combinedanalyses of all the neutrino oscillation data available [25ndash27]also prefer the deviation from maximal mixing for 120579

23 that

is (05minus sin212057923) = 0 In ]

120583survival probability the dominant

term mainly depends on sin2212057923 Now if sin22120579

23differs

from 1 as indicated by the recent neutrino data then we gettwo solutions for 120579

23 one lt 45

∘ named as lower octant(LO) and the other gt 45∘ named as higher octant (HO)In other words if the quantity (05 minus sin2120579

23) is positive

(negative) then 12057923

belongs to LO (HO) This leads to theproblem of octant degeneracy of 120579

23[35] which is a part of

the overall eightfold degeneracy [36 37] where the other twodegeneracies are (120579

13 120575CP) intrinsic degeneracy [38] and the

(hierarchy 120575CP) degeneracy [39] The resolution of the threefundamental issues in the neutrino sector neutrino masshierarchy octant of 120579

23 and CP violation is possible only

by observing the impact of three-flavor effects in neutrinooscillation experiments [40 41]

The information on neutrino mass hierarchy is veryimportant in order to settle the structure of neutrino massmatrix which in turn can give crucial piece of informationtowards the underlying theory of neutrinomasses andmixing[42] This is also a vital ingredient for neutrinoless doublebeta decay searches investigating the Majorana nature ofneutrinos If Δ1198982

31lt 0 and yet no neutrinoless double beta

decay is observed even in the very far future experimentsthat would be a strong hint that neutrinos are not Majo-rana particles [43] Another fundamental missing link thatneeds to be addressed in long-baseline neutrino oscillationexperiments is to measure 120575CP and to explore leptonic CPviolation This new source of low-energy CP violation inneutral lepton sector has drawn tremendous interest becauseof the possibility of leptogenes is leading to baryogenesisand the observed baryon asymmetry in the universe [44]

Leptogenesis demands the existence of CP violation in theleptonic sector for a recent review see [45] The possiblelink between leptogenesis and neutrino oscillations has beenstudied in [46ndash48] It is likely that the CP violating phase inneutrino oscillations is not directly responsible to generatethe CP violation leading to leptogenesis But there is no doubtthat a demonstration of CP violation in neutrino oscillationswill provide a crucial guidepost for models of leptonic CPviolation and leptogenesis Precise measurement of 120579

23and

the determination of its correct octant (if it turns out tobe nonmaximal) are also very vital tasks that need to beundertaken by the current- and next-generation neutrinooscillation experiments These pieces of information willprovide crucial inputs to the theories of neutrino massesand mixing [42 49ndash51] A number of excellent ideas suchas 120583 harr 120591 symmetry [52ndash59] 119860

4flavor symmetry [60ndash

64] quark-lepton complementarity [65ndash68] and neutrinomixing anarchy [69 70] have been proposed to explain theobserved pattern of one small and two large mixing anglesin the neutrino sector Future ultraprecise measurementof 12057923

will severely constrain these models leading to abetter understanding of the theories of neutrino masses andmixing

The outline of this review work is as follows We startin Section 2 by revisiting the phenomenon of neutrinooscillation in the three-neutrino frameworkThenwe discussthe importance of matter effect on neutrino oscillation inSection 3 In Section 4 we take a look at our present under-standing of neutrino oscillation parameters and we identifythe fundamental missing links in the neutrino sector thatcan be answered in the current- and next-generation long-baseline neutrino oscillation experiments Section 5 discussesin detail the three-flavor effects in long-baseline neutrinooscillation experiments with the help of ]

120583rarr ]119890oscillation

probability119875120583119890 Next in Section 6 we study the physics reach

of current-generation long-baseline beam experiments T2Kand NO]A In Section 7 we give an overview on the possibleoptions for next-generation accelerator-driven long-baselineoscillation facilities Finally in Section 8 we conclude with asummary of the main points

2 Three-Neutrino Mixing andOscillation Framework

Bruno Pontecorvo was the pathfinder of neutrino oscillation[74 75] In 1957 he gave this concept [76 77] based on a two-level quantum system Neutrino oscillation is a simple quan-tum mechanical phenomenon in which neutrino changesflavor as it travels This phenomenon arises if neutrinos havenondegenerate masses and there is mixing First we considerthe fact that neutrinos (]

119890 ]120583 ]120591) are produced or detected via

weak interactions and therefore they are referred to as weak-eigenstate neutrinos (denoted as ]

120572) It means that they are

the weak doublet-partners of 119890minus 120583minus and 120591minus respectively Insuch a case if neutrinos are assumed to be massive then ingeneral it is notmandatory that themass-matrix of neutrinoswritten in this weak (flavor) basis will have to be diagonalSo it follows that the mass eigenstate neutrinos ]

119894 119894 = 1 2 3

Advances in High Energy Physics 3

(the basis in which the neutrino mass matrix is diagonal) arenot identical to the weak or flavor basis (the charged leptonmass-matrix is diagonal in this basis) and for three light activeneutrinos we have

1003816100381610038161003816]120572⟩ =3

sum

119894=1

119880lowast

120572119894

1003816100381610038161003816]119894⟩ (1)

where 120572 can be 119890 120583 or 120591 and 119880 is the 3 times 3 unitaryleptonic mixing matrix known as the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix [23 78] This matrix isanalogous to the CKMmatrix in the quark sector We use thestandard Particle Data Group convention [79] to parametrizethe PMNS matrix in terms of the three mixing angles 120579

12

(solar mixing angle) 12057923

(atmospheric mixing angle) and12057913(reactor mixing angle) and one Dirac-type CP phase 120575CP

(ignoring Majorana phases) The mixing matrix 119880 can beparameterized as

119880PMNS = (1 0 0

0 1198882311990423

0 minus1199042311988823

)

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

Atmospheric mixing

times (

11988813

0 11990413119890minus119894120575CP

0 1 0

minus11990413119890119894120575CP 0 119888

13

)

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

Reactor mixing

times (

11988812119904120

minus11990412119888120

0 0 1

)

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

Solar mixing

(2)

where 119888119894119895= cos 120579

119894119895and 119904119894119895= sin 120579

119894119895 The neutrino mixing

matrix finally takes the form

119880PMNS

= (

1198881211988813

1199041211988813

11990413119890minus119894120575CP

minus1199041211988823minus 119888121199042311990413119890119894120575CP 119888

1211988823minus 119904121199042311990413119890119894120575CP 119904

2311988813

1199041211990423minus 119888121198882311990413119890119894120575CP minus119888

1211990423minus 119904121198882311990413119890119894120575CP 119888

2311988813

)

(3)

It is quite interesting to note that three mixing angles aresimply related to the flavor components of the three masseigenstates as

1003816100381610038161003816119880119890210038161003816100381610038162

1003816100381610038161003816119880119890110038161003816100381610038162= tan2120579

12

100381610038161003816100381610038161198801205833

10038161003816100381610038161003816

2

1003816100381610038161003816119880120591310038161003816100381610038162= tan2120579

23

|1198801198903|2= sin2120579

13

(4)

The transition probability that an initial ]120572of energy 119864 gets

converted to a ]120573after traveling a distance 119871 in vacuum is

given by

119875 (]120572997888rarr ]120573) = 119875120572120573=

10038161003816100381610038161003816100381610038161003816100381610038161003816

sum

119895

119880120573119895119890minus1198941198982

1198951198712119864119880lowast

120572119895

10038161003816100381610038161003816100381610038161003816100381610038161003816

2

(5)

where the last factor arises from the decomposition of ]120572into

the mass eigenstates the phase factor in the middle appearsdue to the propagation of each mass eigenstate over distance119871 and the first factor emerges from their recomposition intothe flavor eigenstate ]

120573at the end Equation (5) can also be

written as

119875120572120573= 120575120572120573minus 4

119899

sum

119894gt119895

Re [119880lowast120572119894119880lowast

120573119895119880120573119894119880120572119895] sin2119883

119894119895

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

CP conserving

minus 2

119899

sum

119894gt119895

Im [119880lowast120572119894119880lowast

120573119895119880120573119894119880120572119895] sin2119883

119894119895

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

CP violating

(6)

where

119883119894119895=(1198982

119894minus 1198982

119895) 119871

4119864= 127

Δ1198982

119894119895

eV2119871119864

119898MeV (7)

Δ1198982

119894119895= 1198982

119894minus 1198982

119895is known as the mass splitting and neutrino

oscillations are only sensitive to this mass-squared differencebut not to the absolute neutrino mass scale The transitionprobability (given by (6)) has an oscillatory behaviour withoscillation lengths

119871osc119894119895=4120587119864

Δ1198982119894119895

≃ 248m 119864 (MeV)Δ1198982119894119895(eV2)

= 248 km 119864 (GeV)Δ1198982119894119895(eV2)

(8)

and the amplitudes are proportional to the elements in themixing matrix Since neutrino oscillations can occur only ifthere is a mass difference between at least two neutrinos anobservation of this effect proves that at least one nonzeroneutrino mass exists In a three-flavor framework there aretwo independentmass-squared differences between the threeneutrino masses Δ1198982

21= 1198982

2minus 1198982

1(responsible for solar

neutrino oscillations) and Δ119898231= 1198982

3minus 1198982

1(responsible for

atmospheric neutrino oscillations) The angle 12057913

connectsthe solar sector with the atmospheric one and determinesthe impact of the three-flavor effects The last term of (6)accommodates the CP violating part proportional to sin 120575CPThis contribution can only be probed in a neutrino oscillationexperiment measuring the appearance probability of a newflavor since for disappearance experiments (120572 = 120573) the lastterm becomes zero identically Also the CP violating termchanges sign in going from 119875(]

120572rarr ]120573) to 119875(]

120572rarr ]120573) (for

antineutrino we have to replace119880 by119880lowast) It also changes signin going from 119875(]

120572rarr ]120573) to 119875(]

120573rarr ]120572) since the CPT

invariance ensures that 119875(]120572rarr ]120573) = 119875(]

120573rarr ]120572)

3 Neutrino Propagation through Matter

Oscillation probability changes dramatically when neutrinopasses through matter [80ndash82] During propagation throughmatter the weak interaction couples the neutrinos to matter


Besides few hard scattering events there is also coherentforward elastic scattering of neutrinos with matter particlesthey encounter along the path The important fact is thatthe coherent forward elastic scattering amplitudes are not thesame for all neutrino flavors The ordinary matter consists ofelectrons protons and neutrons but it does not contain anymuons or tau-leptons Neutrinos of all three flavors (]

119890 ]120583

and ]120591) interact with the electrons protons and neutrons of

matter through flavor-independent neutral current interac-tionmediated by1198850 bosonsThese contributions are the samefor neutrinos of all three flavors leading to an overall phasewhich can be subtracted Interestingly the electron neutrinoshave an additional contribution due to their charged currentinteractions with the ambient electrons of the mediumwhichare mediated by the119882plusmn exchangeThis extra matter potentialappears in the form

119860 = plusmn2radic2119866119865119873119890119864 (9)

where 119866119865is the Fermi coupling constant 119873

119890is the electron

number density inside the Earth and119864 is the neutrino energyThe + sign refers to neutrinos while the minus to antineutrinosThe connection between the electron density (119873

119890) and the

matter density (120588) is given by

119881119862119862= radic2119866

119865119873119890≃ 76119884

119890

120588

1014 gcm3eV (10)

where 119884119890= 119873119890(119873119901+ 119873119899) is the relative electron number

density 119873119901 119873119899are the proton and neutron densities in

Earthrsquosmatter respectively In an electrically neutral isoscalarmedium we have 119873

119890= 119873119901= 119873119899and 119884

119890comes out to be

05 If we compare the strength of 119881119862119862

for the Earth withΔ1198982

312119864 then we can judge the importance of Earthrsquos matter

effect on neutrino oscillations If we consider a neutrino of5GeV passing through the core of the Earth (120588 sim 10 gcm3)then 119881

119862119862is comparable with Δ1198982

312119864 (= 24 times 10minus13 eV if

Δ1198982

31= 24 times 10

minus3 eV2)In a two-flavor formalism the time evolution of the flavor

eigenstates in matter is given by the following Schrodingerequation

119894119889

119889119905(]120572

]120573

) =1

2119864[119880(

1198982

10

0 1198982

2

)119880dagger+ (119860 (119871) 0

0 0)](

]120572

]120573

)

(11)

In case of constant matter density the problem boils downto a stationary one and a trivial diagonalization of theHamiltonian can provide the solution In matter the vacuumoscillation parameters are connected to the new parameters(the new parameters in matter carry a superscript 119898) in thefollowing way

(Δ1198982)119898

= radic(Δ1198982 cos 2120579 minus 119860)2 + (Δ1198982 sin 2120579)2

sin 2120579119898 = sin 2120579Δ1198982

(Δ1198982)119898

(12)

The famous MSW-resonance [80ndash83] condition is satisfied at

Δ1198982 cos 2120579 = 119860 (13)

At MSW-resonance sin 2120579119898 = 1 (from (12) and (13) whichimmediately implies that independent of the value of thevacuum mixing angle 120579 the mixing in matter is maximalthat is 120579119898 = 1205874 This resonance occurs for neutrinos(antineutrinos) if Δ1198982 is positive (negative) It suggeststhat the matter potential modifies the oscillation probabilitydifferently depending on the sign of Δ1198982 Following (13) theresonance energy can be expressed as

119864res = 1083GeV[Δ1198982

24 times 10minus3 eV2]

sdot [cos 2120579096

] sdot [28 gcm3

120588]

(14)

When neutrino travels through the upper part of the Earthmantle with 120588 = 28 gcm3 the resonance occurs atroughly 108GeV for positive Δ1198982 of 24 times 10minus3 eV2 TheMSW potential arises due to matter and not antimatterand this fact is responsible for the observed asymmetrybetween neutrino and antineutrino oscillation probabilitieseven in the two-neutrino case In three-flavor scenariobesides the genuine CP asymmetry caused by the CP phase120575CP we also have fake CP asymmetry induced by matterwhich causes hindrances in extracting the information on120575CP

4 Global Status of Oscillation Parameters andMissing Links

Oscillation data cannot predict the lowest neutrino massHowever it can be probed in tritium beta decay [84] orneutrinoless double beta decay [85] processes We can alsomake an estimation of the lowest neutrinomass from the con-tribution of neutrinos to the energy density of the universe[86] Very recent measurements from the Planck experimentin combination with the WMAP polarization and baryonacoustic oscillation data have set an upper bound over thesum of all the neutrino mass eigenvalues ofsum119898

119894le 023 eV at

95CL [87] But oscillation experiments are sensitive to thevalues of two independent mass-squared differences Δ1198982

21

and Δ119898231 Recent global fit [27] of all the available neutrino

oscillation data in three-flavor framework is given as best-fit Δ1198982

21= 75 times 10

minus5 eV2 and |Δ119898231| = 24 times 10

minus3 eV2with the relative 1120590 precision of 24 and 28 respectivelyThe atmospheric mass splitting is 32 times larger than thesolar mass splitting showing the smallness of the ratio 120572 =Δ1198982

21Δ1198982

31≃ 003 At present the 3120590 allowed range for

Δ1198982

21is 70 times 10minus5 eV2 rarr 81 times 10

minus5 eV2 and the same for|Δ1198982

31| is 22 times 10minus3 eV2 rarr 27 times 10

minus5 eV2 Δ119898221is required

to be positive to explain the observed energy dependence ofthe electron neutrino survival probability in solar neutrinoexperiments but Δ1198982

31is allowed to be either positive or

negative by the present oscillation data Hence two patternsof neutrino masses are possible 119898

3gt 1198982gt 1198981 called NH

where Δ119898231is positive and 119898

2gt 1198981gt 1198983 called IH where

Δ1198982

31is negative Determining the sign of Δ1198982

31is one of the


prime goals of the current- andnext-generation long-baselineneutrino oscillation experiments

As far as the mixing angles are concerned the solar neu-trino mixing angle 120579

12is now pretty well determined with a

best-fit value of sin212057912= 03 and the relative 1120590 precision on

this parameter is 4The 3120590 allowed range for this parameteris 027 rarr 035 The smallest lepton mixing angle 120579

13has

been discovered very recently with a moderately large best-fitvalue of sin2120579

13= 0023 The relative 1120590 precision achieved

on this parameter is also quite remarkable which is around10The error in themeasurement of sin2120579

13lies in the range

of 0016 rarr 0029 at 3120590 confidence level The uncertaintyassociated with the choice of reactor ]

119890fluxes [88ndash90] and its

impact on the determination of 12057913

have been discussed indetail in Section 3 of [27] Here we would like to emphasizeon that fact that the values of 120579

13measured by the recent

reactor and accelerator experiments are consistent with eachother within errors providing an important verification ofthe framework of three-neutrino mixing These recent onsetof data from reactor and accelerator experiments will alsoenable us to explore the long expected complementaritybetween these two independent measurements [40 91ndash93]Our understanding of the 2-3 mixing angle 120579

23has also been

refined a lot in recent years The best-fit values and rangesof 12057923

obtained from the three recent global fits [25ndash27] arelisted in Table 1 A common feature that has emerged from allthe three global fits is that we now have hint for nonmaximal12057923 giving two degenerate solutions either 120579

23belongs to the

LO (sin212057923asymp 04) or it lies in the HO (sin2120579

23asymp 06) This

octant ambiguity of 12057923 in principal can be resolved with

the help of ]120583harr ]119890oscillation data The preferred value

would depend on the choice of the neutrino mass orderingHowever as can be seen from Table 1 the fits of [25] do notagree on which value should be preferred even when themass ordering is fixed to be NH LO is preferred over HO forboth NH and IH in [26] Reference [27] marginalizes overthe mass ordering so the degeneracy remains The globalbest-fits in [25 27] do not see any sensitivity to the octantof 12057923unless they add the information from the atmospheric

neutrinos But in [26] they do find a preference for LO evenwithout adding the atmospheric neutrino data At presentthe relative 1120590 precision on sin2120579

23is around 11 Further

improvement in themeasurement of 12057923and settling the issue

of its octant (if it turns out to be nonmaximal) are also thecrucial issues that need to be addressed in current- and next-generation long-baseline experiments Leptonic CP violationcan be established if CP violating phase 120575CP is shown to differfrom 0 and 180∘ We have not seen any signal for CP violationin the data so far Thus 120575CP can have any value in the range[minus180

∘ 180∘] Measuring the value of 120575CP and establishing

the CP violation in the neutral lepton sector would be thetop most priorities for the present and future long-baselineexperiments

Due to the fact that both 120572 and 12057913are small so far it was

possible to analyze the data from each neutrino oscillationexperiment adopting an appropriate effective two-flavoroscillation approach This method has been quite successfulinmeasuring the solar and atmospheric neutrino parametersThe next step must involve probing the full three-flavoreffects including the subleading ones which are proportionalto 120572 These are the key requirements to discover neutrinomass hierarchy CP violation and octant of 120579

23in long-

baseline experiments [94 95]

5 Three-Flavor Effects in ]120583rarr ]119890

Oscillation Channel

To illustrate the impact of three-flavor effects the mostrelevant oscillation channels are ]

120583rarr ]119890and ]

120583rarr ]119890

A study of these oscillation channels at long-baseline super-beam experiments is capable of addressing all the threemajorissues discussed in the previous section In particular theuse of an appearance channel in which the neutrino changesflavor between production and detection is mandatory toexplore CP violation in neutrino oscillations Earthrsquos mattereffects are also going to play a significant role in probingthese fundamental unknowns The exact expressions of thethree-flavor oscillation probabilities including matter effectsare very complicatedTherefore to demonstrate the nature ofneutrino oscillations as a function of baseline andor neutrinoenergy it is quite useful to have an approximate analyticexpression for 119875

120583119890(the 119879-conjugate of 119875

119890120583) in matter [80

82 96] keeping terms only up to second order in the smallquantities 120579

13and 120572 [97ndash99]

119875120583119890≃ sin2120579

23sin22120579

13

sin2 [(1 minus 119860)Δ]

(1 minus 119860)2

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

1198620

+ 1205722cos2120579

23sin22120579

12

sin2(119860Δ)1198602⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

1198621

∓ 120572 sin 212057913cos 12057913sin 2120579

12sin 2120579

23sin (Δ)

sin (119860Δ)

119860

sin [(1 minus 119860)Δ]

(1 minus 119860)⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

119862minus

sin 120575CP


+ 120572 sin 212057913cos 12057913sin 2120579

12sin 2120579

23cos(Δ) sin(119860Δ)

119860

sin[(1 minus 119860)Δ](1 minus 119860)⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

119862+

cos 120575CP

(15)

where

Δ equivΔ1198982

31119871

4119864 119860 equiv

119860

Δ119898231

(16)

Equation (15) has been derived under the constant matterdensity approximation The matter effect is expressed by thedimensionless quantity 119860 The ldquominusrdquo sign which precedes theterm 119862

minusrefers to neutrinos whereas the ldquo+rdquo refers to to

antineutrinos In (15) 120572 Δ and 119860 are sensitive to the signof Δ1198982

31 that is the type of the neutrino mass ordering Note

that the sign of 119860 changes with the sign of Δ119898231

as well asin going from neutrino to the corresponding antineutrinomode The former suggests that the matter effect can beutilized to determine the sign ofΔ1198982

31 while the latter implies

that it can mimic a CP violating effect and hence complicatethe extraction of 120575CP by comparing neutrino and antineutrinodata For large 120579

13 the first term of (15) (119862

0) dominates

and it contains the largest Earth matter effect which cantherefore be used to measure the sign of Δ1198982

31 This term also

depends on sin212057923

and therefore is sensitive to the octantof 12057923 The subdominant terms 119862

minusand 119862

+are suppressed

by 120572 and provide information on 120575CP The term 119862minusis the

CP-violating part The term 119862+ although 120575CP-dependent is

CP-conserving The term 1198621is independent of both 120579

13and

120575CP and depends mainly on the solar parameters Δ119898221

and12057912

51 Hierarchy-120575CP Degeneracy Since the hierarchy and 120575CPare both unknown the interplay of the terms 119862

0 119862minus and

119862+

in (15) gives rise to hierarchy-120575CP degeneracy [39]This degeneracy can be broken completely using the largeEarth matter effects provided by the baselines which aregt1000 km [41 100 101] For these long baselines we canalso observe both the first and second oscillation maximaquite efficiently using the detectors like Liquid Argon TimeProjection Chamber (LArTPC) [102] It helps to evade theproblem of (sgn(Δ1198982

31) 120575CP) degeneracy [39] and (120579

13 120575CP)

intrinsic degeneracy [38] which can cause the 120587-transit [103]effect even for large values of sin22120579

13 Adding data from two

different experiments with different baselines can also be veryuseful to resolve this degeneracy [37 39 104ndash107] Anotherelegant way to tackle these degeneracies is to kill the spuriousclone solutions at the ldquomagicrdquo baseline [36 73 108 109]When sin(119860Δ) = 0 the last three terms in (15) drop out andthe 120575CP dependence disappears from the 119875

120583119890channel which

provides a clean ground for 12057913

and sgn(Δ119898231) measure-

ments Since 119860Δ = plusmn(2radic2119866119865119899119890119871)4 by definition the first

nontrivial solution for the condition sin(119860Δ) = 0 reducesto 120588119871 = radic2120587119866

119865119884119890 This gives (120588[g119888119888])(119871[km]) ≃ 32725

which for the PREM density profile of the Earth is satisfiedfor the ldquomagic baselinerdquo 119871magic ≃ 7690 km The CERNto India-Based Neutrino Observatory (INO) [110] distancecorresponds to 119871 = 7360 km which is tantalizingly close tothis ldquomagicrdquo baseline Performing a long-baseline experimentat ldquoBimagicrdquo baseline can be also very promising to suppressthe effect of these degeneracies [111 112] Note that the low-order expansion of the probability 119875

120583119890given by (15) is valid

only for values of 119864 and Earth matter density 120588 (and hence119871) where flavor oscillations are far from resonance that is119860 ≪ 1 In the limit 119860 sim 1 one can check that eventhough the analytic expression for 119875

120583119890given by (15) remains

finite the resultant probability obtained is incorrect [113 114]Whilewewill use this analytical formula to explain our resultsin some cases all the simulations presented in this reviewarticle are based on the full three-flavor neutrino oscillationprobabilities inmatter using the Preliminary Reference EarthModel (PREM) [115]

The transition probability119875120583119890as a function of the neutrino

energy is shown in Figure 2 We allow 120575CP to vary within therange minus180∘ to 180∘ and the resultant probability is shownas a band with the thickness of the band reflecting theeffect of 120575CP on 119875

120583119890 Inside each band the probability for

120575CP = 90∘ (120575CP = minus90

∘) case is shown explicitly by thesolid (dashed) line In each panel the blue (red) band isfor NH (IH) Left panel (right panel) depicts the probabilityfor neutrino (antineutrino) In upper panels we take thebaseline of 295 kmwhich matches with the distance of Tokai-to-Kamioka (T2K) experiment [116 117] in Japan In lowerpanels we consider the baseline of 810 km which is thedistance between Fermilab and Ash River chosen for theNuMI Off-Axis Neutrino Appearance (NO]A) experiment[118ndash120] in theUnited StatesMatter effect increases119875(]

120583rarr

]119890) for NH and decreases it for IH and vice versa for 119875(]

120583rarr

]119890) For 120575CP in the lower half-plane ((LHP) minus180∘ le 120575CP le0) 119875(]

120583rarr ]

119890) is larger and for 120575CP in the upper half-

plane ((UHP) 0 le 120575CP le 180∘) 119875(]

120583rarr ]119890) is smaller

Hence for the combination (NH LHP) the values of119875(]120583rarr

]119890) are much higher than those for IH (and 119875(]

120583rarr ]119890)

values are much lower) Similarly for the combination (IHUHP) the values of 119875(]

120583rarr ]

119890) are much lower than

those of NH (and 119875(]120583rarr ]119890) values are much higher)

Thus LHP is the favorable half-plane for NH and UHP isfavorable for IH [72 121] For T2K baseline the matter effectis very small and therefore the 120575CP bands drawn for NH andIH overlap for almost entire range of 120575CP (except for themost favorable combinations like NH 120575CP = minus90

∘ and IH120575CP = 90

∘) for almost all the choices of 119864 NO]A has betterchances to discriminate between NH and IH compared toT2K because of its larger baseline causing larger matter effect


Table 1 1120590 bounds on sin212057923from the global fits performed in [25ndash27] The numbers cited from [27] have been obtained by keeping the

reactor fluxes free in the fit and also including the short-baseline reactor data with 119871 ≲ 100m with the mass hierarchy marginalized Thistable has been taken from [71]

Reference Forero et al [25] Fogli et al [26] Gonzalez-Garcia et al [27]sin212057923(NH) 0427

+0034

minus0027oplus 0613

+0022

minus00400386

+0024

minus0021

041+0037

minus0025oplus 059

+0021

minus0022

034 rarr 067

3120590 range 036 rarr 068 0331 rarr 0637

sin212057923(IH) 0600

+0026

minus00310392

+0039

minus0022

3120590 range 037 rarr 067 0335 rarr 0663

But for the unfavorable combinations like NH 120575CP = 90∘

and IH 120575CP = minus90∘ the NH and IH bands still overlap

with each other In the upper panels of Figure 3 we studythe same for the Long-Baseline Neutrino experiment (LBNE)[122ndash125] baseline of 1300 km which is the distance betweenthe Fermilab and the Homestake mine in South Dakotain the United States The lower panels of Figure 3 depictthe hierarchy-120575CP degeneracy pattern for the Long-BaselineNeutrino Oscillation experiment (LBNO) [126ndash130] baselineof 2290 km which is the distance between the CERN and thePyhasalmi mine in Finland For both the LBNE and LBNObaselines thematter effects are substantial and they break thehierarchy-120575CP degeneracy completely

52 Octant-120575119862119875

Degeneracy There is a similar octant-120575CPdegeneracy also in the 119875

120583119890channel which limits our ability

to determine the correct octant of 12057923

[35] The upper left(right) panel of Figure 4 shows 119875

120583119890versus 119864] (119875

120583 119890versus

119864]) for all possible values of 120575CP and for the two differentvalues of sin2120579

23 assuming NH to be the true hierarchy

These plots are drawn for the T2K experiment The lowerpanels show the same for the NO]A baseline As can be seenfrom the upper and lower left panels of Figure 4 for neutrinodata the two octant bands overlap for some values of 120575CPand are distinct for other values The combinations of octantand 120575CP which lie farthest from overlap will be favorablecombinations for octant determination For example LO and120575CP of 90∘ and HO and 120575CP of minus90∘ form the favorablecombinations For the combinations with overlap HO and120575CP of 90∘ and LO and 120575CP of minus90∘ it is impossible todetermine octant using neutrino data alone However as wesee from the upper and lower right panels these unfavorablecombinations for neutrino case are the favorable ones forthe antineutrino case Thus a combination of neutrino andantineutrino data will have a better capability to determineoctant compared to neutrino data alone This is in contrastto the hierarchy-120575CP degeneracy where for a given hierarchythe favorable 120575CP region is the same for both neutrino andantineutrino Thus we draw the conclusion that a balancedneutrino and antineutrino data is imperative for resolvingthe octant ambiguity of 120579

23for all values of 120575CP [71]

The octant-120575CP degeneracy pattern for the LBNE (LBNO)experiment can be seen from the upper (lower) panels ofFigure 5

6 Present-Generation Beam ExperimentsT2K and NO^A

With the aim to unravel the 12057913-driven ]

120583rarr ]119890appearance

oscillation the T2K experiment [116 117] started its journeyin 2010 and the NO]A experiment [118ndash120] in the UnitedStates is now under construction and will start taking datanear the end of this year The detection of electron neu-trino appearance in a ]

120583beam is the prime goal of these

experiments and their experimental setups are optimized toachieve this target Both the T2K and NO]A experimentsuse the classic off-axis beam technique [131] that deliversa narrow peak in the energy spectrum tuned to be at theexpected oscillation maximum Furthermore this off-axistechnology helps to reduce the background coming fromthe intrinsic ]

119890contamination in the beam and a smaller

fraction of high-energy tails reduces the background comingfrom neutral current events As a result it improves thesignal-to-background ratio a lot With the recent discoveryof a moderately large value of 120579

13 these current-generation

experiments are now poised to probe the impact of fullthree-flavor effects to discover neutrino mass hierarchy CPviolation and octant of 120579

23 But to achieve these goals

they need to have very high proton beam powers of order1MW and detectors with huge fiducial masses (of order10 kilotons) and therefore these experiments are knownas ldquosuperbeamrdquo experiments Next we briefly describe themain features of the T2K and NO]A experiments andthen we present the physics reach of these experiments inlight of the recently discovered moderately large value of12057913

61 T2K T2K uses the 50 kilotons Super-Kamiokande waterCherenkov detector (fiducial volume 225 kilotons) as the fardetector for the neutrino beam from J-PARC The detectoris at a distance of 295 km from the source at an off-axisangle of 25∘ [116] The neutrino flux is peaked sharply atthe first oscillation maximum of 06GeV The experiment isscheduled to run for 5 years in the neutrino mode with apower of 075MW Because of the low energy of the peak fluxthe neutral current backgrounds are small and they can berejected based on energy cut The signal efficiency is 87 Toestimate the physics sensitivity the background informationand other details are taken from [132 133]


01

0

009

008

007

006

005

004

003

002

001

02 04 06 08 1 12

E (GeV)

P120583e()

01

0

009

008

007

006

005

004

003

002

001

02 04 06 08 1 12

E (GeV)P120583e(anti-)

L = 295 km sin2212057913 = 0089 sin212057923 = 05

(a)

05 1 15 2 25 3 35 4

01

0

009

008

007

006

005

004

003

002

001

E (GeV)

NHIH

120575CP = minus90∘

120575CP = +90∘

05 1 15 2 25 3 35 4

E (GeV)

NHIH

120575CP = minus90∘

120575CP = +90∘

01

0

009

008

007

006

005

004

003

002

001

L = 810 km sin2212057913 = 0089 sin212057923 = 05

P120583e(anti-)

P120583e()

(b)

Figure 2 The transition probability 119875120583119890as a function of neutrino energy The band reflects the effect of unknown 120575CP Inside each band the

probability for 120575CP = 90∘ (120575CP = minus90

∘) case is shown by the solid (dashed) lineThe blue (red) band is for NH (IH)The left panel (right panel)is for ] (]) The upper panels are drawn for the T2K baseline of 295 kmThe lower panels are for the NO]A baseline of 810 km Here we takesin22120579

13= 0089 and sin2120579

23= 05

62 NO]A NO]A is a 14 kilotons totally active scintillatordetector (TASD) placed at a distance of 810 km from Fermi-lab at a location which is 08∘ off-axis from the NuMI beamBecause of the off-axis location the flux of the neutrinos is

reduced but is sharply peaked around 2GeV again close to thefirst oscillation maximum energy of 17 GeV in 119875(]

120583rarr ]119890)

The most problematic background in NO]A experimentis neutral current interactions which mostly consist in the


012

01

008

006

004

002

01 2 3 4 5 6 7

E (GeV)

012

01

008

006

004

002

01 2 3 4 5 6 7


P120583e()

L = 1300 km sin2212057913 = 0089 sin212057923 = 05

(a)

NHIH

120575CP = minus90∘

120575CP = +90∘

012

01

008

006

004

002

01 2 3 4 5 6 7 8 9 10

E (GeV)

NHIH

120575CP = minus90∘

120575CP = +90∘

1 2 3 4 5 6 7 8 9 10

E (GeV)

012

01

008

006

004

002

0

L = 2290 km sin2212057913 = 0089 sin212057923 = 05

P120583e(anti-)

P120583e()

(b)

Figure 3 119875120583119890as a function of neutrino energy Here the bands correspond to different values of 120575CP from minus180

∘ to 180∘ Inside each bandthe probability for 120575CP = 90

∘ (120575CP = minus90∘) case is shown by the solid (dashed) line The blue (red) band is for NH (IH) The left panel (right

panel) is for ] (]) The upper panels are drawn for the LBNE baseline of 1300 km The lower panels are for the LBNO baseline of 2290 kmHere we take sin22120579

13= 0089 and sin2120579

23= 05

single 1205870 production However the measured energy of thisbackground is shifted to values of energy below the regionwhere the flux is significant Hence this background canbe rejected using a simple kinematic cut The experiment is

scheduled to have three-year run in neutrino mode first andthen later three-year run in antineutrino mode as well witha NuMI beam power of 07MW corresponding to 6 times 1020protons on target per year The details of the experiment


012

01

008

006

004

002

002 04 06 08 1 12

E (GeV)02 04 06 08 1 12

E (GeV)

01

009

008

007

006

005

004

003

002

001

0

L = 295 km sin2212057913 = 0089 NH

P120583e(anti-)

P120583e()

(a)

LOHO

120575CP = minus90∘

120575CP = +90∘

012

01

008

006

004

002

005 15 25 351 2 3 4

E (GeV)

009

008

007

006

005

004

003

002

001

005 15 25 351 2 3 4

E (GeV)

LOHO

120575CP = minus90∘

120575CP = +90∘

L = 810 km sin2212057913 = 0089 NH

P120583e(anti-)

P120583e()

(b)

Figure 4 119875120583119890as a function of neutrino energy Here the bands correspond to different values of 120575CP ranging from minus180

∘ to 180∘ Inside eachband the probability for 120575CP = 90

∘ (120575CP = minus90∘) case is shown by the solid (dashed) line The red (blue) band is for HO with sin2120579

23= 059

(LO with sin212057923= 041)The left panel (right panel) is for ] (])The upper panels are drawn for the T2K baseline of 295 kmThe lower panels

are for the NO]A baseline of 810 km Here we consider sin2212057913= 0089 and NH


E (GeV)

012

01

008

006

004

002

1 2 3 4 5 6 70

E (GeV)1 2 3 4 5 6 7

009

008

007

006

005

004

003

002

001

0

L = 1300 km sin2212057913 = 0089 NH

P120583e(anti-)

P120583e()

(a)

E (GeV)

LOHO

120575CP = minus90∘

120575CP = +90∘

1 2 3 4 5 6 7 8 9 10

012

014

01

008

006

004

002

0

E (GeV)

LOHO

120575CP = minus90∘

120575CP = +90∘

012

01

008

006

004

002

01 2 3 4 5 6 7 8 9 10

P120583e(anti-)

P120583e()

L = 2290 km sin2212057913 = 0089 NH

(b)




23= 059

(LO with sin212057923= 041) The left panel (right panel) is for ] (]) The upper panels are drawn for the LBNE baseline of 1300 km The lower

panels are for the LBNO baseline of 2290 km Here we consider sin2212057913= 0089 and NH

are given in [120] In light of the recent measurement oflarge 120579

13 NO]A has reoptimized its event selection criteria

Relaxing the cuts they now allow more events in both signaland background Additional neutral current backgrounds are

reconstructed at lower energies and can be managed by akinematical cut In our calculations we use these reoptimizedvalues of signal and background the details of which aregiven in [72 134]


63 Mass Ordering and CP Violation Discovery In thissection we describe the capabilities of the T2K and NO]Aexperiments for the determination of mass hierarchy and CPviolation We use GLoBES [135 136] software to simulate thedata for these experiments For the atmosphericacceleratorneutrino parameters we take the following central (true)values

10038161003816100381610038161003816Δ1198982

eff10038161003816100381610038161003816= 24 sdot 10

minus3 eV2 sin2212057923= 10 (17)

where Δ1198982eff is the effective mass-squared difference mea-sured by the accelerator experiments in ]

120583rarr ]

120583disap-

pearance channel [32 33] It is related to the Δ119898231

(larger)and Δ1198982

21(smaller) mass-squared differences through the

expression [137 138]

Δ1198982

eff = Δ1198982

31minus Δ119898

2

21

times (cos212057912minus cos 120575CP sin 12057913 sin 212057912 tan 12057923)

(18)

The value of Δ119898231

is calculated separately for NH and forIH using this equation where Δ1198982eff is taken to be +ve forNH and minusve for IH For 120579

23 we take the maximal mixing

as still favored by the Super-Kamiokande atmospheric data[34 139 140] For 120579

13 we take the best-fit value of sin2120579

13=

0026 The uncertainties in the above parameters are taken tobe 120590(sin2120579

13) = 13 [25] 120590(|Δ1198982eff|) = 4 and 120590(sin22120579

23) =

2 [116] In the calculation these pieces of information areincluded in the form of priors In our 1205942 fit we marginalizeover all oscillation parameterswithin theirplusmn3120590 ranges aswellas themass hierarchy by allowing these parameters to vary inthe fit and picking the smallest value of the 1205942 function Wetake the solar parameters to be

Δ1198982

21= 762 sdot 10

minus5 eV2 sin212057912= 032 (19)

We keep the solar parameters to be fixed throughout the cal-culation because varying them will have negligible effect Wealso take the Earth matter density to be a constant 28 gcm3because the variations and the uncertainties in density can beneglected for the T2K andNO]AbaselinesWhile calculatingthe sensitivity for T2K we include a 2 systematic error onappearance signal events and a (uncorrelated) 5 systematicerror on backgrounds For NO]A we have assumed 5systematic error on appearance signal events and a (uncor-related) 10 systematic error on background events Thesepieces of information on the systematic errors are includedin the 1205942 function using the pull method as described in forexample [103 141] In our definition of the 1205942 function wehave assumed that the neutrino and antineutrino channelsare completely uncorrelated all the energy bins for a givenchannel are fully correlated and the systematic errors onsignal and background are fully uncorrelated We performthe usual 1205942 analysis using a Poissonian likelihood functionadding the information coming from ]

119890appearance and ]

120583

disappearance channelsFor long-baseline experiments the measurement of the

mass hierarchy is easier than a measurement of 120575CP because

matter effects enhance the separation between the oscillationspectra and therefore the event rates of a NH and an IHAdditionally this measurement is one that is ldquodiscreterdquo aswe only need to differentiate between two possibilities Aldquodiscoveryrdquo of the mass hierarchy is defined as the ability toexclude any degenerate solution for the wrong (fit) hierarchyat a given confidence level A ldquodiscoveryrdquo of CP violationif it exists means being able to exclude the CP-conservingvalues of 0∘ 180∘ at a given confidence level Clearly thismeasurement becomes very difficult for the 120575CP values whichare closer to 0∘ 180∘Therefore whilst it is possible to discoverthe mass hierarchy for all possible values of 120575CP the same isnot true for CP violation

In Figure 6 we plot the hierarchy discrimination sensitiv-ity of the old NO]A the new NO]A (with reoptimized eventselection criteria for large 120579

13) and the combined sensitivity

of new NO]A and T2K as a function of the true value of 120575CPIn the left (right) panel we have assumed NH (IH) to be thetrue hierarchy We see that the wrong hierarchy can be ruledout very effectively for 120575CP in the favorable half-plane whichis LHP (UHP) for NH (IH) The new event selection criteriaof NO]A make the experiment even more effective in rulingout the wrong hierarchy for 120575CP in the favorable half-plane Inthe unfavorable half-plane both the old and the new criteriaare equally ineffective However the addition of T2K dataimproves the situation significantly and Δ1205942 increases from 0to ge 2 for all the true values of 120575CP thus making it possible toget a 90CL hint of hierarchy with some additional data Wehave checked that a further increment in the exposure of T2Kor addition of antineutrino data from T2K does not improvethe hierarchy sensitivity much

The prospects of determining the neutrino mass hier-archy with the combined data from T2K NO]A DoubleChooz RENO Daya Bay and the atmospheric neutrinoexperiment ICALINO [110] have been studied in detailin [143] With 10 years of atmospheric ICALINO datacollected by 50 kilotonsmagnetized iron calorimeter detectorcombined with T2K NOvA and reactor data a 23120590 minusminus57120590 discovery of the neutrino mass hierarchy could beachieved depending on the true values of sin2120579

23[04ndash06]

sin2212057913[008ndash012] and 120575CP[0ndash2120587] [143]

Reoptimization of the event selection criteria of NO]Ahas the most dramatic effect on the CP violation discoverypotential of the experiment In Figure 7 we plot the sensi-tivity to rule out the CP conserving scenarios as a functionof true 120575CP in the left (right) panel for NH (IH) being thetrue hierarchy We notice that while in the case of old NO]Athere is no CP violation sensitivity at all at 90 CL there issuch a sensitivity in new NO]A for about one-third fractionof the favorable half-plane Addition of T2K data leads toCP violation sensitivity for about half the region in bothfavorable half planes at 90 confidence level It can be shownthat T2K by itself has no CP violation sensitivity But thesynergistic combination of NO]A and T2K leads to muchbetter CP violation sensitivity compared to the individualcapabilities Here we would like to mention that a large valueof 12057913

always does not help for CP violation discovery As12057913becomes large the number of electron appearance event


120575CP (true)

95 CL

90 CL

Mass hierarchy discovery NH true

minus180 minus90 0 90 180

12

10

8

6

4

2

0

Δ1205942

New NOA (3 + 3)Old NOA (3 + 3)New NOA (3 + 3) + T2K (5 + 0)

(a)

120575CP (true)

95 CL

90 CL

Mass hierarchy discovery IH true


12

10

8

6

4

2

0

Δ1205942


(b)]

Figure 6 Left panel (right panel) shows the Δ1205942 for the mass hierarchy discovery as a function of true value of 120575CP assuming NH (IH) astrue hierarchy This figure has been taken from [72]

120575CP (true)

95 CL

90 CL

CP violation discovery NH true


8

6

5

7

4

2

1

3

0

Δ1205942


(a)

120575CP (true)

95 CL

90 CL

CP violation discovery IH true


8

6

5

7

4

2

1

3

0

Δ1205942


(b)

Figure 7 Left panel (right panel) shows the Δ1205942 for the CP violation discovery as a function of true value of 120575CP assuming NH (IH) as truehierarchy This figure has been taken from [72]


Table 2 Fractions of true values of 120575CP for which a discovery is possible for mass hierarchy and CP violation The numbers without (with)parentheses correspond to 90 (95) CL Here we take the central values sin2120579

13= 0026 and sin2120579

23= 05 The results are shown for both

NH and IH as true hierarchy This table has been taken from [72]

SetupsFraction of 120575CP(true)

Mass hierarchy CP violationNH true IH true NH true IH true

NO]A (3 + 3) 048 (043) 046 (041) 016 (0) 021 (004)NO]A (3 + 3) + T2K (5 + 0) 055 (045) 054 (043) 038 (011) 049 (023)

Table 3 Fractions of true values of 120575CP for which a discovery is possible for mass hierarchy and CP violation The numbers without (with)parentheses correspond to 90 (95) CL Here we take the central value for sin2120579

13to be 0023 as predicted by Daya Bay For sin2120579

23 the

best-fit value that we consider is 0413 The results are shown for both NH and IH as true hierarchy This table has been taken from [72]


MH CPVNH true IH true NH true IH true

NO]A (3 + 3) 039 (033) 037 (031) 02 (01) 022 (013)NO]A (3 + 3) + T2K (5 + 0) 041 (034) 039 (031) 028 (022) 03 (025)

increases reducing the statistical error However the largeatmospheric term acts as a background in the measurementof CP phase In fact the CP asymmetry term is proportionalto 1 sin 2120579

13[144 145] These two contradictory issues

make the measurement of CP phase quite complicated Thesystematic uncertainties are also going to play a crucial rolefor CP violation discovery in light of large 120579

13[146]

A summary of our results is given in Table 2 in terms ofthe fraction of 120575CP values for which mass hierarchy can bedeterminedCP violation can be detected Please note that inderiving the results given in Table 2 we have considered thebest-fit value of sin2120579

13= 0026 and maximal mixing for 120579

23

In Table 3 we present the same for the rather conservativechoices of neutrino mixing angles sin2120579

13= 0023 (the best-

fit value suggested by theDaya Bay experiment) and sin212057923=

0413 (the LO value of sin212057923

as indicated by the recentMINOS accelerator data)

In [72] we further explore the improvement in thehierarchy and CP violation sensitivities for T2K and NO]Adue to the addition of a 10 kilotons LArTPC placed close toNO]A site and exposed to the NuMI beam during NO]Arunning It is expected of course that such a detector willcome on line much later than NO]AThe capabilities of sucha detector are equivalent to those of NO]A in all aspects Wefind that combined data from 10 kilotons LArTPC (3 yearsof ] + 3 years of ] run) NO]A (6 years of ] + 6 years of ]run) and T2K (5 years of ] run) can give a close to 2120590 hint ofhierarchy discovery for all values of 120575CP With this combineddata we can achieve CP violation discovery at 95 CL forroughly 60 values of 120575CP A similar proposal considering6 kilotons LArTPC has been studied recently in detail in[147]

64 Resolving the Octant Ambiguity of 12057923 In this section we

study whether the expected appearance data from the ongo-ing T2K experiment and the upcoming NO]A experimentcan resolve the octant ambiguity of 120579

23or not

In Figure 8 we show neutrino events versus antineutrinoevents for various octant-hierarchy combinations In eachcase with varying values of 120575CP the plot becomes an ellipseThe left panel depicts these ellipses for T2K whereas the rightpanel shows the same for NO]A Here we assume that T2Kwill have equal ] and ] runs of 25 years each In the rightpanel we see that the ellipses for the two mass orderingsoverlap whereas the ellipses of LO are well separated fromthose ofHOHence we can expect thatNO]Awill have betteroctant resolution capability than hierarchy discriminationThis situation is even more dramatic in the left panel wherethere is large overlap between the two hierarchies but clearseparation between the octants Thus it is very likely thatantineutrino data from T2K may play an important role inthe determination of octant

In Figures 9 and 10 we study the behavior ofΔ1205942 betweenthe true and the wrong octants as a function of true 120575CP Herethe Δ1205942 is estimated in the following way First we fix thetrue value of 120575CP We take sin2120579

23to be its best-fit value in

the true octant 041 for LO and 059 for HO If the LO (HO)is the true octant the test values of sin2120579

23in the HO (LO)

are varied within the range [05 063] ([036 05]) where 063(036) is the 2120590 upper (lower) limit of the allowed range ofsin212057923 The Δ1205942 is computed between the spectra with the

best-fit sin212057923

of the true octant and that with various testvalues in the wrong octant and is marginalized over otherneutrino parameters especially the hierarchy sin22120579

13 and

120575CP Figures 9 and 10 portray theminimum of thisΔ1205942 versusthe true value of 120575CP

From Figure 9 we observe that the NO]A data by itselfcan almost rule out the wrong octant at 2120590 if LO is thetrue octant If HO is the true octant then NO]A data isnot sufficient to rule out the wrong octant as can be seenfrom Figure 10 In fact the wrong octant can be ruled outonly for about half of the true 120575CP values As illustratedin Figures 9 and 10 addition of T2K data improves theoctant determination ability significantly From Figure 9 we


20

18

16

14

12

10

8

620 25 30 35 40 45 50 55 60 65 70 75

LO-IH

HO-IH

HO-NH

LO-NH

minus90∘

090∘

180∘

T2K (25 + 25)A

nti-

app

even

ts

app events

(a)

minus90∘

0

90∘

180∘

LO-IH

HO-IH

HO-NH

LO-NH

50

45

40

35

30

25

20

15

1020 30 40 50 60 70 80 90 100 110

NOA (3 + 3)

Ant

i-ap

pev

ents

app events

(b)

Figure 8 Neutrino and antineutrino appearance events for all possible combinations of hierarchy octant and 120575CP The left (right) panel isfor T2K (NO]A) Here sin22120579

13= 0089 For LO (HO) sin2120579

23= 041 (059) Note that for T2K equal ] and ] runs of 25 years each have

been assumed This figure has been taken from [71]

120575CP (true)minus180 minus90 0 90 180

15

10

5

0

Octant discovery LO-NH true

NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

Δ1205942

(a)


15

10

5

0

Octant discovery LO-IH true

NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

Δ1205942

(b)

Figure 9 Octant resolving capability as a function of true 120575CP for various setups In these plots LO is assumed to be the true octant The left(right) panel corresponds to NH (IH) being the true hierarchy This figure has been taken from [71]



15

10

5

0

Octant discovery HO-NH trueΔ1205942

NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

(a)


15

10

5

0

Octant discovery HO-IH true

Δ1205942

NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

(b)

Figure 10 Octant resolving capability as a function of true 120575CP for various setups In these plots HO is assumed to be the true octant Theleft (right) panel corresponds to NH (IH) being the true hierarchy This figure has been taken from [71]

see that the combined data from NO]A and T2K (5-year] run) give a 2120590 octant resolution for all values of true120575CP if LO is the true octant From Figure 10 we see thatthis combined data can rule out the wrong octant at 2120590 forHO-IH but not for HO-NH The problem of HO-NH canbe solved if the T2K has equal ] and ] runs of 25 yearseach This change improves the octant determination for theunfavorable values of true 120575CP (where Δ1205942 is minimum) forall four combinations of hierarchy and octant In particularfor the case of HO-NH it leads to a complete rulingout of the wrong octant at 2120590 for all values of true 120575CPThus balanced runs of T2K in ] minus ] mode are preferredover a pure ] run because of better octant determinationcapability We observe that this feature of LO being morefavorable compared to HO is a consequence of marginal-ization over the oscillation parameters (mainly 120575CP) and thesystematic uncertainties We checked that in the absence ofany kind of marginalization Δ1205942HO is consistently larger thanΔ1205942

LOIn the discussion so far we have assumed the true values

of sin212057923

to be 041 for LO and 059 for HO These areof course the best-fit points from the global analyses Butwe must consider the octant resolution capability for valuesof true sin2120579

23in the full allowed range (034 to 067) In

Figure 11 we plot the 2120590 and 3120590 octant resolution contours intrue sin2120579

23-true 120575CP plane Octant resolution is possible only

for points lying outside the contours These figures clearlyshow that octant resolution is possible at 2120590 for global best-fit points and at 3120590 for MINOS best-fit points The results forthe two hierarchies are quite similar From Figure 11 we cansee that if T2K experiment would have equal neutrino andantineutrino runs of 25 years each a 2120590 resolution of theoctant becomes possible provided sin2120579

23le 043 or ge 058

for any value of 120575CP In [148] the possibility of determiningthe octant of 120579

23in the long-baseline experiments T2K

and NO]A in conjunction with future atmospheric neutrinodetectors has been studiedThe combined data fromT2K andNO]A can provide a sim 2 precision on sin2120579

23at 2120590 using

the information coming from the disappearance channel[71]

In this section we have discussed in detail the physicsreach of current generation long-baseline beam experimentsT2K and NO]A to unravel the neutrino mass hierarchyCP violation and octant of 120579

23 Given their relatively short

baselines narrowband beams and limited statistics theseexperiments suffer a lot from the hierarchy-120575CP and octant-120575CP degeneraciesThey can provide a hint for these unknownissues only for favorable ranges of parameters at limitedconfidence level Hence new long-baseline experiments withintense neutrino beam sources and advanced detector tech-nologies are mandatory [100 149ndash151] to fathom the hithertouncharted parameter space of the neutrino mixing matrixwell beyond the capabilities of T2K and NO]A


035 04 045 05 055 06 065

2120590

3120590 MINOS

sin212057923 (true)

120575CP

(true

) (de

g)

minus180

minus90

0

90

180Octant discovery NOA + T2K (25 + 25) NH

Global best-fit

(a)

035 04 045 05 055 06 065

2120590

3120590 MINOS

sin212057923 (true)

120575CP

(true

) (de

g)

minus180

minus90

0

90

180Octant discovery NOA + T2K (25 + 25) IH

Global best-fit

(b)

Figure 11 Octant resolving capability in the true sin212057923-true 120575CP plane for the combined 3]+ 3] runs of NO]A and 25]+ 25] runs of T2K

Both 2120590 and 3120590 CL contours are plotted The vertical lines correspond to the best-fit values of global data and those of MINOS acceleratordata The left (right) panel corresponds to NH (IH) being the true hierarchy This figure has been taken from [71]

7 Next Generation Long-BaselineBeam Experiments

In this section we briefly review the possible options forfuture high-precision long-baseline beam experiments witha special emphasis on high-power superbeam facilities usingliquid argon and water Cherenkov detectors As discussed inthe literature (see eg [149 152]) the ability of future long-baseline neutrino experiments to discover mass hierarchyoctant of 120579

23 and CP violation depends on the achievable

event statistics and hence strongly on the value of 12057913

The fact that 12057913

is large will have a significant impact onthe realization of future long-baseline neutrino oscillationexperiments for which planning till 2011 was focused ona staged approach to achieve sensitivity to increasinglysmaller values of 120579

13 This approach was exemplified in the

optimization of the neutrino factory [142 153] and beta-beam[154 155] experiments for which it was possible to discovera value of sin22120579

13as small as 10minus4 However following

the recent discovery of a moderately large value of 12057913 the

focus of future optimizations will be on the possibility toexplore mass hierarchy octant of 120579

23 and CP violation for a

given value of 12057913 A relatively large value of 120579

13also allows

us to pursue an incremental program staged in terms ofthe size of the experiment [100] producing significant newresults at each stage Out of the three major unknownsthe discovery of CP violation is the most toughest goal toachieve Hence the determination of mass hierarchy and

octant should be considered as the first step towards thediscovery of leptonic CP violation Future facilities must bedeveloped with the requirements that they should have thecapability to determine hierarchy and octant at 3120590 confidencelevel or better for any possible value of 120575CP during the firststage and discover CP violation and measure 120575CP during thesecond stage An incremental approach is also justified inview of the challenges (some of them are unknown) involvedin operating very-high-power superbeams and in buildinggiant underground neutrino detectors which makes such anapproach effectively safer and possibly more cost-effectiveBoth the proposed LBNE and LBNO facilities have adoptedthis staged approach in light of large 120579

13 First we present a

comparative study of the physics reach that can be achievedduring the first phase of these two proposed experimentsThen we talk about the proposals of J-PARC to Hyper-Kamiokande (T2HK) long-baseline superbeam experiment[156] and CERN to MEMPHYS (at Frejus) SPL super-beam experiment [157ndash160] We also discuss the possibilityto explore leptonic CP violation based on the EuropeanSpallation Source (ESS) proton linac which can deliververy intense cost-effective and high-performance neutrinobeam in parallel with the production of spallation neutron[161 162] Megaton-size water Cherenkov detector is one ofthe key components of these three experimental setups Nextwe discuss the physics prospects of Low-Energy NeutrinoFactory (LENF) [163ndash166] in conjunction with magnetizediron detector (MIND) [142 167 168] which seems to be a very


promising setup to explore leptonic CP violation for large 12057913

Finally wemention few proposals based onmonoflavor beta-beam concept [154 155 169ndash171]

71 Discovery Reach of LBNE and LBNO

LBNE The Long-Baseline Neutrino Experiment (LBNE)[125] is one of the major components of Fermilabrsquos intensityfrontier program In its first phase (LBNE10) it will have anew high-intensity on-axis neutrino beam directed towardsa 10 kilotons LArTPC located at Homestake with a baselineof 1300 km This facility is designed for initial operation ata proton beam power of 708 kW with proton energy of120GeV that will deliver 6 times 1020 protons on target in 230days per calendar year In our simulation we have used thelatest fluxes being considered by the collaboration whichhave been estimated assuming the smaller decay pipe andthe lower horn current compared to the previous studies[172] We have assumed five years of neutrino run and fiveyears of antineutrino run The detector characteristics havebeen taken from Table 1 of [100] To have the LArTPC cross-sections we have scaled the inclusive charged current cross-sections of water by 106 (094) for the ] (]) case [173 174]

LBNO The Long-Baseline Neutrino Oscillation experiment(LBNO) [130] plans to use an experimental setup whereneutrinos produced in a conventional wide-band beam facil-ity at CERN would be observed in a proposed 20 kilotons(in its first phase) LArTPC housed at the Pyhasalmi minein Finland at a distance of 2290 km The fluxes have beencomputed [175] assuming an exposure of 15times1020 protons ontarget in 200 days per calendar year from the SPS acceleratorat 400GeV with a beam power of 750 kW For LBNO alsowe consider five years of neutrino run and five years ofantineutrino run We assume the same detector properties asthose of LBNE

Event Spectrum at LBNE10 and LBNO Figure 12 portraysthe expected signal and background event spectra in the ]

119890

appearance channel as a function of reconstructed neutrinoenergy including the efficiency and background rejectioncapabilities for LBNE10 (left panel) and LBNO (right panel)setups In both panels of Figure 12 one can clearly see asystematic downward bias in the reconstructed energy forneutral current background events due to the final stateneutrino included using the migration matrices The bluedot-dashed and the orange dotted vertical lines displaythe locations of the first and second oscillation maximaThe green double-dotted-dashed histogram shows the signalevent rate Although we have some statistics around the sec-ond oscillation maximum for both the baselines its impactis limited due to the fact that the event samples are highlycontaminated with neutral current and other backgrounds atlower energies

Physics with Bievents Plots In Figure 13 we have plotted]119890versus ]

119890appearance events for LBNE10 and 05lowastLBNO

for the four possible combinations of hierarchy and octantSince 120575CP is unknown events are generated for [minus180

∘ 180∘]

leading to the ellipses Here we take sin2212057913= 0089 For

the lower octant (LO) of 12057923 the value sin2120579

23= 041 is

chosen and for higher octant (HO) it is taken to be 059 Notethat in Figure 13 we have plotted the total number of eventswhereas the actual analysis will be done based on the spectralinformation Nevertheless the contours in Figure 13 containvery important information regarding the physics capabilitiesof the experiments An experiment can determine both thehierarchy and the octant if every point on a given ellipse iswell separated from every point on each of the other threeellipses The larger the separation the better the confidencewith which the above parameters can be determined

For 05lowastLBNO the two (LOHO)-IH ellipses are wellseparated from the two (LOHO)-NH ellipses in theirnumber of neutrino events Hence 05lowastLBNO has excellenthierarchy determination capability with just neutrino dataHowever only neutrino data alone will not be sufficient todetermine the octant in case of IH because various pointson (LOHO)-IH ellipses have the same number of neutrinoevents Likewise only antineutrino data cannot determinethe octant in case of NH Therefore balanced neutrinoand antineutrino data is mandatory to make an effectivedistinction between (LOHO)-IH ellipses and also between(LOHO)-NH ellipses

For LBNE10 ] data alone cannot determine hierarchybecause various points on LO-NH and HO-IH ellipses havethe same number of ]

119890events Thus ] data is also needed

Even with ] data hierarchy determination can be difficultto achieve if nature chooses LO and one of the two worst-case combinations of hierarchy and 120575CP which are (NH90∘) or (IH minus90∘) In such a situation the ]

119890and ]

119890events

are rather close to each other and it will be very difficultfor LBNE10 to reject the wrong combination Regardingoctant determination the capability of LBNE10 is very similarto that of 05lowastLBNO because the separations between theellipses belonging to LO andHO are very similar for the twoexperiments

Hierarchy and Octant Discovery with LBNE10 and LBNOMeasurement of hierarchy and octant should be consideredas a prerequisite for the discovery of leptonic CP violation Topresent the results for mass hierarchy and octant discoverywe consider three experimental setups LBNE10 LBNO anda possible LBNO configuration with a detector half the mass(10 kilotons) which we denote as 05lowastLBNO Scaling downthe detector size of LBNO by half makes the exposures ofthese two experiments very similar Therefore considering05lowastLBNO enables us to make a direct comparison betweenthe inherent properties of the two baselines involved BothLBNE and LBNO will operate at multi-GeV energies withvery long baselines This will lead to a large enough mattereffect to break the hierarchy-120575CP degeneracy completelyTheyare also scheduled to have equal neutrino and antineutrinoruns tackling the octant-120575CP degeneracy These experimentsare planning to use LArTPCs [102 176] which have excellentkinematic reconstruction capability for all the observed


NC

101

100

10minus11 2 3 4 5

2nd OSC max

1st OSC max

Even

ts pe

r0125

GeV

bin

in5

yrs

Reconstructed neutrino energy (GeV)

Int (e)Mis-id (120583)Signal (120583 rarr e)

kt LAr at Homestake site (NH)10

(a)

101

100

10minus1

1 2 3 4 5 6 7 8

20 kt LAr at Phyasalmi site (NH)

2nd OSC max1st OSC max

NCEv

ents

per0125

GeV

bin

in5

yrs



(b)

Figure 12 Expected signal and background event rates in the ]119890appearance channel as a function of the reconstructed neutrino energy

including the efficiency and background rejection capabilities Here we consider sin2212057913= 00975 and 120575CP = 0

∘ Left panel (right panel) isfor LBNE10 (LBNO) A normal hierarchy has been assumed In both panels the blue dot-dashed and the orange dotted vertical lines displaythe locations of the first and second oscillation maxima

100

80

60

40

20

00 50 100 150 200 250

minus90∘

0

90∘

180∘

HO-IHHO-IH

HO-NH

HO-NHLO-NH

LO-NH

LO-IHLO-IH

LBNE10

Ant

i-ap

pev

ents

app events

05lowastLBNO

Electron appearance events for 05lowastLBNO and LBNE10

Figure 13 Bievents (]119890and ]

119890appearance) plots for the four octant-

hierarchy combinations and all possible 120575CP valuesThe experimentsconsidered are LBNE10 and 05lowastLBNO Here sin22120579

13= 0089 For

LO (HO) sin212057923= 041 (059) This figure has been taken from

[41]

particles This feature helps in rejecting quite a large fractionof neutral current background

We study the hierarchy discovery potential for two truevalues of sin2120579

23 041 (LO) and 05 (MM) If HO is true

the results will be better than those for the case of MM Thisgives us four true combinations of 120579

23-hierarchy LO-NH

LO-IH MM-NH and MM-IH Δ1205942 is calculated for eachof these four combinations assuming the opposite hierarchyto be the test hierarchy In the fit we marginalize over testsin212057923

in its 3120590 range and Δ119898231

and sin2212057913

in their 2120590ranges We considered 5 uncertainty in the matter density120588 Priors were added for 120588 (120590 = 5) Δ1198982

31(120590 = 4) and

sin2212057913(120590 = 5 as expected by the end of Daya Bayrsquos run)

Δ1205942 is also marginalized over the uncorrelated systematic

uncertainties (5 on signal and 5 on background) in thesetups so as to obtain a Δ1205942min for every 120575CP(true)

Figure 14 shows the discovery reach for hierarchy as afunction of 120575CP(true) We see that even 05lowastLBNO has ≳ 10120590hierarchy discovery for all values of 120575CP(true) and for allfour 120579

23-hierarchy combinations The potential of LBNO is

even better The LBNO baseline is close to Bimagic whichgives it a particular advantage [111 112] For LBNE10 a 5120590discovery of hierarchy is possible for only sim 50 of the120575CP(true) irrespective of the true 12057923-hierarchy combinationFor the unfavorable hierarchy-120575CP combinations that is NHwith 120575CP in the upper half-plane or IH with 120575CP in the lowerhalf-plane the performance of LBNE10 suffers In particularfor LO and the worst-case combinations ((NH 90∘) and(IH minus90∘)) LBNE10 will not be able to provide even a 3120590hierarchy discrimination Therefore LBNE10 must increasetheir statistics if NO]A data indicate that the unfavorablecombinations are true The discovery potential for all threesetups will be better if 120579

23happens to lie in HO But we


Hierarchy discovery Hierarchy discovery



101

102

103

LO-NH true


LO-IH true

LBNO

LBNE10


101

100

100

101

102

103

100

102

103

101

100

102

103

MM-NH true

LBNO

LBNE10


MM-IH true

Δ1205942

Δ1205942

Δ1205942

Δ1205942

05lowastLBNO 05lowastLBNO

120575CP (true) (deg) 120575CP (true) (deg)


Figure 14 Hierarchy discovery reach for LBNO 05lowastLBNO and LBNE10 Results are shown for the four possible true 12057923-hierarchy

combinations

checked that even then a 5120590 discovery is not possible withLBNE10 for sim 30 of the upper half-plane of 120575CP for HO-NHtrue andsim 70of the lower half-plane of 120575CP forHO-IH true

We next consider the discovery reach of the same setupsfor excluding thewrong octantWe consider the true values ofsin212057923= 041(LO) and sin2120579

23= 059(HO) so that we have

the following four true combinations of octant and hierarchyLO-NH LO-IH HO-NH and HO-IH Δ1205942 is calculated foreach of these four combinations assuming test sin2120579

23values

from the other octant For LO (HO) true we consider thetest sin2120579

23range from 05 to 067 (034 to 05) The rest of

the marginalization procedure (over oscillation parametersas well as systematic uncertainties) is the same as that in thecase of hierarchy exclusion exceptwith another difference thefinal Δ1205942 is marginalized over both the hierarchies as the testhierarchy to obtain Δ1205942min

Figure 15 shows the discovery reach for octant as afunction of 120575CP(true) It can be seen that for (LOHO)-IH

true the sensitivities of LBNE10 and 05lowastLBNO are quitesimilar whereas they are somewhat better for 05lowastLBNO if(LOHO)-NH are the true combinations For LO-(NHIH)both LBNE10 and 05lowastLBNO have more than 3120590 discoveryof octant while for HO-(NHIH) the Δ1205942min varies from sim6to sim11 However with full LBNO we have more than 35120590discovery of octant for all octant-hierarchy combinations A5120590 discovery of octant is possible only for LO-NH true for120575CP(true) isin (sim 20

∘ sim 150

∘)

CP Violation Discovery with LBNE10 and LBNO In their firstphases both LBNE10 and LBNO will have very minimal CPviolation reach Figure 16 depicts the CP violation discoveryreach for LBNE10 and LBNO In the left panel (right panel)we have considered NH (IH) as true hierarchy In Table 4 wemention the fraction of 120575CP values for which CP violation canbe detected for these two experimental setups Both LBNE10and LBNO have CP violation reach for around 50 values oftrue 120575CP at 2120590 confidence level At 3120590 their CP violation reachis quite minimal only for 10ndash20 of the entire range


Octant discovery Octant discovery



LO-NH true


LO-IH true

LBNO

LBNE10


HO-NH true

LBNO

LBNE10


HO-IH true

20

25

10

15

5

0

20

25

10

15

5

0

20

25

10

15

5

0

20

25

10

15

5

0

Δ1205942

Δ1205942

Δ1205942

Δ1205942


120575CP(true) (deg) 120575

CP(true) (deg)


Figure 15 Octant resolving capability for LBNO 05lowastLBNO and LBNE10 Results are shown for the four possible true octant-hierarchycombinations

Table 4 Fractions of 120575CP(true) for which a discovery is possible forCP violation The numbers without (with) parentheses correspondto NH (IH) as true hierarchy The results are presented at 2120590 and 3120590confidence level

Setups Fraction of 120575CP(true)2 120590 3 120590

LBNE10 (5 years ] + 5 years ]) 052 (056) 009 (026)LBNO (5 years ] + 5 years ]) 051 (054) 017 (019)

72 T2HK CERN-MEMPHYS and ESS LINAC ProposalsThe T2HK proposal [156] plans to use a 166MW super-beam from the upgraded J-PARC proton synchrotron facilitydirected to a 1 megaton water Cherenkov detector (withfiducial mass of 560 kilotons) located at a distance of 295 kmfrom the source at an off-axis angle of 25∘ A proposedlocation for this detector is about 8 km south of Super-Kamiokande at an underground depth of 1750 meters waterequivalentThemain purpose of this experiment is to achievean unprecedented discovery reach for CP violationThewater

Cherenkov detector provides an excellent energy resolutionfor sub-GeV low-multiplicity final-state events Both thehigh-power narrowband beamand themegaton-size detectorplay an important role to have large numbers of ]

119890and

]119890appearance events at the first oscillation maximum This

experiment plans to have 15 years of neutrino run and 35years of antineutrino run with one year given by 107 secondsThe baseline of this experiment is too short to have anymattereffect Therefore its mass hierarchy discovery reach is verylimited The expected accuracy in the determination of CPphase is better than 20∘ at 1120590 confidence level assuming thatmass hierarchy is known For sin22120579

13= 01 the CP violation

can be established at 3120590CL for 74 of the 120575CP values providedthat we fix the hierarchy in the fit This CP coverage reducesto 55 if wemarginalize over both the choices of hierarchy inthe fit [156]

Like T2HK proposal there is a superbeam configurationwhich is under consideration in Europe [157 159 160] usingthe CERN to Frejus baseline of 130 km The aim of thisproposal is to send a 4MW high-power superbeam from




LBNE10LBNO

12

10

8

2

4

6

0

2120590

3120590

Δ1205942

120575CP (true)

(a)



LBNE10LBNO

12

10

8

2

4

6

0

2120590

3120590

Δ1205942

120575CP (true)

(b)

Figure 16 Left panel (right panel) shows the Δ1205942 for the CP violation discovery as a function of true value of 120575CP assuming NH (IH) as truehierarchy

CERN towards a 440 kilotons MEMPHYS water Cherenkovdetector [158] located 130 km away at Frejus Using thissetup CP violation can be established for roughly 60 valuesof 120575CP at 3120590 confidence level [158] assuming two yearsof neutrino run and eight years of antineutrino run withuncorrelated systematic uncertainties of 5 on signal and10 on background

Another interesting possibility to explore leptonic CPviolation using a very intense cost-effective and high-performance neutrino beam from the proton linac of theESS facility currently under construction in Lund Swedenhas been studied recently in detail in [161 162] A high-power superbeam from this proton linac in conjunctionwith a megaton-size water Cherenkov detector located in theexisting mines at a distance of 300 to 600 km from the ESSfacility can discover leptonic CP violation at 5120590 confidencelevel for 50 of the 120575CP values [162]

73 Neutrino Factory The term ldquoNeutrino Factoryrdquo [149150 177 178] has been associated to describe neutrino beamscreated by the decays of high-energy muons (obtained viapion decay) which are circulated in a storage ring withlong straight sections The decay of muons in these straightsections produces an intense well-known and pure beam of]120583and ]

119890 If 120583+ are stored 120583+ rarr 119890

+]119890]120583decays generate

a beam consisting of equal numbers of ]119890and ]

120583 The most

promising avenue to explore CP violation neutrino masshierarchy and octant of 120579

23at a neutrino factory is the

subdominant ]119890rarr ]120583oscillation channel which produces

muons of the opposite charge (wrong-sign muons) to thosestored in the storage ring and these can be detected with thehelp of the charge identification capability of a magnetizediron neutrino detector (MIND) [97 167] In the most recentanalysis [167] of MIND low-energy neutrino signal eventsdown to 1GeV were selected with an efficiency plateau ofsim 60 for ]

120583and sim80 for ]

120583events starting at sim5GeV

while maintaining the background level at or below 10minus4For the neutral current background the impact of migrationis nonnegligible and it is peaked at lower energies Thisfeed-down is the strongest effect of migration and thushas potential impact on the energy optimization since itpenalizes neutrino flux at high energies where there is littleoscillation but a large increase in fed-down background

In light of recently discovered moderately large value of12057913 shorter baselines and lower energies are preferred to

achieve high performance in exploring CP violation Even 119864120583

as low as 5 to 8GeV at the Fermilab-Homestake baseline ofabout 1300 km is quite close to the optimal choice (see upperleft panel of Figure 17) which means that the MIND detectorapproaches the magnetized totally active scintillator detectorperformance of the Low-Energy Neutrino Factory (LENF)[163] With the present baseline choice of the NeutrinoFactory (119864

120583= 10GeV and 119871 = 2000 km) and a 50 kilotons

MIND detector CP violation can be established for around80 values of 120575CP at 3120590 CL considering 5 times 10

21 useful muondecays in total


sin2212057913 = 10minus1 sin

2212057913 = 10minus2

sin2212057913 = 10minus3 sin

2212057913 = 10minus4

065

065

07

07

07

04

03 035

07

08

075

055

065

045

045

075

25

25

20

15

10

5

5

20

15

10

E120583(G

eV)

E120583(G

eV)

1000 10002000 3000 4000 5000 6000

1000 2000 3000 4000 5000 6000

2000 3000 4000 5000 6000

L (km)L (km)

L (km)

25

20

15

10

5

E120583(G

eV)

25

20

15

10

5

E120583(G

eV)

1000 2000 3000 4000 5000 6000

L (km)

Figure 17 Fraction of 120575CP(true) for which CP violation will be discovered at 3120590 CL as a function of 119871 and 119864120583for the single-baseline Neutrino

Factory The different panels correspond to different true values of sin2212057913 as given there Here we consider 5 times 1021 useful muon decays in

total with a 50 kilotons MIND detector The optimal performance is marked by a dot (2200 1000) (2288 1362) (3390 2000) and (43452208) with regard to their best reaches of the fraction of 120575CP(true) at 077 084 067 and 042 This figure has been taken from [142]

74 Beta-Beams Zucchelli [169] put forward the novel idea ofa beta-beam [73 170 171 179] which is based on the conceptof creating a pure well-understood intense collimated beamof ]119890or ]119890through the beta-decay of completely ionized

radioactive ions Firstly radioactive nuclides are created byimpinging a target by accelerated protons These unstablenuclides are collected fully ionized bunched acceleratedand then stored in a decay ring The decay of these highlyboosted ions in the straight sections of the decay ringproduces the so-called beta-beam It has been proposed to

produce ]119890beams through the decay of highly accelerated

18Ne ions (1810Ne rarr 18

9F + 119890+ + ]

119890) and ]

119890from 6He (6

2He rarr

6

3Li+119890minus+]

119890) [169]More recently 8B (8

5B rarr 8

4Be+119890++]

119890) and

8Li (83Li rarr 8

4Be + 119890minus + ]

119890) [180ndash182] with much larger end-

point energy have been suggested as alternate sources sincethese ions can yield higher energy ]

119890and ]119890 respectively with

lower values of the Lorentz boost 120574 [154 183ndash186] Details ofthe four beta-beam candidate ions can be found in Table 5It may be possible to store radioactive ions producing beamswith both polarities in the same ringThis will enable running


Table 5 Beta decay parameters lifetime 120591 electron total end-pointenergy 119864

0 119891-value and decay fraction for various ions This table

has been taken from [73]

Ion 120591 (s) 1198640(MeV) 119891 Decay fraction Beam

18

10Ne 241 392 82037 921 ]

119890

6

2He 117 402 93453 100 ]

119890

8

5B 111 1443 60087207 100 ]

119890

8

3Li 120 1347 42535516 100 ]

119890

the experiment in the ]119890and ]119890modes simultaneously In the

low 120574 design of beta-beams the standard luminosity taken forthe 18Ne and 6He is 11 times 1018 (]

119890) and 29 times 1018 (]

119890) useful

decays per year respectivelyWithin the EURISOL Design Study [171] the 120574 = 100

option with 6He and 18Ne ions has been studied quiteextensively The energy spectrum of the emitted neutrinosfrom these radioactive ions with 120574 = 100 suits well theCERN to Frejus baseline of 130 km Compared to superbeamthe main advantage of using beta-beam is that it is anextremely pure beam with no beam contamination occurs atthe source Combining beta-beam with superbeam we canstudy the T-conjugated oscillation channels [187 188] andthis combined setup can provide an excellent reach for CPviolation discovery

8 Summary and Conclusions

The discovery of neutrino mixing and oscillations providesstrong evidence that neutrinos are massive and leptonsflavors are mixed with each other which leads to physicsbeyond the Standard Model of particle physics With therecent determination of 120579

13 for the first time a clear and

comprehensive picture of the three-flavor leptonic mixingmatrix has been established This impressive discovery hascrucial consequences for future theoretical and experimentalefforts It has opened up exciting prospects for currentand future long-baseline neutrino oscillation experimentstowards addressing the remaining fundamental questionsin particular the type of the neutrino mass hierarchy thepossible presence of a CP-violating phase in the neutrinosector and the correct octant of 120579

23(if it turns out to be

nonmaximal establishing the recent claims) In this paperwe have made an attempt to review the phenomenology oflong-baseline neutrino oscillationswith a special emphasis onsubleading three-flavor effects which will play a crucial rolein resolving these unknowns in light of recent measurementof a moderately large value of 120579

13 We have discussed in

detail the physics reach of current-generation long-baselineexperiments T2K and NO]A which have very limited reachin addressing these unknowns for only favorable ranges ofparameters Hence future facilities are indispensable to coverthe entire parameter space at unprecedented confidence levelA number of high-precision long-baseline neutrino oscilla-tion experiments have been plannedproposed to sharpenour understanding about these tiny particles In this reviewwe have discussed in detail the physics capabilities of few of

such proposals based on superbeams neutrino factory andbeta-beam

Conflict of Interests

The author declares that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

Sanjib Kumar Agarwalla would like to thank all his collabo-rators with whom he has worked on long-baseline neutrinooscillation physics Sanjib Kumar Agarwalla acknowledgesthe support from DSTINSPIRE Research Grant (IFA-PH-12) Department of Science and Technology India

References

[1] B T Cleveland T Daily R Davis Jr et al ldquoMeasurement ofthe solar electron neutrino flux with the homestake chlorinedetectorrdquo Astrophysical Journal Letters vol 496 no 1 pp 505ndash526 1998

[2] M Altmann M Balata P Belli et al ldquoComplete results for fiveyears of GNO solar neutrino observationsrdquo Physics Letters Bvol 616 no 3-4 pp 174ndash190 2005

[3] J Hosaka K Ishihara1 J Kameda et al ldquoSolar neutrinomeasurements in Super-Kamiokande-Irdquo Physical ReviewD vol73 no 11 Article ID 112001 33 pages 2006

[4] Q Ahmad R C Allen T C Andersen et al ldquoDirect evidencefor neutrino flavor transformation from neutral-current inter-actions in the Sudbury Neutrino Observatoryrdquo Phyiscal ReviewLetters vol 89 no 1 Article ID 011301 6 pages 2002

[5] B Aharmim S N Ahmed J F Amsbaugh et al ldquoIndependentmeasurement of the total active 8119861 solar neutrino flux usingan array of 3119867119890 proportional counters at the Sudbury NeutrinoObservatoryrdquo Physical Review Letters vol 101 no 11 Article ID111301 5 pages 2008

[6] B Aharmim S N Ahmed A E Anthony et al ldquoLow-energy-threshold analysis of the phase I and phase II data sets of theSudbury Neutrino Observatoryrdquo Physical Review C vol 81 no5 Article ID 055504 49 pages 2010

[7] C Arpesella H O Back M Balata et al ldquoDirect measurementof the 7119861119890 solar neutrino flux with 192 days of borexino datardquoPhysical ReviewLetters vol 101 no 9 Article ID091302 6 pages2008

[8] Y Fukuda T Hayakawa1 E Ichihara et al ldquoEvidence foroscillation of atmospheric neutrinosrdquo Physical Review Lettersvol 81 no 8 pp 1562ndash1567 1998

[9] Y Ashie J Hosaka K Ishihara et al ldquoMeasurement of atmo-spheric neutrino oscillation parameters by Super-KamiokandeIrdquo Physical Review D vol 71 no 11 Article ID 112005 35 pages2005

[10] T Araki K Eguchi1 S Enomoto et al ldquoMeasurement ofneutrino oscillation with KamLAND evidence of spectraldistortionrdquo Physical Review Letters vol 94 no 8 Article ID081801 5 pages 2005

[11] S Abe T Ebihara S Enomoto et al ldquoPrecision measurementof neutrino oscillation parameters with KamLANDrdquo PhysicalReview Letters vol 100 no 22 Article ID 221803 5 pages 2008


[12] F P An J Z Bai A B Balantekin et al ldquoObservationof electron-antineutrino disappearance at Daya Bayrdquo PhysicalReview Letters vol 108 no 17 Article ID 171803 7 pages 2012

[13] F P An Q An J Z Bai et al ldquoImproved measurementof electron antineutrino disappearance at Daya Bayrdquo ChinesePhysics C vol 37 no 1 Article ID 011001 2013

[14] J K Ahn S Chebotaryov J H Choi et al ldquoObservationof reactor electron antineutrinos disappearance in the RENOexperimentrdquo Physical Review Letters vol 108 no 19 Article ID191802 6 pages 2012

[15] Y Abe C Aberle T Akiri et al ldquoIndication of reactor 119881119890

disappearance in the Double Chooz Experimentrdquo PhysicalReview Letters vol 108 no 13 Article ID 131801 7 pages 2012

[16] Y Abe C Aberle J C Dos Anjos et al ldquoReactor 119881119890disappear-

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[17] M H Ahn E Aliu S Andringa et al ldquoMeasurement ofneutrino oscillation by the K2K experimentrdquo Physical ReviewD vol 74 no 7 Article ID 072003 39 pages 2006

[18] P Adamson C Andreopoulos K E Arms et al ldquoMeasurementof neutrino oscillations with theMINOS detectors in the NuMIbeamrdquo Physical Review Letters vol 101 no 13 Article ID 1318025 pages 2008

[19] P Adamson D J Auty D S Ayres et al ldquoImproved search formuon-neutrino to electron-neutrino oscillations in MINOSrdquoPhysical Review Letters vol 107 no 18 Article ID 181802 6pages 2011

[20] P Adamson I Anghel C Backhouse et al ldquoMeasurementof neutrino and antineutrino oscillations using beam andatmospheric data in MINOSrdquo Physical Review Letters vol 110no 25 Article ID 251801 6 pages 2013

[21] K Abe N Abgrall Y Ajima et al ldquoIndication of electronneutrino appearance from an accelerator-produced off-axismuon neutrino beamrdquo Physical Review Letters vol 107 no 4Article ID 041801 8 pages 2011

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[23] B Pontecorvo ldquoNeutrino experiments and the problem ofconservation of leptonic chargerdquo Soviet Physics Journal ofExperimental andTheoretical Physics vol 26 no 5 p 984 1968

[24] V Gribov and B Pontecorvo ldquoNeutrino astronomy and leptonchargerdquo Physics Letters B vol 28 no 7 pp 493ndash496 1969

[25] D Forero M Tortola and J Valle ldquoGlobal status of neutrinooscillation parameters after Neutrino-2012rdquo Physical Review Dvol 86 no 7 Article ID 073012 8 pages 2012

[26] G Fogli E Lisi A Marrone et al ldquoGlobal analysis of neutrinomasses mixings and phases entering the era of leptonic CPviolation searchesrdquo Physical Review D vol 86 no 1 Article ID013012 10 pages 2012

[27] M Gonzalez-Garcia M Maltoni J Salvado and T SchwetzldquoGlobal fit to three neutrino mixing critical look at presentprecisionrdquo Journal of High Energy Physics vol 2012 article 1232012

[28] X Qian R Rosero B Roskovec et al ldquoInternational workshopon neutrino factories super beams and beta beamsrdquo in Proceed-ings of theNuFact ConferenceWilliamsburg VaUSA July 2012

[29] J Hewett H Weerts R Brock et al ldquoFundamental physics atthe intensity frontierrdquo httparxivorgabs12052671

[30] H Minakata ldquoPhenomenology of future neutrino experimentswith large 120579

13rdquoNuclear Physics B vol 235-236 pp 173ndash179 2013

[31] P Machado H Minakata H Nunokawa and R Z FunchalldquoWhat can we learn about the lepton CP phase in the next 10yearsrdquo httparxivorgabs13073248

[32] R Nichol T C Nicholls J P Ochoa-Ricoux et al ldquoNew resultsfromMINOSrdquoNuclear Physics B vol 235-236 pp 105ndash111 2013


[34] Y Itow in Proceedings of the 25th International Conference onNeutrino Physics and Astrophysics (Neutrino rsquo12) Kyoto JapanJune 2012

[35] G L Fogli and E Lisi ldquoTests of three-flavor mixing in long-baseline neutrino oscillation experimentsrdquo Physical Review Dvol 54 no 5 pp 3667ndash3670 1996

[36] V Barger D Marfatia and K Whisnant ldquoBreaking eightfolddegeneracies in neutrino CP violation mixing and masshierarchyrdquo Physical Review D vol 65 no 7 Article ID 07302317 pages 2002

[37] H Minakata H Nunokawa and S J Parke ldquoParameter degen-eracies in neutrino oscillation measurement of leptonic CP andT violationrdquo Physical Review D vol 66 no 9 Article ID 09301215 pages 2002

[38] Y Itow ldquoAtmospheric neutrinos results from running experi-mentsrdquo in Proceedings of the 25th International Conference onNeutrino Physics and Astrophysics (Neutrino rsquo12) Kyoto JapanJune 2012

[39] H Minakata and H Nunokawa ldquoExploring neutrino mixingwith low energy superbeamsrdquo Journal of High Energy Physicsvol 2001 no 10 article 001 2001

[40] S Pascoli and T Schwetz ldquoProspects for neutrino oscillationphysicsrdquo Advances in High Energy Physics vol 2013 Article ID503401 29 pages 2013

[41] S K Agarwalla S Prakash and S U Sankar ldquoResolvingthe octant of 120579

23with T2K and NOvArdquo httpxxxlanlgov

abs13012574[42] C H Albright and M-C Chen ldquoModel predictions for neu-

trino oscillation parametersrdquo Physical Review D vol 74 no 11Article ID 113006 11 pages 2006

[43] S Pascoli S Petcov and T Schwetz ldquoThe absolute neutrinomass scale neutrino mass spectrum majorana CP-violationand neutrinoless double-beta decayrdquoNuclear Physics B vol 734no 1-2 pp 24ndash49 2006

[44] M Fukugita and T Yanagida ldquoBarygenesis without grandunificationrdquo Physics Letters B vol 174 no 1 pp 45ndash47 1986

[45] P Di Bari ldquoAn introduction to leptogenesis and neutrinopropertiesrdquo Contemporary Physics vol 53 no 4 pp 315ndash3382012

[46] A S Joshipura E A Paschos and W Rodejohann ldquoA simpleconnection between neutrino oscillation and leptogenesisrdquoJournal of High Energy Physics vol 2001 no 8 article 029 2001

[47] T Endoh S Kaneko S K Kang T Morozumi and M Tani-moto ldquoCP violation in neutrino oscillation and leptogenesisrdquoPhysical Review Letters vol 89 no 23 Article ID 231601 4pages 2002

[48] J C Pati ldquoLeptogenesis and neutrino oscillations within apredictive G(224)SO(10) frameworkrdquo Physical Review D vol68 no 7 Article ID 072002 11 pages 2003

[49] R Mohapatra and A Smirnov ldquoNeutrino mass and newphysicsrdquo Annual Review of Nuclear and Particle Science vol 56pp 569ndash628 2006


[50] C H Albright A Dueck and W Rodejohann ldquoPossiblealternatives to tri-bimaximal mixingrdquo The European PhysicalJournal C vol 70 no 4 pp 1099ndash1110 2010

[51] S F King andC Luhn ldquoNeutrinomass andmixingwith discretesymmetryrdquo httpxxxlanlgovabs13011340

[52] T Fukuyama and H Nishiura ldquoMass matrix of majorananeutrinosrdquo httpxxxlanlgovabshep-ph9702253

[53] R N Mohapatra and S Nussinov ldquoBimaximal neutrino mixingand neutrino mass matrixrdquo Physical Review D vol 60 no 1Article ID 013002 4 pages 1999

[54] C Lam ldquoA 2-3 symmetry in neutrino oscillationsrdquo PhysicsLetters B vol 507 no 1ndash4 pp 214ndash218 2001

[55] P Harrison and W Scott ldquo120583-120591 reflection symmetry in leptonmixing and neutrino oscillationsrdquo Physics Letters B vol 547 no3-4 pp 219ndash228 2002

[56] T Kitabayashi and M Yasue ldquo1198782119871

permutation symmetry forleft-handed 120583 and 120591 families and neutrino oscillations in an119878119880(3)

119871times 119880(1)

119873gauge modelrdquo Physical Review D vol 67 no

1 Article ID 015006 16 pages 2003[57] W Grimus and L Lavoura ldquoA discrete symmetry group for

maximal atmospheric neutrino mixingrdquo Physics Letters B vol572 no 3-4 pp 189ndash195 2003

[58] Y Koide ldquoUniversal texture of quark and lepton mass matriceswith an extended flavor 2harr3 symmetryrdquo Physical ReviewD vol69 no 9 Article ID 093001 9 pages 2004

[59] R Mohapatra and W Rodejohann ldquoBroken 120583-120591 symmetry andleptonic CP violationrdquo Physical Review D vol 72 no 5 ArticleID 053001 7 pages 2005

[60] E Ma ldquoPlatorsquos fire and the neutrino mass matrixrdquo ModernPhysics Letters A vol 17 no 36 pp 2361ndash2370 2002

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neutrino mass matrix and the quark mixing matrixrdquo PhysicsLetters B vol 552 no 3-4 pp 207ndash213 2003

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matricesrdquo Journal of High Energy Physics vol 2005 no 8 article013 2005

[64] E Ma ldquoTetrahedral family symmetry and the neutrino mixingmatrixrdquoModern Physics Letters A vol 20 no 34 pp 2601ndash26062005

[65] M Raidal ldquoRelation between the neutrino and quark mixingangles and grand unificationrdquo Physical Review Letters vol 93no 16 Article ID 161801 4 pages 2004

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[68] S Antusch S F King and R N Mohapatra ldquoQuark-leptoncomplementarity in unified theoriesrdquo Physics Letters B vol 618no 1ndash4 pp 150ndash161 2005

[69] L J Hall H Murayama and N Weiner ldquoNeutrino massanarchyrdquo Physical Review Letters vol 84 no 12 pp 2572ndash25752000

[70] A de Gouvea and H Murayama ldquoNeutrino mixing anarchyalive and kickingrdquo httparxivorgabs12041249

[71] S K Agarwalla S Prakash and S U Sankar ldquoResolving theoctant of 120579

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Physics vol 2013 article 131 2013[72] S K Agarwalla S Prakash S K Raut and S U Sankar ldquoPoten-

tial of optimized NO]A for large 12057923amp combined performance

with a LArTPCampT2Krdquo Journal ofHigh Energy Physics vol 2012article 75 2012

[73] S K Agarwalla ldquoSome aspects of neutrino mixing and oscilla-tionsrdquo httpxxxlanlgovabs09084267

[74] S Bilenky ldquoBruno pontecorvo mister neutrinordquo httparxivorgabsphysics0603039

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[78] Z Maki M Nakagawa and S Sakata ldquoRemarks on the unifiedmodel of elementary particlesrdquo Progress of Theoretical Physicsvol 28 no 5 pp 870ndash880 1962

[79] J Beringer J-F Arguin R M Barnett et al ldquoReview of particlephysicsrdquoPhysical ReviewD vol 86 no 1 Article ID 010001 1528pages 2012

[80] S P Mikheev and A Y Smirnov ldquoResonance enhancement ofoscillations in matter and solar neutrino spectroscopyrdquo SovietJournal of Nuclear Physics vol 42 pp 913ndash917 1985 YadernayaFizika vol 42 pp 1441ndash1448 1985

[81] S Mikheev and A Y Smirnov ldquoResonant amplification of] oscillations in matter and solar-neutrino spectroscopyrdquo IlNuovo Cimento C vol 9 no 1 pp 17ndash26 1986

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[83] L Wolfenstein ldquoNeutrino oscillations and stellar collapserdquoPhysical Review D vol 20 no 10 pp 2634ndash2635 1979

[84] A Osipowicz H Blumer G Drexlinb et al ldquoKATRIN-a nextgeneration tritium beta decay experiment with sub-eV sensitiv-ity for the electron neutrino massrdquo httpxxxlanlgovabshep-ex0109033

[85] I Avignone T Frank S R Elliott and J Engel ldquoDouble betadecay majorana neutrinos and neutrino massrdquo Reviews ofModern Physics vol 80 no 2 pp 481ndash516 2008

[86] J Lesgourgues and S Pastor ldquoNeutrino mass from cosmologyrdquoAdvances in High Energy Physics vol 2012 Article ID 60851534 pages 2012

[87] P A R Ade N Aghanim C Armitage-Caplan et al ldquoPlanck2013 results XVI cosmological parametersrdquo httparxivorgabs13035076

[88] T Mueller D Lhuillier M Fallot et al ldquoImproved predictionsof reactor antineutrino spectrardquo Physical Review C vol 83 no5 Article ID 054615 17 pages 2011

[89] GMentionM Fechner T Lasserre et al ldquoReactor antineutrinoanomalyrdquo Physical ReviewD vol 83 no 7 Article ID 073006 20pages 2011

[90] P Huber ldquoDetermination of antineutrino spectra from nuclearreactorsrdquo Physical Review C vol 84 no 2 Article ID 024617 16pages 2011

[91] HMinakata H Sugiyama O Yasuda K Inoue and F SuekaneldquoReactor measurement of 120579

13and its complementarity to long-

baseline experimentsrdquo Physical Review D vol 68 no 3 ArticleID 033017 12 pages 2003


[92] P Huber M Lindner T Schwetz andWWinter ldquoReactor neu-trino experiments compared to superbeamsrdquoNuclear Physics Bvol 665 pp 487ndash519 2003

[93] D Roy ldquoDetermination of the third neutrino-mixing angle 12057913

and its implicationsrdquo Journal of Physics G vol 40 no 5 ArticleID 053001 2013

[94] G Feldman J Hartnell and T Kobayashi ldquoLong-baselineneutrino oscillation experimentsrdquo Advances in High EnergyPhysics vol 2013 Article ID 475749 30 pages 2013

[95] M Diwan R Edgecock T Hasegawa et al ldquoFuture long-baseline neutrino facilities and detectorsrdquo Advances in HighEnergy Physics vol 2013 Article ID 460123 35 pages 2013

[96] V Barger KWhisnant S Pakvasa and R J N Phillips ldquoMattereffects on three-neutrino oscillationsrdquo Physical Review D vol22 no 11 pp 2718ndash2726 1980

[97] A Cervera A Doninib MB Gavelab et al ldquoGolden measure-ments at a neutrino factoryrdquo Nuclear Physics B vol 597 no 1-2pp 17ndash55 2000

[98] M Freund P Huber and M Lindner ldquoSystematic explorationof the neutrino factory parameter space including errors andcorrelationsrdquo Nuclear Physics B vol 615 no 1ndash3 pp 331ndash3572001

[99] E K Akhmedov R Johansson M Lindner T Ohlsson andT Schwetz ldquoSeries expansions for three-flavor neutrino oscil-lation probabilities in matterrdquo Journal of High Energy Physicsvol 2004 no 4 article 078 2004

[100] S K Agarwalla T Li and A Rubbia ldquoAn incremental approachto unravel the neutrino mass hierarchy and CP violation with along-baseline superbeam for large 120579

13rdquo Journal of High Energy

Physics vol 2012 aricle 154 2012[101] S K Agarwalla ldquoNeutrino mass hierarchy in future long-

baseline experimentsrdquo Nuclear Physics B vol 237-238 pp 196ndash198 2013

[102] S Amerio S Amorusob M Antonello et al ldquoDesign con-struction and tests of the ICARUS T600 detectorrdquo NuclearInstruments and Methods in Physics Research A vol 527 no 3pp 329ndash410 2004

[103] P Huber M Lindner andWWinter ldquoSuperbeams vs neutrinofactoriesrdquo Nuclear Physics B vol 645 no 1-2 pp 3ndash48 2002

[104] V Barger D Marfatia and K Whisnant ldquoOff-axis beams anddetector clusters resolving neutrino parameter degeneraciesrdquoPhysical Review D vol 66 no 5 Article ID 053007 2002

[105] J Burguet-Castell M Gavela J Gomez-Cadenas P Hernandezand O Mena ldquoSuperbeams plus neutrino factory the goldenpath to leptonic CP violationrdquo Nuclear Physics B vol 646 no1-2 pp 301ndash320 2002

[106] V Barger D Marfatia and K Whisnant ldquoHow two neutrinosuperbeam experiments do better than onerdquo Physics Letters Bvol 560 no 1-2 pp 75ndash86 2003

[107] P Huber M Lindner and W Winter ldquoSynergies between thefirst-generation JHF-SK and NuMI superbeam experimentsrdquoNuclear Physics B vol 654 no 1-2 pp 3ndash29 2003

[108] P Huber and W Winter ldquoNeutrino factories and the ldquomagicrdquobaselinerdquo Physical Review D vol 68 no 3 Article ID 037301 4pages 2003

[109] A Y Smirnov ldquoNeutrino oscillations what is magic about theldquomagicrdquo baselinerdquo httpxxxlanlgovabshep-ph0610198

[110] India-Based Neutrino Observatory (INO) httpwwwinotifrresinino

[111] S K Raut R S Singh and S U Sankar ldquoMagical properties ofa 2540 km baseline superbeam experimentrdquo Physics Letters Bvol 696 no 3 pp 227ndash231 2011

[112] A Dighe S Goswami and S Ray ldquo2540 km bimagic baselinefor neutrino oscillation parametersrdquo Physical Review Lettersvol 105 no 26 Article ID 261802 4 pages 2010

[113] A Takamura and K Kimura ldquoLarge non-perturbative effects ofsmall Δm2

21Δm231

and sin 12057913

on neutrino oscillation and CPviolation in matterrdquo Journal of High Energy Physics vol 2006no 01 article 053 2006

[114] S K Agarwalla Y Kao and T Takeuchi ldquoAnalytical approx-imation of the neutrino oscillation probabilities at large 120579

13rdquo

httparxivorgabs13026773[115] A M Dziewonski and D L Anderson ldquoPreliminary reference

Earth modelrdquo Physics of the Earth and Planetary Interiors vol25 no 4 pp 297ndash356 1981

[116] Y Itow T Kajita andK Kaneyuki ldquoThe JHF-Kamioka neutrinoprojectrdquo httparxivorgabshep-ex0106019

[117] K Abe N Abgrallp H Aihara et al ldquoThe T2K experimentrdquoNuclear Instruments andMethods in Physics ResearchA vol 659no 1 pp 106ndash135 2011

[118] D Ayres G DrakeM Goodman et al ldquoLetter of intent to buildan off-axis detector to study numu to nue oscillations with theNuMI neutrino beamrdquo httpxxxlanlgovabshep-ex0210005

[119] D S Ayres G RDrakeMCGoodman et al ldquoNOvAproposalto build a 30 kiloton off-axis detector to study neutrino oscilla-tions in the fermilab NuMI beamlinerdquo httpxxxlanlgovabshep-ex0503053

[120] D S Ayres G R Drake M C Goodman et al ldquoThe NOvAtechnical design reportrdquo Tech Rep FERMILAB-DESIGN-2007-01 2007

[121] S Prakash S K Raut and S U Sankar ldquoGetting the best outof T2K and NO]Ardquo Physical Review D vol 86 no 3 Article ID033012 14 pages 2012

[122] M Diwan D Beavis M-C Chen et al ldquoVery long baselineneutrino oscillation experiments for precise measurements ofmixing parameters and CP violating effectsrdquo Physical Review Dvol 68 no 1 Article ID 012002 10 pages 2003

[123] V Barger M Bishai D Bogert et al ldquoReport of the USlong baseline neutrino experiment studyrdquo httparxivorgabs07054396

[124] P Huber and J Kopp ldquoTwo experiments for the price of onethe role of the second oscillation maximum in long baselineneutrino experimentsrdquo Journal of High Energy Physics vol 2011article 13 2011

[125] T Akiri D Allspach M Andrews et al ldquoThe 2010 interimreport of the long-baseline neutrino experiment collaborationphysics working groupsrdquo httpxxxlanlgovabs11106249

[126] D Autiero J Aysto A Badertscher et al ldquoLarge under-ground liquid based detectors for astro-particle physics inEurope scientific case and prospectsrdquo Journal of Cosmology andAstroparticle Physics vol 2007 article 011 no 11 2007

[127] A Rubbia ldquoA CERN-based high-intensity high-energy pro-ton source for long baseline neutrino oscillation experimentswith next-generation large underground detectors for pro-ton decay searches and neutrino physics and astrophysicsrdquohttpxxxlanlgovabs10031921

[128] D Angus A Ariga D Autiero et al ldquoThe LAGUNA DesignStudy- towards giant liquid based underground detectors forneutrino physics and astrophysics and proton decay searchesrdquohttpxxxlanlgovabs10010077

[129] A Rubbia ldquoThe Laguna design study-towards giant liquidbased underground detectors for neutrino physics and astro-physics and proton decay searchesrdquoActa Physica Polonica B vol41 no 7 pp 1727ndash1732 2010


[130] A Stahl C Wiebusch A Guler M Kamiscioglu and RSever ldquoExpression of Interest for a very long baseline neutrinooscillation experiment (LBNO)rdquo Tech Rep CERN-SPSC-2012-021 SPSC-EOI-007 2012

[131] A Para and M Szleper ldquoNeutrino oscillations experimentsusing off-axis NuMI beamrdquo httparxivorgabshep-ex0110032

[132] M Fechner Presented on 9 May 2006[133] P Huber M Lindner T Schwetz and W Winter ldquoFirst

hint for CP violation in neutrino oscillations from upcomingsuperbeam and reactor experimentsrdquo Journal of High EnergyPhysics vol 2009 no 11 article 044 2009

[134] R Patterson ldquoThe NOvA experiment status and outlookrdquoNuclear Physics B vol 235-236 pp 151ndash157 2013

[135] P Huber M Lindner and W Winter ldquoSimulation of long-baseline neutrino oscillation experiments with GLoBES (Gen-eral Long Baseline Experiment Simulator)rdquo Computer PhysicsCommunications vol 167 no 3 pp 195ndash202 2005

[136] P Huber J KoppM Lindner M Rolinec andWWinter ldquoNewfeatures in the simulation of neutrino oscillation experimentswith GLoBES 30 (General Long Baseline Experiment Simu-lator)rdquo Computer Physics Communications vol 177 no 5 pp432ndash438 2007

[137] H Nunokawa S J Parke and R Zukanovich Funchal ldquoAnotherpossible way to determine the neutrino mass hierarchyrdquo Physi-cal Review D vol 72 no 1 Article ID 013009 6 pages 2005

[138] A de Gouvea J Jenkins and B Kayser ldquoNeutrino masshierarchy vacuum oscillations and vanishing |119880

1198903|rdquo Physical

Review D vol 71 no 11 Article ID 113009 13 pages 2005[139] R Wendell ldquoSuper-Kamiokande atmospheric neutrino oscilla-

tion analysisrdquoNuclear Physics B vol 237-238 pp 163ndash165 2013[140] R Wendell C Ishihara K Abe et al ldquoAtmospheric neu-

trino oscillation analysis with subleading effects in Super-Kamiokande I II and IIIrdquo vol 81 no 9 Article ID 092004 16pages 2010

[141] G Fogli E Lisi A Marrone et al ldquoSolar neutrino oscillationparameters after first KamLAND resultsrdquo Physical Review Dvol 67 no 7 Article ID 073002 10 pages 2003

[142] S K Agarwalla P Huber J Tang andWWinter ldquoOptimizationof the neutrino factory revisitedrdquo Journal of High EnergyPhysics vol 2011 article 120 2011

[143] A Ghosh T Thakore and S Choubey ldquoDetermining theneutrino mass hierarchy with INO T2K NOvA and reactorexperimentsrdquo Journal of High Energy Physics vol 2013 article9 2013

[144] K Dick M Freund M Lindner and A Romanino ldquoCP-violation in neutrino oscillationsrdquo Nuclear Physics B vol 562no 1-2 pp 29ndash56 1999

[145] A Donini M Gavela P Hernandez and S Rigolin ldquoNeutrinomixing and CP-violationrdquo Nuclear Physics B vol 574 no 1-2pp 23ndash42 2000

[146] P Coloma P Huber J Kopp and W Winter ldquoSystematicuncertainties in long-baseline neutrino oscillations for large12057913rdquoPhysical ReviewD vol 87 no 3 Article ID033004 12 pages

2013[147] P Adamson J Evans P Guzowski et al ldquoRampD argon detector

at Ash River (RADAR)mdashletter of intentrdquo httparxivorgabs13076507

[148] A Chatterjee P Ghoshal S Goswami and S K Raut ldquoOctantsensitivity for large 120579

13in atmospheric and long-baseline neu-

trino experimentsrdquo Journal of High Energy Physics vol 2013article 10 2013

[149] A Bandyopadhyay S Choubey R Gandhi et al ldquoPhysics ata future neutrino factory and super-beam facilityrdquo Reports onProgress in Physics vol 72 no 10 Article ID 106201 2009

[150] S Choubey D Cline J Cobb and P Coloma ldquoInterim designreportrdquo httpxxxlanlgovabs11122853

[151] P Coloma A Donini E Fernandez-Martinez and P Hernan-dez ldquoPrecision on leptonic mixing parameters at future neu-trino oscillation experimentsrdquo Journal of High Energy Physicsvol 2012 article 73 2012

[152] M Mezzetto and T Schwetz ldquo12057913 phenomenology present

status and prospectrdquo Journal of Physics G vol 37 no 10 ArticleID 103001 2010

[153] PHuberM LindnerM Rolinec andWWinter ldquoOptimizationof a neutrino factory oscillation experimentrdquoPhysical ReviewDvol 74 no 7 Article ID 073003 31 pages 2006

[154] S K Agarwalla S Choubey and A Raychaudhuri ldquoNeutrinomass hierarchy and 120579

13with a magic baseline beta-beam

experimentrdquo Nuclear Physics B vol 771 no 1-2 pp 1ndash27 2007[155] S K Agarwalla S Choubey A Raychaudhuri and W Winter

ldquoOptimizing the greenfield Beta-beamrdquo Journal of High EnergyPhysics vol 2008 no 6 article 090 2008

[156] K Abe T Abe H Aihara et al ldquoLetter of Intent the Hyper-Kamiokande experimentmdashdetector design and physics poten-tialrdquo httpxxxlanlgovabs11093262

[157] J-E Campagne M Maltoni M Mezzetto and T SchwetzldquoPhysics potential of the CERN-MEMPHYS neutrino oscilla-tion projectrdquo Journal of High Energy Physics vol 2007 no 4article 003 2007

[158] L Agostino M Buizza-Avanzini M Dracos et al ldquoStudy ofthe performance of a large scale water-Cherenkov detector(MEMPHYS)rdquo Journal of Cosmology and Astroparticle Physicsvol 2013 no 1 article 024 2013

[159] E Baussan J Bielski C Bobeth et al ldquoThe SPL-based neutrinosuper beamrdquo httparxivorgabs12120732

[160] T Edgecock O Caretta T Davenne et al ldquoHigh intensityneutrino oscillation facilities in EuroperdquoPhysical Review SpecialTopics vol 16 no 2 Article ID 021002 18 pages 2013

[161] E BaussanMDracos T Ekelof E FMartinez andHOhmanldquoThe use of a high intensity neutrino beam from the ESSproton linac for measurement of neutrino CP violation andmass hierarchyrdquo httparxivorgabs12125048

[162] E Baussan M Blennow M Bogomilov et al ldquoA very intenseneutrino super beam experiment for leptonic CP violationdiscovery based on the European spallation source linac asnowmass 2013 white paperrdquo httparxivorgabs13097022

[163] S Geer O Mena and S Pascoli ldquoA low energy neutrino factoryfor large 120579

13rdquo Physical ReviewD vol 75 no 9 Article ID 093001

13 pages 2007[164] A D BrossM Ellis S Geer OMena and S Pascoli ldquoNeutrino

factory for both large and small 12057913rdquo Physical Review D vol 77

no 9 Article ID 093012 12 pages 2008[165] E FernandezMartinez T Li S Pascoli andOMena ldquoImprove-

ment of the low energy neutrino factoryrdquo Physical ReviewD vol81 no 7 Article ID 073010 13 pages 2010

[166] P Ballett and S Pascoli ldquoUnderstanding the performance ofthe low-energy neutrino factory the dependence on baselinedistance and stored-muon energyrdquo Physical Review D vol 86no 5 Article ID 053002 14 pages 2012

[167] A Cervera A Laing JMartin-Albo and F Soler ldquoPerformanceof theMIND detector at a neutrino factory using realistic muonreconstructionrdquo Nuclear Instruments and Methods in PhysicsResearch A vol 624 no 3 pp 601ndash614 2010


[168] R Bayes A Laing F Soler et al ldquoGolden channel at a neutrinofactory revisited improved sensitivities from amagnetized ironneutrino detectorrdquo Physical Review D vol 86 no 9 Article ID093015 27 pages 2012

[169] P Zucchelli ldquoA novel concept for a V119890V119890neutrino factory the

beta-beamrdquoPhysics Letters B vol 532 no 3-4 pp 166ndash172 2002[170] MMezzetto ldquoPhysics reach of the beta beamrdquo Journal of Physics

G vol 29 no 8 p 1771 2003[171] M Benedikt A Bechtold F Borgnolutti et al ldquoConceptual

design report for a Beta-Beam facilityrdquo The European PhysicalJournal A vol 47 article 24 2011

[172] M Bishai ldquoPrivate communicationrdquo 2012[173] G Zeller ldquoPrivate communicationrdquo 2012[174] R Petti and G Zeller ldquoNuclear effects in water vs argonrdquo Tech

Rep 740 LBNE DocDB[175] S di Luise ldquoOptimization of neutrino fluxes for future long

baseline neutrino experimentrdquo in Proceedings of the 36thInternational Conference on High Energy Physics (ICHEP rsquo12)Melbourne Australia July 2012

[176] A Rubbia ldquoUnderground neutrino detectors for particle andastroparticle science the giant liquid argon charge imagingexperiment (GLACIER)rdquo Journal of Physics vol 171 no 1Article ID 012020 2009

[177] S Geer ldquoNeutrino beams from muon storage rings character-istics and physics potentialrdquo Physical Review D vol 57 no 11pp 6989ndash6997 1998

[178] A De Rujula M Gavela and P Hernandez ldquoNeutrino oscilla-tion physics with a neutrino factoryrdquoNuclear Physics B vol 547no 1-2 pp 21ndash38 1999

[179] C Volpe ldquoBeta-beams rdquo Journal of Physics G vol 34 no 1article R1 2007

[180] C Rubbia A Ferrari Y Kadi andVVlachoudis ldquoBeam coolingwith ionization lossesrdquo Nuclear Instruments and Methods inPhysics Research A vol 568 no 2 pp 475ndash487 2006

[181] C Rubbia ldquoIonization cooled ultra pure beta-beams for longdistance neu-e to neu-mu transitions 120579

13phase and CP-

violationrdquo httparxivorgabshep-ph0609235[182] Y Mori ldquoDevelopment of FFAG accelerators and their appli-

cations for intense secondary particle productionrdquo NuclearInstruments and Methods in Physics Research A vol 562 no 2pp 591ndash595 2006

[183] S K Agarwalla S Choubey and A Raychaudhuri ldquoUnravelingneutrino parameters with a magical beta-beam experiment atINOrdquo Nuclear Physics B vol 798 no 1-2 pp 124ndash145 2008

[184] S KAgarwalla S Choubey andA Raychaudhuri ldquoExceptionalsensitivity to neutrino parameters with a two-baseline Beta-beam set-uprdquo Nuclear Physics B vol 805 no 1-2 pp 305ndash3252008

[185] P Coloma A Donini E Fernandez-Martınez and J Lopez-Pavon ldquo120579

13 120575 and the neutrino mass hierarchy at a 120574 = 350

double baseline LiB 120573-beamrdquo Journal of High Energy Physicsvol 2008 no 5 article 050 2008

[186] A Donini and E Fernandez-Martinez ldquoAlternating ions in a 120573-beam to solve degeneraciesrdquo Physics Letters B vol 641 no 6 pp432ndash439 2006

[187] A Donini E Fernandez-Martinez P Migliozzi S Rigolin andL Scotto Lavina ldquoStudy of the eightfold degeneracy with astandard 120573-beam and a super-beam facilityrdquo Nuclear Physics Bvol 710 no 1-2 pp 402ndash424 2005

[188] A Donini E Fernandez-Martınez and S Rigolin ldquoAppearanceand disappearance signals at a 120573-beam and a super-beamfacilityrdquo Physics Letters B vol 621 no 3-4 pp 276ndash287 2005

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


FluidsJournal of

Atomic and Molecular Physics

Journal of



Advances in Condensed Matter Physics

OpticsInternational Journal of



AstronomyAdvances in

International Journal of


Superconductivity


Statistical MechanicsInternational Journal of


GravityJournal of


AstrophysicsJournal of


Physics Research International


Solid State PhysicsJournal of

Computational Methods in Physics

Journal of



Soft MatterJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

AerodynamicsJournal of

Volume 2014


PhotonicsJournal of


Journal of

Biophysics


ThermodynamicsJournal of


Mass

Atmosph

eric

1

1

2

23

3

Normalhierarchy hierarchy

Inverted

solarΔm2

solarΔm2

Δm2

e 120583 120591

Figure 1The sign of Δ119898231equiv 1198982

3minus1198982

1is unknownThe hierarchy of

the neutrino mass spectrum can be normal or inverted

mass hierarchy (two possibilities are there it can be eithernormal (NH) if Δ1198982

31equiv 1198982

3minus 1198982

1gt 0 or inverted (IH) if

Δ1198982

31lt 0 as described in Figure 1) using the Earth matter

effects and to search for leptonic CP violation (if the Dirac CPphase 120575CP differs from 0

∘ or 180∘) in accelerator-based long-baseline neutrino oscillation experiments [30 31] Anotherrecent and important development related to neutrino mix-ing parameters is the hint of nonmaximal 2-3 mixing bythe MINOS accelerator experiment [32 33] However themaximal value of 120579

23is still favored by the atmospheric neu-

trino data dominated by Super-Kamiokande [34] Combinedanalyses of all the neutrino oscillation data available [25ndash27]also prefer the deviation from maximal mixing for 120579

23 that

is (05minus sin212057923) = 0 In ]

120583survival probability the dominant

term mainly depends on sin2212057923 Now if sin22120579

23differs

from 1 as indicated by the recent neutrino data then we gettwo solutions for 120579

23 one lt 45

∘ named as lower octant(LO) and the other gt 45∘ named as higher octant (HO)In other words if the quantity (05 minus sin2120579

23) is positive

(negative) then 12057923

belongs to LO (HO) This leads to theproblem of octant degeneracy of 120579

23[35] which is a part of

the overall eightfold degeneracy [36 37] where the other twodegeneracies are (120579

13 120575CP) intrinsic degeneracy [38] and the

(hierarchy 120575CP) degeneracy [39] The resolution of the threefundamental issues in the neutrino sector neutrino masshierarchy octant of 120579

23 and CP violation is possible only

by observing the impact of three-flavor effects in neutrinooscillation experiments [40 41]

The information on neutrino mass hierarchy is veryimportant in order to settle the structure of neutrino massmatrix which in turn can give crucial piece of informationtowards the underlying theory of neutrinomasses andmixing[42] This is also a vital ingredient for neutrinoless doublebeta decay searches investigating the Majorana nature ofneutrinos If Δ1198982

31lt 0 and yet no neutrinoless double beta

decay is observed even in the very far future experimentsthat would be a strong hint that neutrinos are not Majo-rana particles [43] Another fundamental missing link thatneeds to be addressed in long-baseline neutrino oscillationexperiments is to measure 120575CP and to explore leptonic CPviolation This new source of low-energy CP violation inneutral lepton sector has drawn tremendous interest becauseof the possibility of leptogenes is leading to baryogenesisand the observed baryon asymmetry in the universe [44]

Leptogenesis demands the existence of CP violation in theleptonic sector for a recent review see [45] The possiblelink between leptogenesis and neutrino oscillations has beenstudied in [46ndash48] It is likely that the CP violating phase inneutrino oscillations is not directly responsible to generatethe CP violation leading to leptogenesis But there is no doubtthat a demonstration of CP violation in neutrino oscillationswill provide a crucial guidepost for models of leptonic CPviolation and leptogenesis Precise measurement of 120579

23and

the determination of its correct octant (if it turns out tobe nonmaximal) are also very vital tasks that need to beundertaken by the current- and next-generation neutrinooscillation experiments These pieces of information willprovide crucial inputs to the theories of neutrino massesand mixing [42 49ndash51] A number of excellent ideas suchas 120583 harr 120591 symmetry [52ndash59] 119860

4flavor symmetry [60ndash

64] quark-lepton complementarity [65ndash68] and neutrinomixing anarchy [69 70] have been proposed to explain theobserved pattern of one small and two large mixing anglesin the neutrino sector Future ultraprecise measurementof 12057923

will severely constrain these models leading to abetter understanding of the theories of neutrino masses andmixing

The outline of this review work is as follows We startin Section 2 by revisiting the phenomenon of neutrinooscillation in the three-neutrino frameworkThenwe discussthe importance of matter effect on neutrino oscillation inSection 3 In Section 4 we take a look at our present under-standing of neutrino oscillation parameters and we identifythe fundamental missing links in the neutrino sector thatcan be answered in the current- and next-generation long-baseline neutrino oscillation experiments Section 5 discussesin detail the three-flavor effects in long-baseline neutrinooscillation experiments with the help of ]

120583rarr ]119890oscillation

probability119875120583119890 Next in Section 6 we study the physics reach

of current-generation long-baseline beam experiments T2Kand NO]A In Section 7 we give an overview on the possibleoptions for next-generation accelerator-driven long-baselineoscillation facilities Finally in Section 8 we conclude with asummary of the main points

2 Three-Neutrino Mixing andOscillation Framework

Bruno Pontecorvo was the pathfinder of neutrino oscillation[74 75] In 1957 he gave this concept [76 77] based on a two-level quantum system Neutrino oscillation is a simple quan-tum mechanical phenomenon in which neutrino changesflavor as it travels This phenomenon arises if neutrinos havenondegenerate masses and there is mixing First we considerthe fact that neutrinos (]

119890 ]120583 ]120591) are produced or detected via

weak interactions and therefore they are referred to as weak-eigenstate neutrinos (denoted as ]

120572) It means that they are

the weak doublet-partners of 119890minus 120583minus and 120591minus respectively Insuch a case if neutrinos are assumed to be massive then ingeneral it is notmandatory that themass-matrix of neutrinoswritten in this weak (flavor) basis will have to be diagonalSo it follows that the mass eigenstate neutrinos ]

119894 119894 = 1 2 3



1003816100381610038161003816]120572⟩ =3

sum

119894=1

119880lowast

120572119894

1003816100381610038161003816]119894⟩ (1)


12




119880PMNS = (1 0 0

0 1198882311990423

0 minus1199042311988823

)

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

Atmospheric mixing

times (

11988813

0 11990413119890minus119894120575CP

0 1 0

minus11990413119890119894120575CP 0 119888

13

)

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

Reactor mixing

times (

11988812119904120

minus11990412119888120

0 0 1

)

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

Solar mixing

(2)

where 119888119894119895= cos 120579

119894119895and 119904119894119895= sin 120579



119880PMNS

= (

1198881211988813

1199041211988813

11990413119890minus119894120575CP

minus1199041211988823minus 119888121199042311990413119890119894120575CP 119888

1211988823minus 119904121199042311990413119890119894120575CP 119904

2311988813

1199041211990423minus 119888121198882311990413119890119894120575CP minus119888

1211990423minus 119904121198882311990413119890119894120575CP 119888

2311988813

)

(3)


1003816100381610038161003816119880119890210038161003816100381610038162

1003816100381610038161003816119880119890110038161003816100381610038162= tan2120579

12

100381610038161003816100381610038161198801205833

10038161003816100381610038161003816

2

1003816100381610038161003816119880120591310038161003816100381610038162= tan2120579

23

|1198801198903|2= sin2120579

13

(4)



given by

119875 (]120572997888rarr ]120573) = 119875120572120573=

10038161003816100381610038161003816100381610038161003816100381610038161003816

sum

119895

119880120573119895119890minus1198941198982

1198951198712119864119880lowast

120572119895

10038161003816100381610038161003816100381610038161003816100381610038161003816

2

(5)




written as

119875120572120573= 120575120572120573minus 4

119899

sum

119894gt119895

Re [119880lowast120572119894119880lowast

120573119895119880120573119894119880120572119895] sin2119883

119894119895

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

CP conserving

minus 2

119899

sum

119894gt119895

Im [119880lowast120572119894119880lowast

120573119895119880120573119894119880120572119895] sin2119883

119894119895

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

CP violating

(6)

where

119883119894119895=(1198982

119894minus 1198982

119895) 119871

4119864= 127

Δ1198982

119894119895

eV2119871119864

119898MeV (7)

Δ1198982

119894119895= 1198982

119894minus 1198982



119871osc119894119895=4120587119864

Δ1198982119894119895

≃ 248m 119864 (MeV)Δ1198982119894119895(eV2)

= 248 km 119864 (GeV)Δ1198982119894119895(eV2)

(8)


21= 1198982

2minus 1198982



3minus 1198982

1(responsible for



120572rarr ]120573) to 119875(]

120572rarr ]120573) (for


120572rarr ]120573) to 119875(]



120573rarr ]120572)





119890 ]120583



119860 = plusmn2radic2119866119865119873119890119864 (9)




119890) and the


119881119862119862= radic2119866

119865119873119890≃ 76119884

119890

120588

1014 gcm3eV (10)




119890= 119873119901= 119873119899and 119884







312119864 (= 24 times 10minus13 eV if

Δ1198982

31= 24 times 10



119894119889

119889119905(]120572

]120573

) =1

2119864[119880(

1198982

10

0 1198982

2

)119880dagger+ (119860 (119871) 0

0 0)](

]120572

]120573

)

(11)


(Δ1198982)119898


sin 2120579119898 = sin 2120579Δ1198982

(Δ1198982)119898

(12)


Δ1198982 cos 2120579 = 119860 (13)


119864res = 1083GeV[Δ1198982


sdot [cos 2120579096

] sdot [28 gcm3

120588]

(14)




119894le 023 eV at


21



21= 75 times 10



21Δ1198982


Δ1198982








3gt 1198982gt 1198981 called NH



Δ1198982


31is one of the







13has




13lies in the range







23has also been



23belongs to the


23asymp 06) This












23in long-



Oscillation Channel


120583rarr ]119890and ]

120583rarr ]119890


120583119890(the 119879-conjugate of 119875

119890120583) in matter [80


13and 120572 [97ndash99]

119875120583119890≃ sin2120579

23sin22120579

13

sin2 [(1 minus 119860)Δ]

(1 minus 119860)2

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

1198620

+ 1205722cos2120579

23sin22120579

12

sin2(119860Δ)1198602⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

1198621

∓ 120572 sin 212057913cos 12057913sin 2120579

12sin 2120579

23sin (Δ)

sin (119860Δ)

119860

sin [(1 minus 119860)Δ]

(1 minus 119860)⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

119862minus

sin 120575CP


+ 120572 sin 212057913cos 12057913sin 2120579

12sin 2120579

23cos(Δ) sin(119860Δ)

119860

sin[(1 minus 119860)Δ](1 minus 119860)⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

119862+

cos 120575CP

(15)

where

Δ equivΔ1198982

31119871

4119864 119860 equiv

119860

Δ119898231

(16)










0) dominates


31 This term also



minusand 119862

+are suppressed




13and


and12057912


0 119862minus and

119862+



13 120575CP)









119865119884119890 This gives (120588[g119888119888])(119871[km]) ≃ 32725









120575CP = 90∘ (120575CP = minus90


120583rarr


120583rarr


120583rarr ]


plane ((UHP) 0 le 120575CP le 180∘) 119875(]




120583rarr ]119890)


120583rarr ]




∘ and IH120575CP = 90






+0034

minus0027oplus 0613

+0022

minus00400386

+0024

minus0021

041+0037

minus0025oplus 059

+0021

minus0022

034 rarr 067

3120590 range 036 rarr 068 0331 rarr 0637

sin212057923(IH) 0600

+0026

minus00310392

+0039

minus0022

3120590 range 037 rarr 067 0335 rarr 0663




52 Octant-120575119862119875





120583119890versus 119864] (119875

120583 119890versus




















01

0

009

008

007

006

005

004

003

002

001

02 04 06 08 1 12

E (GeV)

P120583e()

01

0

009

008

007

006

005

004

003

002

001

02 04 06 08 1 12


L = 295 km sin2212057913 = 0089 sin212057923 = 05

(a)

05 1 15 2 25 3 35 4

01

0

009

008

007

006

005

004

003

002

001

E (GeV)

NHIH

120575CP = minus90∘

120575CP = +90∘

05 1 15 2 25 3 35 4

E (GeV)

NHIH

120575CP = minus90∘

120575CP = +90∘

01

0

009

008

007

006

005

004

003

002

001

L = 810 km sin2212057913 = 0089 sin212057923 = 05

P120583e(anti-)

P120583e()

(b)




13= 0089 and sin2120579

23= 05



120583rarr ]119890)



012

01

008

006

004

002

01 2 3 4 5 6 7

E (GeV)

012

01

008

006

004

002

01 2 3 4 5 6 7


P120583e()

L = 1300 km sin2212057913 = 0089 sin212057923 = 05

(a)

NHIH

120575CP = minus90∘

120575CP = +90∘

012

01

008

006

004

002

01 2 3 4 5 6 7 8 9 10

E (GeV)

NHIH

120575CP = minus90∘

120575CP = +90∘

1 2 3 4 5 6 7 8 9 10

E (GeV)

012

01

008

006

004

002

0

L = 2290 km sin2212057913 = 0089 sin212057923 = 05

P120583e(anti-)

P120583e()

(b)





13= 0089 and sin2120579

23= 05




012

01

008

006

004

002

002 04 06 08 1 12

E (GeV)02 04 06 08 1 12

E (GeV)

01

009

008

007

006

005

004

003

002

001

0

L = 295 km sin2212057913 = 0089 NH

P120583e(anti-)

P120583e()

(a)

LOHO

120575CP = minus90∘

120575CP = +90∘

012

01

008

006

004

002

005 15 25 351 2 3 4

E (GeV)

009

008

007

006

005

004

003

002

001

005 15 25 351 2 3 4

E (GeV)

LOHO

120575CP = minus90∘

120575CP = +90∘

L = 810 km sin2212057913 = 0089 NH

P120583e(anti-)

P120583e()

(b)




23= 059




E (GeV)

012

01

008

006

004

002

1 2 3 4 5 6 70

E (GeV)1 2 3 4 5 6 7

009

008

007

006

005

004

003

002

001

0

L = 1300 km sin2212057913 = 0089 NH

P120583e(anti-)

P120583e()

(a)

E (GeV)

LOHO

120575CP = minus90∘

120575CP = +90∘

1 2 3 4 5 6 7 8 9 10

012

014

01

008

006

004

002

0

E (GeV)

LOHO

120575CP = minus90∘

120575CP = +90∘

012

01

008

006

004

002

01 2 3 4 5 6 7 8 9 10

P120583e(anti-)

P120583e()

L = 2290 km sin2212057913 = 0089 NH

(b)




23= 059









10038161003816100381610038161003816Δ1198982

eff10038161003816100381610038161003816= 24 sdot 10

minus3 eV2 sin2212057923= 10 (17)


120583rarr ]

120583disap-





Δ1198982

eff = Δ1198982

31minus Δ119898

2

21


(18)






13=


13) = 13 [25] 120590(|Δ1198982eff|) = 4 and 120590(sin22120579

23) =


Δ1198982

21= 762 sdot 10

minus5 eV2 sin212057912= 032 (19)



120583








23[04ndash06]





120575CP (true)

95 CL

90 CL



12

10

8

6

4

2

0

Δ1205942


(a)

120575CP (true)

95 CL

90 CL



12

10

8

6

4

2

0

Δ1205942


(b)]


120575CP (true)

95 CL

90 CL



8

6

5

7

4

2

1

3

0

Δ1205942


(a)

120575CP (true)

95 CL

90 CL



8

6

5

7

4

2

1

3

0

Δ1205942


(b)




13= 0026 and sin2120579





NO]A (3 + 3) 048 (043) 046 (041) 016 (0) 021 (004)NO]A (3 + 3) + T2K (5 + 0) 055 (045) 054 (043) 038 (011) 049 (023)



23 the




NO]A (3 + 3) 039 (033) 037 (031) 02 (01) 022 (013)NO]A (3 + 3) + T2K (5 + 0) 041 (034) 039 (031) 028 (022) 03 (025)




13[146]



23


13= 0023 (the best-







23or not





23in the HO (LO)




13 and




20

18

16

14

12

10

8

620 25 30 35 40 45 50 55 60 65 70 75

LO-IH

HO-IH

HO-NH

LO-NH

minus90∘

090∘

180∘

T2K (25 + 25)A

nti-

app

even

ts

app events

(a)

minus90∘

0

90∘

180∘

LO-IH

HO-IH

HO-NH

LO-NH

50

45

40

35

30

25

20

15

1020 30 40 50 60 70 80 90 100 110

NOA (3 + 3)

Ant

i-ap

pev

ents

app events

(b)


13= 0089 For LO (HO) sin2120579




15

10

5

0


NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

Δ1205942

(a)


15

10

5

0


NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

Δ1205942

(b)




15

10

5

0


NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

(a)


15

10

5

0


Δ1205942

NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

(b)




of sin212057923






23le 043 or ge 058




23at 2120590 using






035 04 045 05 055 06 065

2120590

3120590 MINOS

sin212057923 (true)

120575CP

(true

) (de

g)

minus180

minus90

0

90


Global best-fit

(a)

035 04 045 05 055 06 065

2120590

3120590 MINOS

sin212057923 (true)

120575CP

(true

) (de

g)

minus180

minus90

0

90


Global best-fit

(b)
















13also allows












119890





∘ 180∘]



23= 041 is






119890and ]

119890events




NC

101

100

10minus11 2 3 4 5

2nd OSC max

1st OSC max

Even

ts pe

r0125

GeV

bin

in5

yrs




(a)

101

100

10minus1

1 2 3 4 5 6 7 8



NCEv

ents

per0125

GeV

bin

in5

yrs



(b)




100

80

60

40

20

00 50 100 150 200 250

minus90∘

0

90∘

180∘

HO-IHHO-IH

HO-NH

HO-NHLO-NH

LO-NH

LO-IHLO-IH

LBNE10

Ant

i-ap

pev

ents

app events

05lowastLBNO





13= 0089 For


[41]





23-hierarchy LO-NH



and sin2212057913


31(120590 = 4) and












101

102

103

LO-NH true


LO-IH true

LBNO

LBNE10


101

100

100

101

102

103

100

102

103

101

100

102

103

MM-NH true

LBNO

LBNE10


MM-IH true

Δ1205942

Δ1205942

Δ1205942

Δ1205942





combinations





23values






∘ sim 150

∘)






LO-NH true


LO-IH true

LBNO

LBNE10


HO-NH true

LBNO

LBNE10


HO-IH true

20

25

10

15

5

0

20

25

10

15

5

0

20

25

10

15

5

0

20

25

10

15

5

0

Δ1205942

Δ1205942

Δ1205942

Δ1205942


120575CP(true) (deg) 120575

CP(true) (deg)








119890and









LBNE10LBNO

12

10

8

2

4

6

0

2120590

3120590

Δ1205942

120575CP (true)

(a)



LBNE10LBNO

12

10

8

2

4

6

0

2120590

3120590

Δ1205942

120575CP (true)

(b)








120583 The most















sin2212057913 = 10minus1 sin

2212057913 = 10minus2

sin2212057913 = 10minus3 sin

2212057913 = 10minus4

065

065

07

07

07

04

03 035

07

08

075

055

065

045

045

075

25

25

20

15

10

5

5

20

15

10

E120583(G

eV)

E120583(G

eV)

1000 10002000 3000 4000 5000 6000

1000 2000 3000 4000 5000 6000

2000 3000 4000 5000 6000

L (km)L (km)

L (km)

25

20

15

10

5

E120583(G

eV)

25

20

15

10

5

E120583(G

eV)

1000 2000 3000 4000 5000 6000

L (km)








9F + 119890+ + ]

119890) and ]

119890from 6He (6

2He rarr

6

3Li+119890minus+]


5B rarr 8

4Be+119890++]

119890) and

8Li (83Li rarr 8

4Be + 119890minus + ]










18

10Ne 241 392 82037 921 ]

119890

6

2He 117 402 93453 100 ]

119890

8

5B 111 1443 60087207 100 ]

119890

8

3Li 120 1347 42535516 100 ]

119890



119890) and 29 times 1018 (]

119890) useful














Acknowledgments


References

































































119871times 119880(1)








































































21Δm231

and sin 12057913



13rdquo


















































































13phase and CP-
















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics





1003816100381610038161003816]120572⟩ =3

sum

119894=1

119880lowast

120572119894

1003816100381610038161003816]119894⟩ (1)


12




119880PMNS = (1 0 0

0 1198882311990423

0 minus1199042311988823

)

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

Atmospheric mixing

times (

11988813

0 11990413119890minus119894120575CP

0 1 0

minus11990413119890119894120575CP 0 119888

13

)

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

Reactor mixing

times (

11988812119904120

minus11990412119888120

0 0 1

)

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

Solar mixing

(2)

where 119888119894119895= cos 120579

119894119895and 119904119894119895= sin 120579



119880PMNS

= (

1198881211988813

1199041211988813

11990413119890minus119894120575CP

minus1199041211988823minus 119888121199042311990413119890119894120575CP 119888

1211988823minus 119904121199042311990413119890119894120575CP 119904

2311988813

1199041211990423minus 119888121198882311990413119890119894120575CP minus119888

1211990423minus 119904121198882311990413119890119894120575CP 119888

2311988813

)

(3)


1003816100381610038161003816119880119890210038161003816100381610038162

1003816100381610038161003816119880119890110038161003816100381610038162= tan2120579

12

100381610038161003816100381610038161198801205833

10038161003816100381610038161003816

2

1003816100381610038161003816119880120591310038161003816100381610038162= tan2120579

23

|1198801198903|2= sin2120579

13

(4)



given by

119875 (]120572997888rarr ]120573) = 119875120572120573=

10038161003816100381610038161003816100381610038161003816100381610038161003816

sum

119895

119880120573119895119890minus1198941198982

1198951198712119864119880lowast

120572119895

10038161003816100381610038161003816100381610038161003816100381610038161003816

2

(5)




written as

119875120572120573= 120575120572120573minus 4

119899

sum

119894gt119895

Re [119880lowast120572119894119880lowast

120573119895119880120573119894119880120572119895] sin2119883

119894119895

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

CP conserving

minus 2

119899

sum

119894gt119895

Im [119880lowast120572119894119880lowast

120573119895119880120573119894119880120572119895] sin2119883

119894119895

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

CP violating

(6)

where

119883119894119895=(1198982

119894minus 1198982

119895) 119871

4119864= 127

Δ1198982

119894119895

eV2119871119864

119898MeV (7)

Δ1198982

119894119895= 1198982

119894minus 1198982



119871osc119894119895=4120587119864

Δ1198982119894119895

≃ 248m 119864 (MeV)Δ1198982119894119895(eV2)

= 248 km 119864 (GeV)Δ1198982119894119895(eV2)

(8)


21= 1198982

2minus 1198982



3minus 1198982

1(responsible for



120572rarr ]120573) to 119875(]

120572rarr ]120573) (for


120572rarr ]120573) to 119875(]



120573rarr ]120572)





119890 ]120583



119860 = plusmn2radic2119866119865119873119890119864 (9)




119890) and the


119881119862119862= radic2119866

119865119873119890≃ 76119884

119890

120588

1014 gcm3eV (10)




119890= 119873119901= 119873119899and 119884







312119864 (= 24 times 10minus13 eV if

Δ1198982

31= 24 times 10



119894119889

119889119905(]120572

]120573

) =1

2119864[119880(

1198982

10

0 1198982

2

)119880dagger+ (119860 (119871) 0

0 0)](

]120572

]120573

)

(11)


(Δ1198982)119898


sin 2120579119898 = sin 2120579Δ1198982

(Δ1198982)119898

(12)


Δ1198982 cos 2120579 = 119860 (13)


119864res = 1083GeV[Δ1198982


sdot [cos 2120579096

] sdot [28 gcm3

120588]

(14)




119894le 023 eV at


21



21= 75 times 10



21Δ1198982


Δ1198982








3gt 1198982gt 1198981 called NH



Δ1198982


31is one of the







13has




13lies in the range







23has also been



23belongs to the


23asymp 06) This












23in long-



Oscillation Channel


120583rarr ]119890and ]

120583rarr ]119890


120583119890(the 119879-conjugate of 119875

119890120583) in matter [80


13and 120572 [97ndash99]

119875120583119890≃ sin2120579

23sin22120579

13

sin2 [(1 minus 119860)Δ]

(1 minus 119860)2

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

1198620

+ 1205722cos2120579

23sin22120579

12

sin2(119860Δ)1198602⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

1198621

∓ 120572 sin 212057913cos 12057913sin 2120579

12sin 2120579

23sin (Δ)

sin (119860Δ)

119860

sin [(1 minus 119860)Δ]

(1 minus 119860)⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

119862minus

sin 120575CP


+ 120572 sin 212057913cos 12057913sin 2120579

12sin 2120579

23cos(Δ) sin(119860Δ)

119860

sin[(1 minus 119860)Δ](1 minus 119860)⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

119862+

cos 120575CP

(15)

where

Δ equivΔ1198982

31119871

4119864 119860 equiv

119860

Δ119898231

(16)










0) dominates


31 This term also



minusand 119862

+are suppressed




13and


and12057912


0 119862minus and

119862+



13 120575CP)









119865119884119890 This gives (120588[g119888119888])(119871[km]) ≃ 32725









120575CP = 90∘ (120575CP = minus90


120583rarr


120583rarr


120583rarr ]


plane ((UHP) 0 le 120575CP le 180∘) 119875(]




120583rarr ]119890)


120583rarr ]




∘ and IH120575CP = 90






+0034

minus0027oplus 0613

+0022

minus00400386

+0024

minus0021

041+0037

minus0025oplus 059

+0021

minus0022

034 rarr 067

3120590 range 036 rarr 068 0331 rarr 0637

sin212057923(IH) 0600

+0026

minus00310392

+0039

minus0022

3120590 range 037 rarr 067 0335 rarr 0663




52 Octant-120575119862119875





120583119890versus 119864] (119875

120583 119890versus




















01

0

009

008

007

006

005

004

003

002

001

02 04 06 08 1 12

E (GeV)

P120583e()

01

0

009

008

007

006

005

004

003

002

001

02 04 06 08 1 12


L = 295 km sin2212057913 = 0089 sin212057923 = 05

(a)

05 1 15 2 25 3 35 4

01

0

009

008

007

006

005

004

003

002

001

E (GeV)

NHIH

120575CP = minus90∘

120575CP = +90∘

05 1 15 2 25 3 35 4

E (GeV)

NHIH

120575CP = minus90∘

120575CP = +90∘

01

0

009

008

007

006

005

004

003

002

001

L = 810 km sin2212057913 = 0089 sin212057923 = 05

P120583e(anti-)

P120583e()

(b)




13= 0089 and sin2120579

23= 05



120583rarr ]119890)



012

01

008

006

004

002

01 2 3 4 5 6 7

E (GeV)

012

01

008

006

004

002

01 2 3 4 5 6 7


P120583e()

L = 1300 km sin2212057913 = 0089 sin212057923 = 05

(a)

NHIH

120575CP = minus90∘

120575CP = +90∘

012

01

008

006

004

002

01 2 3 4 5 6 7 8 9 10

E (GeV)

NHIH

120575CP = minus90∘

120575CP = +90∘

1 2 3 4 5 6 7 8 9 10

E (GeV)

012

01

008

006

004

002

0

L = 2290 km sin2212057913 = 0089 sin212057923 = 05

P120583e(anti-)

P120583e()

(b)





13= 0089 and sin2120579

23= 05




012

01

008

006

004

002

002 04 06 08 1 12

E (GeV)02 04 06 08 1 12

E (GeV)

01

009

008

007

006

005

004

003

002

001

0

L = 295 km sin2212057913 = 0089 NH

P120583e(anti-)

P120583e()

(a)

LOHO

120575CP = minus90∘

120575CP = +90∘

012

01

008

006

004

002

005 15 25 351 2 3 4

E (GeV)

009

008

007

006

005

004

003

002

001

005 15 25 351 2 3 4

E (GeV)

LOHO

120575CP = minus90∘

120575CP = +90∘

L = 810 km sin2212057913 = 0089 NH

P120583e(anti-)

P120583e()

(b)




23= 059




E (GeV)

012

01

008

006

004

002

1 2 3 4 5 6 70

E (GeV)1 2 3 4 5 6 7

009

008

007

006

005

004

003

002

001

0

L = 1300 km sin2212057913 = 0089 NH

P120583e(anti-)

P120583e()

(a)

E (GeV)

LOHO

120575CP = minus90∘

120575CP = +90∘

1 2 3 4 5 6 7 8 9 10

012

014

01

008

006

004

002

0

E (GeV)

LOHO

120575CP = minus90∘

120575CP = +90∘

012

01

008

006

004

002

01 2 3 4 5 6 7 8 9 10

P120583e(anti-)

P120583e()

L = 2290 km sin2212057913 = 0089 NH

(b)




23= 059









10038161003816100381610038161003816Δ1198982

eff10038161003816100381610038161003816= 24 sdot 10

minus3 eV2 sin2212057923= 10 (17)


120583rarr ]

120583disap-





Δ1198982

eff = Δ1198982

31minus Δ119898

2

21


(18)






13=


13) = 13 [25] 120590(|Δ1198982eff|) = 4 and 120590(sin22120579

23) =


Δ1198982

21= 762 sdot 10

minus5 eV2 sin212057912= 032 (19)



120583








23[04ndash06]





120575CP (true)

95 CL

90 CL



12

10

8

6

4

2

0

Δ1205942


(a)

120575CP (true)

95 CL

90 CL



12

10

8

6

4

2

0

Δ1205942


(b)]


120575CP (true)

95 CL

90 CL



8

6

5

7

4

2

1

3

0

Δ1205942


(a)

120575CP (true)

95 CL

90 CL



8

6

5

7

4

2

1

3

0

Δ1205942


(b)




13= 0026 and sin2120579





NO]A (3 + 3) 048 (043) 046 (041) 016 (0) 021 (004)NO]A (3 + 3) + T2K (5 + 0) 055 (045) 054 (043) 038 (011) 049 (023)



23 the




NO]A (3 + 3) 039 (033) 037 (031) 02 (01) 022 (013)NO]A (3 + 3) + T2K (5 + 0) 041 (034) 039 (031) 028 (022) 03 (025)




13[146]



23


13= 0023 (the best-







23or not





23in the HO (LO)




13 and




20

18

16

14

12

10

8

620 25 30 35 40 45 50 55 60 65 70 75

LO-IH

HO-IH

HO-NH

LO-NH

minus90∘

090∘

180∘

T2K (25 + 25)A

nti-

app

even

ts

app events

(a)

minus90∘

0

90∘

180∘

LO-IH

HO-IH

HO-NH

LO-NH

50

45

40

35

30

25

20

15

1020 30 40 50 60 70 80 90 100 110

NOA (3 + 3)

Ant

i-ap

pev

ents

app events

(b)


13= 0089 For LO (HO) sin2120579




15

10

5

0


NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

Δ1205942

(a)


15

10

5

0


NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

Δ1205942

(b)




15

10

5

0


NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

(a)


15

10

5

0


Δ1205942

NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

(b)




of sin212057923






23le 043 or ge 058




23at 2120590 using






035 04 045 05 055 06 065

2120590

3120590 MINOS

sin212057923 (true)

120575CP

(true

) (de

g)

minus180

minus90

0

90


Global best-fit

(a)

035 04 045 05 055 06 065

2120590

3120590 MINOS

sin212057923 (true)

120575CP

(true

) (de

g)

minus180

minus90

0

90


Global best-fit

(b)
















13also allows












119890





∘ 180∘]



23= 041 is






119890and ]

119890events




NC

101

100

10minus11 2 3 4 5

2nd OSC max

1st OSC max

Even

ts pe

r0125

GeV

bin

in5

yrs




(a)

101

100

10minus1

1 2 3 4 5 6 7 8



NCEv

ents

per0125

GeV

bin

in5

yrs



(b)




100

80

60

40

20

00 50 100 150 200 250

minus90∘

0

90∘

180∘

HO-IHHO-IH

HO-NH

HO-NHLO-NH

LO-NH

LO-IHLO-IH

LBNE10

Ant

i-ap

pev

ents

app events

05lowastLBNO





13= 0089 For


[41]





23-hierarchy LO-NH



and sin2212057913


31(120590 = 4) and












101

102

103

LO-NH true


LO-IH true

LBNO

LBNE10


101

100

100

101

102

103

100

102

103

101

100

102

103

MM-NH true

LBNO

LBNE10


MM-IH true

Δ1205942

Δ1205942

Δ1205942

Δ1205942





combinations





23values






∘ sim 150

∘)






LO-NH true


LO-IH true

LBNO

LBNE10


HO-NH true

LBNO

LBNE10


HO-IH true

20

25

10

15

5

0

20

25

10

15

5

0

20

25

10

15

5

0

20

25

10

15

5

0

Δ1205942

Δ1205942

Δ1205942

Δ1205942


120575CP(true) (deg) 120575

CP(true) (deg)








119890and









LBNE10LBNO

12

10

8

2

4

6

0

2120590

3120590

Δ1205942

120575CP (true)

(a)



LBNE10LBNO

12

10

8

2

4

6

0

2120590

3120590

Δ1205942

120575CP (true)

(b)








120583 The most















sin2212057913 = 10minus1 sin

2212057913 = 10minus2

sin2212057913 = 10minus3 sin

2212057913 = 10minus4

065

065

07

07

07

04

03 035

07

08

075

055

065

045

045

075

25

25

20

15

10

5

5

20

15

10

E120583(G

eV)

E120583(G

eV)

1000 10002000 3000 4000 5000 6000

1000 2000 3000 4000 5000 6000

2000 3000 4000 5000 6000

L (km)L (km)

L (km)

25

20

15

10

5

E120583(G

eV)

25

20

15

10

5

E120583(G

eV)

1000 2000 3000 4000 5000 6000

L (km)








9F + 119890+ + ]

119890) and ]

119890from 6He (6

2He rarr

6

3Li+119890minus+]


5B rarr 8

4Be+119890++]

119890) and

8Li (83Li rarr 8

4Be + 119890minus + ]










18

10Ne 241 392 82037 921 ]

119890

6

2He 117 402 93453 100 ]

119890

8

5B 111 1443 60087207 100 ]

119890

8

3Li 120 1347 42535516 100 ]

119890



119890) and 29 times 1018 (]

119890) useful














Acknowledgments


References

































































119871times 119880(1)








































































21Δm231

and sin 12057913



13rdquo


















































































13phase and CP-
















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics





119890 ]120583



119860 = plusmn2radic2119866119865119873119890119864 (9)




119890) and the


119881119862119862= radic2119866

119865119873119890≃ 76119884

119890

120588

1014 gcm3eV (10)




119890= 119873119901= 119873119899and 119884







312119864 (= 24 times 10minus13 eV if

Δ1198982

31= 24 times 10



119894119889

119889119905(]120572

]120573

) =1

2119864[119880(

1198982

10

0 1198982

2

)119880dagger+ (119860 (119871) 0

0 0)](

]120572

]120573

)

(11)


(Δ1198982)119898


sin 2120579119898 = sin 2120579Δ1198982

(Δ1198982)119898

(12)


Δ1198982 cos 2120579 = 119860 (13)


119864res = 1083GeV[Δ1198982


sdot [cos 2120579096

] sdot [28 gcm3

120588]

(14)




119894le 023 eV at


21



21= 75 times 10



21Δ1198982


Δ1198982








3gt 1198982gt 1198981 called NH



Δ1198982


31is one of the







13has




13lies in the range







23has also been



23belongs to the


23asymp 06) This












23in long-



Oscillation Channel


120583rarr ]119890and ]

120583rarr ]119890


120583119890(the 119879-conjugate of 119875

119890120583) in matter [80


13and 120572 [97ndash99]

119875120583119890≃ sin2120579

23sin22120579

13

sin2 [(1 minus 119860)Δ]

(1 minus 119860)2

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

1198620

+ 1205722cos2120579

23sin22120579

12

sin2(119860Δ)1198602⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

1198621

∓ 120572 sin 212057913cos 12057913sin 2120579

12sin 2120579

23sin (Δ)

sin (119860Δ)

119860

sin [(1 minus 119860)Δ]

(1 minus 119860)⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

119862minus

sin 120575CP


+ 120572 sin 212057913cos 12057913sin 2120579

12sin 2120579

23cos(Δ) sin(119860Δ)

119860

sin[(1 minus 119860)Δ](1 minus 119860)⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

119862+

cos 120575CP

(15)

where

Δ equivΔ1198982

31119871

4119864 119860 equiv

119860

Δ119898231

(16)










0) dominates


31 This term also



minusand 119862

+are suppressed




13and


and12057912


0 119862minus and

119862+



13 120575CP)









119865119884119890 This gives (120588[g119888119888])(119871[km]) ≃ 32725









120575CP = 90∘ (120575CP = minus90


120583rarr


120583rarr


120583rarr ]


plane ((UHP) 0 le 120575CP le 180∘) 119875(]




120583rarr ]119890)


120583rarr ]




∘ and IH120575CP = 90






+0034

minus0027oplus 0613

+0022

minus00400386

+0024

minus0021

041+0037

minus0025oplus 059

+0021

minus0022

034 rarr 067

3120590 range 036 rarr 068 0331 rarr 0637

sin212057923(IH) 0600

+0026

minus00310392

+0039

minus0022

3120590 range 037 rarr 067 0335 rarr 0663




52 Octant-120575119862119875





120583119890versus 119864] (119875

120583 119890versus




















01

0

009

008

007

006

005

004

003

002

001

02 04 06 08 1 12

E (GeV)

P120583e()

01

0

009

008

007

006

005

004

003

002

001

02 04 06 08 1 12


L = 295 km sin2212057913 = 0089 sin212057923 = 05

(a)

05 1 15 2 25 3 35 4

01

0

009

008

007

006

005

004

003

002

001

E (GeV)

NHIH

120575CP = minus90∘

120575CP = +90∘

05 1 15 2 25 3 35 4

E (GeV)

NHIH

120575CP = minus90∘

120575CP = +90∘

01

0

009

008

007

006

005

004

003

002

001

L = 810 km sin2212057913 = 0089 sin212057923 = 05

P120583e(anti-)

P120583e()

(b)




13= 0089 and sin2120579

23= 05



120583rarr ]119890)



012

01

008

006

004

002

01 2 3 4 5 6 7

E (GeV)

012

01

008

006

004

002

01 2 3 4 5 6 7


P120583e()

L = 1300 km sin2212057913 = 0089 sin212057923 = 05

(a)

NHIH

120575CP = minus90∘

120575CP = +90∘

012

01

008

006

004

002

01 2 3 4 5 6 7 8 9 10

E (GeV)

NHIH

120575CP = minus90∘

120575CP = +90∘

1 2 3 4 5 6 7 8 9 10

E (GeV)

012

01

008

006

004

002

0

L = 2290 km sin2212057913 = 0089 sin212057923 = 05

P120583e(anti-)

P120583e()

(b)





13= 0089 and sin2120579

23= 05




012

01

008

006

004

002

002 04 06 08 1 12

E (GeV)02 04 06 08 1 12

E (GeV)

01

009

008

007

006

005

004

003

002

001

0

L = 295 km sin2212057913 = 0089 NH

P120583e(anti-)

P120583e()

(a)

LOHO

120575CP = minus90∘

120575CP = +90∘

012

01

008

006

004

002

005 15 25 351 2 3 4

E (GeV)

009

008

007

006

005

004

003

002

001

005 15 25 351 2 3 4

E (GeV)

LOHO

120575CP = minus90∘

120575CP = +90∘

L = 810 km sin2212057913 = 0089 NH

P120583e(anti-)

P120583e()

(b)




23= 059




E (GeV)

012

01

008

006

004

002

1 2 3 4 5 6 70

E (GeV)1 2 3 4 5 6 7

009

008

007

006

005

004

003

002

001

0

L = 1300 km sin2212057913 = 0089 NH

P120583e(anti-)

P120583e()

(a)

E (GeV)

LOHO

120575CP = minus90∘

120575CP = +90∘

1 2 3 4 5 6 7 8 9 10

012

014

01

008

006

004

002

0

E (GeV)

LOHO

120575CP = minus90∘

120575CP = +90∘

012

01

008

006

004

002

01 2 3 4 5 6 7 8 9 10

P120583e(anti-)

P120583e()

L = 2290 km sin2212057913 = 0089 NH

(b)




23= 059









10038161003816100381610038161003816Δ1198982

eff10038161003816100381610038161003816= 24 sdot 10

minus3 eV2 sin2212057923= 10 (17)


120583rarr ]

120583disap-





Δ1198982

eff = Δ1198982

31minus Δ119898

2

21


(18)






13=


13) = 13 [25] 120590(|Δ1198982eff|) = 4 and 120590(sin22120579

23) =


Δ1198982

21= 762 sdot 10

minus5 eV2 sin212057912= 032 (19)



120583








23[04ndash06]





120575CP (true)

95 CL

90 CL



12

10

8

6

4

2

0

Δ1205942


(a)

120575CP (true)

95 CL

90 CL



12

10

8

6

4

2

0

Δ1205942


(b)]


120575CP (true)

95 CL

90 CL



8

6

5

7

4

2

1

3

0

Δ1205942


(a)

120575CP (true)

95 CL

90 CL



8

6

5

7

4

2

1

3

0

Δ1205942


(b)




13= 0026 and sin2120579





NO]A (3 + 3) 048 (043) 046 (041) 016 (0) 021 (004)NO]A (3 + 3) + T2K (5 + 0) 055 (045) 054 (043) 038 (011) 049 (023)



23 the




NO]A (3 + 3) 039 (033) 037 (031) 02 (01) 022 (013)NO]A (3 + 3) + T2K (5 + 0) 041 (034) 039 (031) 028 (022) 03 (025)




13[146]



23


13= 0023 (the best-







23or not





23in the HO (LO)




13 and




20

18

16

14

12

10

8

620 25 30 35 40 45 50 55 60 65 70 75

LO-IH

HO-IH

HO-NH

LO-NH

minus90∘

090∘

180∘

T2K (25 + 25)A

nti-

app

even

ts

app events

(a)

minus90∘

0

90∘

180∘

LO-IH

HO-IH

HO-NH

LO-NH

50

45

40

35

30

25

20

15

1020 30 40 50 60 70 80 90 100 110

NOA (3 + 3)

Ant

i-ap

pev

ents

app events

(b)


13= 0089 For LO (HO) sin2120579




15

10

5

0


NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

Δ1205942

(a)


15

10

5

0


NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

Δ1205942

(b)




15

10

5

0


NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

(a)


15

10

5

0


Δ1205942

NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

(b)




of sin212057923






23le 043 or ge 058




23at 2120590 using






035 04 045 05 055 06 065

2120590

3120590 MINOS

sin212057923 (true)

120575CP

(true

) (de

g)

minus180

minus90

0

90


Global best-fit

(a)

035 04 045 05 055 06 065

2120590

3120590 MINOS

sin212057923 (true)

120575CP

(true

) (de

g)

minus180

minus90

0

90


Global best-fit

(b)
















13also allows












119890





∘ 180∘]



23= 041 is






119890and ]

119890events




NC

101

100

10minus11 2 3 4 5

2nd OSC max

1st OSC max

Even

ts pe

r0125

GeV

bin

in5

yrs




(a)

101

100

10minus1

1 2 3 4 5 6 7 8



NCEv

ents

per0125

GeV

bin

in5

yrs



(b)




100

80

60

40

20

00 50 100 150 200 250

minus90∘

0

90∘

180∘

HO-IHHO-IH

HO-NH

HO-NHLO-NH

LO-NH

LO-IHLO-IH

LBNE10

Ant

i-ap

pev

ents

app events

05lowastLBNO





13= 0089 For


[41]





23-hierarchy LO-NH



and sin2212057913


31(120590 = 4) and












101

102

103

LO-NH true


LO-IH true

LBNO

LBNE10


101

100

100

101

102

103

100

102

103

101

100

102

103

MM-NH true

LBNO

LBNE10


MM-IH true

Δ1205942

Δ1205942

Δ1205942

Δ1205942





combinations





23values






∘ sim 150

∘)






LO-NH true


LO-IH true

LBNO

LBNE10


HO-NH true

LBNO

LBNE10


HO-IH true

20

25

10

15

5

0

20

25

10

15

5

0

20

25

10

15

5

0

20

25

10

15

5

0

Δ1205942

Δ1205942

Δ1205942

Δ1205942


120575CP(true) (deg) 120575

CP(true) (deg)








119890and









LBNE10LBNO

12

10

8

2

4

6

0

2120590

3120590

Δ1205942

120575CP (true)

(a)



LBNE10LBNO

12

10

8

2

4

6

0

2120590

3120590

Δ1205942

120575CP (true)

(b)








120583 The most















sin2212057913 = 10minus1 sin

2212057913 = 10minus2

sin2212057913 = 10minus3 sin

2212057913 = 10minus4

065

065

07

07

07

04

03 035

07

08

075

055

065

045

045

075

25

25

20

15

10

5

5

20

15

10

E120583(G

eV)

E120583(G

eV)

1000 10002000 3000 4000 5000 6000

1000 2000 3000 4000 5000 6000

2000 3000 4000 5000 6000

L (km)L (km)

L (km)

25

20

15

10

5

E120583(G

eV)

25

20

15

10

5

E120583(G

eV)

1000 2000 3000 4000 5000 6000

L (km)








9F + 119890+ + ]

119890) and ]

119890from 6He (6

2He rarr

6

3Li+119890minus+]


5B rarr 8

4Be+119890++]

119890) and

8Li (83Li rarr 8

4Be + 119890minus + ]










18

10Ne 241 392 82037 921 ]

119890

6

2He 117 402 93453 100 ]

119890

8

5B 111 1443 60087207 100 ]

119890

8

3Li 120 1347 42535516 100 ]

119890



119890) and 29 times 1018 (]

119890) useful














Acknowledgments


References

































































119871times 119880(1)








































































21Δm231

and sin 12057913



13rdquo


















































































13phase and CP-
















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics









13has




13lies in the range







23has also been



23belongs to the


23asymp 06) This












23in long-



Oscillation Channel


120583rarr ]119890and ]

120583rarr ]119890


120583119890(the 119879-conjugate of 119875

119890120583) in matter [80


13and 120572 [97ndash99]

119875120583119890≃ sin2120579

23sin22120579

13

sin2 [(1 minus 119860)Δ]

(1 minus 119860)2

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

1198620

+ 1205722cos2120579

23sin22120579

12

sin2(119860Δ)1198602⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

1198621

∓ 120572 sin 212057913cos 12057913sin 2120579

12sin 2120579

23sin (Δ)

sin (119860Δ)

119860

sin [(1 minus 119860)Δ]

(1 minus 119860)⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

119862minus

sin 120575CP


+ 120572 sin 212057913cos 12057913sin 2120579

12sin 2120579

23cos(Δ) sin(119860Δ)

119860

sin[(1 minus 119860)Δ](1 minus 119860)⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

119862+

cos 120575CP

(15)

where

Δ equivΔ1198982

31119871

4119864 119860 equiv

119860

Δ119898231

(16)










0) dominates


31 This term also



minusand 119862

+are suppressed




13and


and12057912


0 119862minus and

119862+



13 120575CP)









119865119884119890 This gives (120588[g119888119888])(119871[km]) ≃ 32725









120575CP = 90∘ (120575CP = minus90


120583rarr


120583rarr


120583rarr ]


plane ((UHP) 0 le 120575CP le 180∘) 119875(]




120583rarr ]119890)


120583rarr ]




∘ and IH120575CP = 90






+0034

minus0027oplus 0613

+0022

minus00400386

+0024

minus0021

041+0037

minus0025oplus 059

+0021

minus0022

034 rarr 067

3120590 range 036 rarr 068 0331 rarr 0637

sin212057923(IH) 0600

+0026

minus00310392

+0039

minus0022

3120590 range 037 rarr 067 0335 rarr 0663




52 Octant-120575119862119875





120583119890versus 119864] (119875

120583 119890versus




















01

0

009

008

007

006

005

004

003

002

001

02 04 06 08 1 12

E (GeV)

P120583e()

01

0

009

008

007

006

005

004

003

002

001

02 04 06 08 1 12


L = 295 km sin2212057913 = 0089 sin212057923 = 05

(a)

05 1 15 2 25 3 35 4

01

0

009

008

007

006

005

004

003

002

001

E (GeV)

NHIH

120575CP = minus90∘

120575CP = +90∘

05 1 15 2 25 3 35 4

E (GeV)

NHIH

120575CP = minus90∘

120575CP = +90∘

01

0

009

008

007

006

005

004

003

002

001

L = 810 km sin2212057913 = 0089 sin212057923 = 05

P120583e(anti-)

P120583e()

(b)




13= 0089 and sin2120579

23= 05



120583rarr ]119890)



012

01

008

006

004

002

01 2 3 4 5 6 7

E (GeV)

012

01

008

006

004

002

01 2 3 4 5 6 7


P120583e()

L = 1300 km sin2212057913 = 0089 sin212057923 = 05

(a)

NHIH

120575CP = minus90∘

120575CP = +90∘

012

01

008

006

004

002

01 2 3 4 5 6 7 8 9 10

E (GeV)

NHIH

120575CP = minus90∘

120575CP = +90∘

1 2 3 4 5 6 7 8 9 10

E (GeV)

012

01

008

006

004

002

0

L = 2290 km sin2212057913 = 0089 sin212057923 = 05

P120583e(anti-)

P120583e()

(b)





13= 0089 and sin2120579

23= 05




012

01

008

006

004

002

002 04 06 08 1 12

E (GeV)02 04 06 08 1 12

E (GeV)

01

009

008

007

006

005

004

003

002

001

0

L = 295 km sin2212057913 = 0089 NH

P120583e(anti-)

P120583e()

(a)

LOHO

120575CP = minus90∘

120575CP = +90∘

012

01

008

006

004

002

005 15 25 351 2 3 4

E (GeV)

009

008

007

006

005

004

003

002

001

005 15 25 351 2 3 4

E (GeV)

LOHO

120575CP = minus90∘

120575CP = +90∘

L = 810 km sin2212057913 = 0089 NH

P120583e(anti-)

P120583e()

(b)




23= 059




E (GeV)

012

01

008

006

004

002

1 2 3 4 5 6 70

E (GeV)1 2 3 4 5 6 7

009

008

007

006

005

004

003

002

001

0

L = 1300 km sin2212057913 = 0089 NH

P120583e(anti-)

P120583e()

(a)

E (GeV)

LOHO

120575CP = minus90∘

120575CP = +90∘

1 2 3 4 5 6 7 8 9 10

012

014

01

008

006

004

002

0

E (GeV)

LOHO

120575CP = minus90∘

120575CP = +90∘

012

01

008

006

004

002

01 2 3 4 5 6 7 8 9 10

P120583e(anti-)

P120583e()

L = 2290 km sin2212057913 = 0089 NH

(b)




23= 059









10038161003816100381610038161003816Δ1198982

eff10038161003816100381610038161003816= 24 sdot 10

minus3 eV2 sin2212057923= 10 (17)


120583rarr ]

120583disap-





Δ1198982

eff = Δ1198982

31minus Δ119898

2

21


(18)






13=


13) = 13 [25] 120590(|Δ1198982eff|) = 4 and 120590(sin22120579

23) =


Δ1198982

21= 762 sdot 10

minus5 eV2 sin212057912= 032 (19)



120583








23[04ndash06]





120575CP (true)

95 CL

90 CL



12

10

8

6

4

2

0

Δ1205942


(a)

120575CP (true)

95 CL

90 CL



12

10

8

6

4

2

0

Δ1205942


(b)]


120575CP (true)

95 CL

90 CL



8

6

5

7

4

2

1

3

0

Δ1205942


(a)

120575CP (true)

95 CL

90 CL



8

6

5

7

4

2

1

3

0

Δ1205942


(b)




13= 0026 and sin2120579





NO]A (3 + 3) 048 (043) 046 (041) 016 (0) 021 (004)NO]A (3 + 3) + T2K (5 + 0) 055 (045) 054 (043) 038 (011) 049 (023)



23 the




NO]A (3 + 3) 039 (033) 037 (031) 02 (01) 022 (013)NO]A (3 + 3) + T2K (5 + 0) 041 (034) 039 (031) 028 (022) 03 (025)




13[146]



23


13= 0023 (the best-







23or not





23in the HO (LO)




13 and




20

18

16

14

12

10

8

620 25 30 35 40 45 50 55 60 65 70 75

LO-IH

HO-IH

HO-NH

LO-NH

minus90∘

090∘

180∘

T2K (25 + 25)A

nti-

app

even

ts

app events

(a)

minus90∘

0

90∘

180∘

LO-IH

HO-IH

HO-NH

LO-NH

50

45

40

35

30

25

20

15

1020 30 40 50 60 70 80 90 100 110

NOA (3 + 3)

Ant

i-ap

pev

ents

app events

(b)


13= 0089 For LO (HO) sin2120579




15

10

5

0


NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

Δ1205942

(a)


15

10

5

0


NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

Δ1205942

(b)




15

10

5

0


NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

(a)


15

10

5

0


Δ1205942

NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

(b)




of sin212057923






23le 043 or ge 058




23at 2120590 using






035 04 045 05 055 06 065

2120590

3120590 MINOS

sin212057923 (true)

120575CP

(true

) (de

g)

minus180

minus90

0

90


Global best-fit

(a)

035 04 045 05 055 06 065

2120590

3120590 MINOS

sin212057923 (true)

120575CP

(true

) (de

g)

minus180

minus90

0

90


Global best-fit

(b)
















13also allows












119890





∘ 180∘]



23= 041 is






119890and ]

119890events




NC

101

100

10minus11 2 3 4 5

2nd OSC max

1st OSC max

Even

ts pe

r0125

GeV

bin

in5

yrs




(a)

101

100

10minus1

1 2 3 4 5 6 7 8



NCEv

ents

per0125

GeV

bin

in5

yrs



(b)




100

80

60

40

20

00 50 100 150 200 250

minus90∘

0

90∘

180∘

HO-IHHO-IH

HO-NH

HO-NHLO-NH

LO-NH

LO-IHLO-IH

LBNE10

Ant

i-ap

pev

ents

app events

05lowastLBNO





13= 0089 For


[41]





23-hierarchy LO-NH



and sin2212057913


31(120590 = 4) and












101

102

103

LO-NH true


LO-IH true

LBNO

LBNE10


101

100

100

101

102

103

100

102

103

101

100

102

103

MM-NH true

LBNO

LBNE10


MM-IH true

Δ1205942

Δ1205942

Δ1205942

Δ1205942





combinations





23values






∘ sim 150

∘)






LO-NH true


LO-IH true

LBNO

LBNE10


HO-NH true

LBNO

LBNE10


HO-IH true

20

25

10

15

5

0

20

25

10

15

5

0

20

25

10

15

5

0

20

25

10

15

5

0

Δ1205942

Δ1205942

Δ1205942

Δ1205942


120575CP(true) (deg) 120575

CP(true) (deg)








119890and









LBNE10LBNO

12

10

8

2

4

6

0

2120590

3120590

Δ1205942

120575CP (true)

(a)



LBNE10LBNO

12

10

8

2

4

6

0

2120590

3120590

Δ1205942

120575CP (true)

(b)








120583 The most















sin2212057913 = 10minus1 sin

2212057913 = 10minus2

sin2212057913 = 10minus3 sin

2212057913 = 10minus4

065

065

07

07

07

04

03 035

07

08

075

055

065

045

045

075

25

25

20

15

10

5

5

20

15

10

E120583(G

eV)

E120583(G

eV)

1000 10002000 3000 4000 5000 6000

1000 2000 3000 4000 5000 6000

2000 3000 4000 5000 6000

L (km)L (km)

L (km)

25

20

15

10

5

E120583(G

eV)

25

20

15

10

5

E120583(G

eV)

1000 2000 3000 4000 5000 6000

L (km)








9F + 119890+ + ]

119890) and ]

119890from 6He (6

2He rarr

6

3Li+119890minus+]


5B rarr 8

4Be+119890++]

119890) and

8Li (83Li rarr 8

4Be + 119890minus + ]










18

10Ne 241 392 82037 921 ]

119890

6

2He 117 402 93453 100 ]

119890

8

5B 111 1443 60087207 100 ]

119890

8

3Li 120 1347 42535516 100 ]

119890



119890) and 29 times 1018 (]

119890) useful














Acknowledgments


References

































































119871times 119880(1)








































































21Δm231

and sin 12057913



13rdquo


















































































13phase and CP-
















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




+ 120572 sin 212057913cos 12057913sin 2120579

12sin 2120579

23cos(Δ) sin(119860Δ)

119860

sin[(1 minus 119860)Δ](1 minus 119860)⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

119862+

cos 120575CP

(15)

where

Δ equivΔ1198982

31119871

4119864 119860 equiv

119860

Δ119898231

(16)










0) dominates


31 This term also



minusand 119862

+are suppressed




13and


and12057912


0 119862minus and

119862+



13 120575CP)









119865119884119890 This gives (120588[g119888119888])(119871[km]) ≃ 32725









120575CP = 90∘ (120575CP = minus90


120583rarr


120583rarr


120583rarr ]


plane ((UHP) 0 le 120575CP le 180∘) 119875(]




120583rarr ]119890)


120583rarr ]




∘ and IH120575CP = 90






+0034

minus0027oplus 0613

+0022

minus00400386

+0024

minus0021

041+0037

minus0025oplus 059

+0021

minus0022

034 rarr 067

3120590 range 036 rarr 068 0331 rarr 0637

sin212057923(IH) 0600

+0026

minus00310392

+0039

minus0022

3120590 range 037 rarr 067 0335 rarr 0663




52 Octant-120575119862119875





120583119890versus 119864] (119875

120583 119890versus




















01

0

009

008

007

006

005

004

003

002

001

02 04 06 08 1 12

E (GeV)

P120583e()

01

0

009

008

007

006

005

004

003

002

001

02 04 06 08 1 12


L = 295 km sin2212057913 = 0089 sin212057923 = 05

(a)

05 1 15 2 25 3 35 4

01

0

009

008

007

006

005

004

003

002

001

E (GeV)

NHIH

120575CP = minus90∘

120575CP = +90∘

05 1 15 2 25 3 35 4

E (GeV)

NHIH

120575CP = minus90∘

120575CP = +90∘

01

0

009

008

007

006

005

004

003

002

001

L = 810 km sin2212057913 = 0089 sin212057923 = 05

P120583e(anti-)

P120583e()

(b)




13= 0089 and sin2120579

23= 05



120583rarr ]119890)



012

01

008

006

004

002

01 2 3 4 5 6 7

E (GeV)

012

01

008

006

004

002

01 2 3 4 5 6 7


P120583e()

L = 1300 km sin2212057913 = 0089 sin212057923 = 05

(a)

NHIH

120575CP = minus90∘

120575CP = +90∘

012

01

008

006

004

002

01 2 3 4 5 6 7 8 9 10

E (GeV)

NHIH

120575CP = minus90∘

120575CP = +90∘

1 2 3 4 5 6 7 8 9 10

E (GeV)

012

01

008

006

004

002

0

L = 2290 km sin2212057913 = 0089 sin212057923 = 05

P120583e(anti-)

P120583e()

(b)





13= 0089 and sin2120579

23= 05




012

01

008

006

004

002

002 04 06 08 1 12

E (GeV)02 04 06 08 1 12

E (GeV)

01

009

008

007

006

005

004

003

002

001

0

L = 295 km sin2212057913 = 0089 NH

P120583e(anti-)

P120583e()

(a)

LOHO

120575CP = minus90∘

120575CP = +90∘

012

01

008

006

004

002

005 15 25 351 2 3 4

E (GeV)

009

008

007

006

005

004

003

002

001

005 15 25 351 2 3 4

E (GeV)

LOHO

120575CP = minus90∘

120575CP = +90∘

L = 810 km sin2212057913 = 0089 NH

P120583e(anti-)

P120583e()

(b)




23= 059




E (GeV)

012

01

008

006

004

002

1 2 3 4 5 6 70

E (GeV)1 2 3 4 5 6 7

009

008

007

006

005

004

003

002

001

0

L = 1300 km sin2212057913 = 0089 NH

P120583e(anti-)

P120583e()

(a)

E (GeV)

LOHO

120575CP = minus90∘

120575CP = +90∘

1 2 3 4 5 6 7 8 9 10

012

014

01

008

006

004

002

0

E (GeV)

LOHO

120575CP = minus90∘

120575CP = +90∘

012

01

008

006

004

002

01 2 3 4 5 6 7 8 9 10

P120583e(anti-)

P120583e()

L = 2290 km sin2212057913 = 0089 NH

(b)




23= 059









10038161003816100381610038161003816Δ1198982

eff10038161003816100381610038161003816= 24 sdot 10

minus3 eV2 sin2212057923= 10 (17)


120583rarr ]

120583disap-





Δ1198982

eff = Δ1198982

31minus Δ119898

2

21


(18)






13=


13) = 13 [25] 120590(|Δ1198982eff|) = 4 and 120590(sin22120579

23) =


Δ1198982

21= 762 sdot 10

minus5 eV2 sin212057912= 032 (19)



120583








23[04ndash06]





120575CP (true)

95 CL

90 CL



12

10

8

6

4

2

0

Δ1205942


(a)

120575CP (true)

95 CL

90 CL



12

10

8

6

4

2

0

Δ1205942


(b)]


120575CP (true)

95 CL

90 CL



8

6

5

7

4

2

1

3

0

Δ1205942


(a)

120575CP (true)

95 CL

90 CL



8

6

5

7

4

2

1

3

0

Δ1205942


(b)




13= 0026 and sin2120579





NO]A (3 + 3) 048 (043) 046 (041) 016 (0) 021 (004)NO]A (3 + 3) + T2K (5 + 0) 055 (045) 054 (043) 038 (011) 049 (023)



23 the




NO]A (3 + 3) 039 (033) 037 (031) 02 (01) 022 (013)NO]A (3 + 3) + T2K (5 + 0) 041 (034) 039 (031) 028 (022) 03 (025)




13[146]



23


13= 0023 (the best-







23or not





23in the HO (LO)




13 and




20

18

16

14

12

10

8

620 25 30 35 40 45 50 55 60 65 70 75

LO-IH

HO-IH

HO-NH

LO-NH

minus90∘

090∘

180∘

T2K (25 + 25)A

nti-

app

even

ts

app events

(a)

minus90∘

0

90∘

180∘

LO-IH

HO-IH

HO-NH

LO-NH

50

45

40

35

30

25

20

15

1020 30 40 50 60 70 80 90 100 110

NOA (3 + 3)

Ant

i-ap

pev

ents

app events

(b)


13= 0089 For LO (HO) sin2120579




15

10

5

0


NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

Δ1205942

(a)


15

10

5

0


NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

Δ1205942

(b)




15

10

5

0


NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

(a)


15

10

5

0


Δ1205942

NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

(b)




of sin212057923






23le 043 or ge 058




23at 2120590 using






035 04 045 05 055 06 065

2120590

3120590 MINOS

sin212057923 (true)

120575CP

(true

) (de

g)

minus180

minus90

0

90


Global best-fit

(a)

035 04 045 05 055 06 065

2120590

3120590 MINOS

sin212057923 (true)

120575CP

(true

) (de

g)

minus180

minus90

0

90


Global best-fit

(b)
















13also allows












119890





∘ 180∘]



23= 041 is






119890and ]

119890events




NC

101

100

10minus11 2 3 4 5

2nd OSC max

1st OSC max

Even

ts pe

r0125

GeV

bin

in5

yrs




(a)

101

100

10minus1

1 2 3 4 5 6 7 8



NCEv

ents

per0125

GeV

bin

in5

yrs



(b)




100

80

60

40

20

00 50 100 150 200 250

minus90∘

0

90∘

180∘

HO-IHHO-IH

HO-NH

HO-NHLO-NH

LO-NH

LO-IHLO-IH

LBNE10

Ant

i-ap

pev

ents

app events

05lowastLBNO





13= 0089 For


[41]





23-hierarchy LO-NH



and sin2212057913


31(120590 = 4) and












101

102

103

LO-NH true


LO-IH true

LBNO

LBNE10


101

100

100

101

102

103

100

102

103

101

100

102

103

MM-NH true

LBNO

LBNE10


MM-IH true

Δ1205942

Δ1205942

Δ1205942

Δ1205942





combinations





23values






∘ sim 150

∘)






LO-NH true


LO-IH true

LBNO

LBNE10


HO-NH true

LBNO

LBNE10


HO-IH true

20

25

10

15

5

0

20

25

10

15

5

0

20

25

10

15

5

0

20

25

10

15

5

0

Δ1205942

Δ1205942

Δ1205942

Δ1205942


120575CP(true) (deg) 120575

CP(true) (deg)








119890and









LBNE10LBNO

12

10

8

2

4

6

0

2120590

3120590

Δ1205942

120575CP (true)

(a)



LBNE10LBNO

12

10

8

2

4

6

0

2120590

3120590

Δ1205942

120575CP (true)

(b)








120583 The most















sin2212057913 = 10minus1 sin

2212057913 = 10minus2

sin2212057913 = 10minus3 sin

2212057913 = 10minus4

065

065

07

07

07

04

03 035

07

08

075

055

065

045

045

075

25

25

20

15

10

5

5

20

15

10

E120583(G

eV)

E120583(G

eV)

1000 10002000 3000 4000 5000 6000

1000 2000 3000 4000 5000 6000

2000 3000 4000 5000 6000

L (km)L (km)

L (km)

25

20

15

10

5

E120583(G

eV)

25

20

15

10

5

E120583(G

eV)

1000 2000 3000 4000 5000 6000

L (km)








9F + 119890+ + ]

119890) and ]

119890from 6He (6

2He rarr

6

3Li+119890minus+]


5B rarr 8

4Be+119890++]

119890) and

8Li (83Li rarr 8

4Be + 119890minus + ]










18

10Ne 241 392 82037 921 ]

119890

6

2He 117 402 93453 100 ]

119890

8

5B 111 1443 60087207 100 ]

119890

8

3Li 120 1347 42535516 100 ]

119890



119890) and 29 times 1018 (]

119890) useful














Acknowledgments


References

































































119871times 119880(1)








































































21Δm231

and sin 12057913



13rdquo


















































































13phase and CP-
















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics







+0034

minus0027oplus 0613

+0022

minus00400386

+0024

minus0021

041+0037

minus0025oplus 059

+0021

minus0022

034 rarr 067

3120590 range 036 rarr 068 0331 rarr 0637

sin212057923(IH) 0600

+0026

minus00310392

+0039

minus0022

3120590 range 037 rarr 067 0335 rarr 0663




52 Octant-120575119862119875





120583119890versus 119864] (119875

120583 119890versus




















01

0

009

008

007

006

005

004

003

002

001

02 04 06 08 1 12

E (GeV)

P120583e()

01

0

009

008

007

006

005

004

003

002

001

02 04 06 08 1 12


L = 295 km sin2212057913 = 0089 sin212057923 = 05

(a)

05 1 15 2 25 3 35 4

01

0

009

008

007

006

005

004

003

002

001

E (GeV)

NHIH

120575CP = minus90∘

120575CP = +90∘

05 1 15 2 25 3 35 4

E (GeV)

NHIH

120575CP = minus90∘

120575CP = +90∘

01

0

009

008

007

006

005

004

003

002

001

L = 810 km sin2212057913 = 0089 sin212057923 = 05

P120583e(anti-)

P120583e()

(b)




13= 0089 and sin2120579

23= 05



120583rarr ]119890)



012

01

008

006

004

002

01 2 3 4 5 6 7

E (GeV)

012

01

008

006

004

002

01 2 3 4 5 6 7


P120583e()

L = 1300 km sin2212057913 = 0089 sin212057923 = 05

(a)

NHIH

120575CP = minus90∘

120575CP = +90∘

012

01

008

006

004

002

01 2 3 4 5 6 7 8 9 10

E (GeV)

NHIH

120575CP = minus90∘

120575CP = +90∘

1 2 3 4 5 6 7 8 9 10

E (GeV)

012

01

008

006

004

002

0

L = 2290 km sin2212057913 = 0089 sin212057923 = 05

P120583e(anti-)

P120583e()

(b)





13= 0089 and sin2120579

23= 05




012

01

008

006

004

002

002 04 06 08 1 12

E (GeV)02 04 06 08 1 12

E (GeV)

01

009

008

007

006

005

004

003

002

001

0

L = 295 km sin2212057913 = 0089 NH

P120583e(anti-)

P120583e()

(a)

LOHO

120575CP = minus90∘

120575CP = +90∘

012

01

008

006

004

002

005 15 25 351 2 3 4

E (GeV)

009

008

007

006

005

004

003

002

001

005 15 25 351 2 3 4

E (GeV)

LOHO

120575CP = minus90∘

120575CP = +90∘

L = 810 km sin2212057913 = 0089 NH

P120583e(anti-)

P120583e()

(b)




23= 059




E (GeV)

012

01

008

006

004

002

1 2 3 4 5 6 70

E (GeV)1 2 3 4 5 6 7

009

008

007

006

005

004

003

002

001

0

L = 1300 km sin2212057913 = 0089 NH

P120583e(anti-)

P120583e()

(a)

E (GeV)

LOHO

120575CP = minus90∘

120575CP = +90∘

1 2 3 4 5 6 7 8 9 10

012

014

01

008

006

004

002

0

E (GeV)

LOHO

120575CP = minus90∘

120575CP = +90∘

012

01

008

006

004

002

01 2 3 4 5 6 7 8 9 10

P120583e(anti-)

P120583e()

L = 2290 km sin2212057913 = 0089 NH

(b)




23= 059









10038161003816100381610038161003816Δ1198982

eff10038161003816100381610038161003816= 24 sdot 10

minus3 eV2 sin2212057923= 10 (17)


120583rarr ]

120583disap-





Δ1198982

eff = Δ1198982

31minus Δ119898

2

21


(18)






13=


13) = 13 [25] 120590(|Δ1198982eff|) = 4 and 120590(sin22120579

23) =


Δ1198982

21= 762 sdot 10

minus5 eV2 sin212057912= 032 (19)



120583








23[04ndash06]





120575CP (true)

95 CL

90 CL



12

10

8

6

4

2

0

Δ1205942


(a)

120575CP (true)

95 CL

90 CL



12

10

8

6

4

2

0

Δ1205942


(b)]


120575CP (true)

95 CL

90 CL



8

6

5

7

4

2

1

3

0

Δ1205942


(a)

120575CP (true)

95 CL

90 CL



8

6

5

7

4

2

1

3

0

Δ1205942


(b)




13= 0026 and sin2120579





NO]A (3 + 3) 048 (043) 046 (041) 016 (0) 021 (004)NO]A (3 + 3) + T2K (5 + 0) 055 (045) 054 (043) 038 (011) 049 (023)



23 the




NO]A (3 + 3) 039 (033) 037 (031) 02 (01) 022 (013)NO]A (3 + 3) + T2K (5 + 0) 041 (034) 039 (031) 028 (022) 03 (025)




13[146]



23


13= 0023 (the best-







23or not





23in the HO (LO)




13 and




20

18

16

14

12

10

8

620 25 30 35 40 45 50 55 60 65 70 75

LO-IH

HO-IH

HO-NH

LO-NH

minus90∘

090∘

180∘

T2K (25 + 25)A

nti-

app

even

ts

app events

(a)

minus90∘

0

90∘

180∘

LO-IH

HO-IH

HO-NH

LO-NH

50

45

40

35

30

25

20

15

1020 30 40 50 60 70 80 90 100 110

NOA (3 + 3)

Ant

i-ap

pev

ents

app events

(b)


13= 0089 For LO (HO) sin2120579




15

10

5

0


NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

Δ1205942

(a)


15

10

5

0


NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

Δ1205942

(b)




15

10

5

0


NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

(a)


15

10

5

0


Δ1205942

NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

(b)




of sin212057923






23le 043 or ge 058




23at 2120590 using






035 04 045 05 055 06 065

2120590

3120590 MINOS

sin212057923 (true)

120575CP

(true

) (de

g)

minus180

minus90

0

90


Global best-fit

(a)

035 04 045 05 055 06 065

2120590

3120590 MINOS

sin212057923 (true)

120575CP

(true

) (de

g)

minus180

minus90

0

90


Global best-fit

(b)
















13also allows












119890





∘ 180∘]



23= 041 is






119890and ]

119890events




NC

101

100

10minus11 2 3 4 5

2nd OSC max

1st OSC max

Even

ts pe

r0125

GeV

bin

in5

yrs




(a)

101

100

10minus1

1 2 3 4 5 6 7 8



NCEv

ents

per0125

GeV

bin

in5

yrs



(b)




100

80

60

40

20

00 50 100 150 200 250

minus90∘

0

90∘

180∘

HO-IHHO-IH

HO-NH

HO-NHLO-NH

LO-NH

LO-IHLO-IH

LBNE10

Ant

i-ap

pev

ents

app events

05lowastLBNO





13= 0089 For


[41]





23-hierarchy LO-NH



and sin2212057913


31(120590 = 4) and












101

102

103

LO-NH true


LO-IH true

LBNO

LBNE10


101

100

100

101

102

103

100

102

103

101

100

102

103

MM-NH true

LBNO

LBNE10


MM-IH true

Δ1205942

Δ1205942

Δ1205942

Δ1205942





combinations





23values






∘ sim 150

∘)






LO-NH true


LO-IH true

LBNO

LBNE10


HO-NH true

LBNO

LBNE10


HO-IH true

20

25

10

15

5

0

20

25

10

15

5

0

20

25

10

15

5

0

20

25

10

15

5

0

Δ1205942

Δ1205942

Δ1205942

Δ1205942


120575CP(true) (deg) 120575

CP(true) (deg)








119890and









LBNE10LBNO

12

10

8

2

4

6

0

2120590

3120590

Δ1205942

120575CP (true)

(a)



LBNE10LBNO

12

10

8

2

4

6

0

2120590

3120590

Δ1205942

120575CP (true)

(b)








120583 The most















sin2212057913 = 10minus1 sin

2212057913 = 10minus2

sin2212057913 = 10minus3 sin

2212057913 = 10minus4

065

065

07

07

07

04

03 035

07

08

075

055

065

045

045

075

25

25

20

15

10

5

5

20

15

10

E120583(G

eV)

E120583(G

eV)

1000 10002000 3000 4000 5000 6000

1000 2000 3000 4000 5000 6000

2000 3000 4000 5000 6000

L (km)L (km)

L (km)

25

20

15

10

5

E120583(G

eV)

25

20

15

10

5

E120583(G

eV)

1000 2000 3000 4000 5000 6000

L (km)








9F + 119890+ + ]

119890) and ]

119890from 6He (6

2He rarr

6

3Li+119890minus+]


5B rarr 8

4Be+119890++]

119890) and

8Li (83Li rarr 8

4Be + 119890minus + ]










18

10Ne 241 392 82037 921 ]

119890

6

2He 117 402 93453 100 ]

119890

8

5B 111 1443 60087207 100 ]

119890

8

3Li 120 1347 42535516 100 ]

119890



119890) and 29 times 1018 (]

119890) useful














Acknowledgments


References

































































119871times 119880(1)








































































21Δm231

and sin 12057913



13rdquo


















































































13phase and CP-
















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




01

0

009

008

007

006

005

004

003

002

001

02 04 06 08 1 12

E (GeV)

P120583e()

01

0

009

008

007

006

005

004

003

002

001

02 04 06 08 1 12


L = 295 km sin2212057913 = 0089 sin212057923 = 05

(a)

05 1 15 2 25 3 35 4

01

0

009

008

007

006

005

004

003

002

001

E (GeV)

NHIH

120575CP = minus90∘

120575CP = +90∘

05 1 15 2 25 3 35 4

E (GeV)

NHIH

120575CP = minus90∘

120575CP = +90∘

01

0

009

008

007

006

005

004

003

002

001

L = 810 km sin2212057913 = 0089 sin212057923 = 05

P120583e(anti-)

P120583e()

(b)




13= 0089 and sin2120579

23= 05



120583rarr ]119890)



012

01

008

006

004

002

01 2 3 4 5 6 7

E (GeV)

012

01

008

006

004

002

01 2 3 4 5 6 7


P120583e()

L = 1300 km sin2212057913 = 0089 sin212057923 = 05

(a)

NHIH

120575CP = minus90∘

120575CP = +90∘

012

01

008

006

004

002

01 2 3 4 5 6 7 8 9 10

E (GeV)

NHIH

120575CP = minus90∘

120575CP = +90∘

1 2 3 4 5 6 7 8 9 10

E (GeV)

012

01

008

006

004

002

0

L = 2290 km sin2212057913 = 0089 sin212057923 = 05

P120583e(anti-)

P120583e()

(b)





13= 0089 and sin2120579

23= 05




012

01

008

006

004

002

002 04 06 08 1 12

E (GeV)02 04 06 08 1 12

E (GeV)

01

009

008

007

006

005

004

003

002

001

0

L = 295 km sin2212057913 = 0089 NH

P120583e(anti-)

P120583e()

(a)

LOHO

120575CP = minus90∘

120575CP = +90∘

012

01

008

006

004

002

005 15 25 351 2 3 4

E (GeV)

009

008

007

006

005

004

003

002

001

005 15 25 351 2 3 4

E (GeV)

LOHO

120575CP = minus90∘

120575CP = +90∘

L = 810 km sin2212057913 = 0089 NH

P120583e(anti-)

P120583e()

(b)




23= 059




E (GeV)

012

01

008

006

004

002

1 2 3 4 5 6 70

E (GeV)1 2 3 4 5 6 7

009

008

007

006

005

004

003

002

001

0

L = 1300 km sin2212057913 = 0089 NH

P120583e(anti-)

P120583e()

(a)

E (GeV)

LOHO

120575CP = minus90∘

120575CP = +90∘

1 2 3 4 5 6 7 8 9 10

012

014

01

008

006

004

002

0

E (GeV)

LOHO

120575CP = minus90∘

120575CP = +90∘

012

01

008

006

004

002

01 2 3 4 5 6 7 8 9 10

P120583e(anti-)

P120583e()

L = 2290 km sin2212057913 = 0089 NH

(b)




23= 059









10038161003816100381610038161003816Δ1198982

eff10038161003816100381610038161003816= 24 sdot 10

minus3 eV2 sin2212057923= 10 (17)


120583rarr ]

120583disap-





Δ1198982

eff = Δ1198982

31minus Δ119898

2

21


(18)






13=


13) = 13 [25] 120590(|Δ1198982eff|) = 4 and 120590(sin22120579

23) =


Δ1198982

21= 762 sdot 10

minus5 eV2 sin212057912= 032 (19)



120583








23[04ndash06]





120575CP (true)

95 CL

90 CL



12

10

8

6

4

2

0

Δ1205942


(a)

120575CP (true)

95 CL

90 CL



12

10

8

6

4

2

0

Δ1205942


(b)]


120575CP (true)

95 CL

90 CL



8

6

5

7

4

2

1

3

0

Δ1205942


(a)

120575CP (true)

95 CL

90 CL



8

6

5

7

4

2

1

3

0

Δ1205942


(b)




13= 0026 and sin2120579





NO]A (3 + 3) 048 (043) 046 (041) 016 (0) 021 (004)NO]A (3 + 3) + T2K (5 + 0) 055 (045) 054 (043) 038 (011) 049 (023)



23 the




NO]A (3 + 3) 039 (033) 037 (031) 02 (01) 022 (013)NO]A (3 + 3) + T2K (5 + 0) 041 (034) 039 (031) 028 (022) 03 (025)




13[146]



23


13= 0023 (the best-







23or not





23in the HO (LO)




13 and




20

18

16

14

12

10

8

620 25 30 35 40 45 50 55 60 65 70 75

LO-IH

HO-IH

HO-NH

LO-NH

minus90∘

090∘

180∘

T2K (25 + 25)A

nti-

app

even

ts

app events

(a)

minus90∘

0

90∘

180∘

LO-IH

HO-IH

HO-NH

LO-NH

50

45

40

35

30

25

20

15

1020 30 40 50 60 70 80 90 100 110

NOA (3 + 3)

Ant

i-ap

pev

ents

app events

(b)


13= 0089 For LO (HO) sin2120579




15

10

5

0


NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

Δ1205942

(a)


15

10

5

0


NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

Δ1205942

(b)




15

10

5

0


NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

(a)


15

10

5

0


Δ1205942

NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

(b)




of sin212057923






23le 043 or ge 058




23at 2120590 using






035 04 045 05 055 06 065

2120590

3120590 MINOS

sin212057923 (true)

120575CP

(true

) (de

g)

minus180

minus90

0

90


Global best-fit

(a)

035 04 045 05 055 06 065

2120590

3120590 MINOS

sin212057923 (true)

120575CP

(true

) (de

g)

minus180

minus90

0

90


Global best-fit

(b)
















13also allows












119890





∘ 180∘]



23= 041 is






119890and ]

119890events




NC

101

100

10minus11 2 3 4 5

2nd OSC max

1st OSC max

Even

ts pe

r0125

GeV

bin

in5

yrs




(a)

101

100

10minus1

1 2 3 4 5 6 7 8



NCEv

ents

per0125

GeV

bin

in5

yrs



(b)




100

80

60

40

20

00 50 100 150 200 250

minus90∘

0

90∘

180∘

HO-IHHO-IH

HO-NH

HO-NHLO-NH

LO-NH

LO-IHLO-IH

LBNE10

Ant

i-ap

pev

ents

app events

05lowastLBNO





13= 0089 For


[41]





23-hierarchy LO-NH



and sin2212057913


31(120590 = 4) and












101

102

103

LO-NH true


LO-IH true

LBNO

LBNE10


101

100

100

101

102

103

100

102

103

101

100

102

103

MM-NH true

LBNO

LBNE10


MM-IH true

Δ1205942

Δ1205942

Δ1205942

Δ1205942





combinations





23values






∘ sim 150

∘)






LO-NH true


LO-IH true

LBNO

LBNE10


HO-NH true

LBNO

LBNE10


HO-IH true

20

25

10

15

5

0

20

25

10

15

5

0

20

25

10

15

5

0

20

25

10

15

5

0

Δ1205942

Δ1205942

Δ1205942

Δ1205942


120575CP(true) (deg) 120575

CP(true) (deg)








119890and









LBNE10LBNO

12

10

8

2

4

6

0

2120590

3120590

Δ1205942

120575CP (true)

(a)



LBNE10LBNO

12

10

8

2

4

6

0

2120590

3120590

Δ1205942

120575CP (true)

(b)








120583 The most















sin2212057913 = 10minus1 sin

2212057913 = 10minus2

sin2212057913 = 10minus3 sin

2212057913 = 10minus4

065

065

07

07

07

04

03 035

07

08

075

055

065

045

045

075

25

25

20

15

10

5

5

20

15

10

E120583(G

eV)

E120583(G

eV)

1000 10002000 3000 4000 5000 6000

1000 2000 3000 4000 5000 6000

2000 3000 4000 5000 6000

L (km)L (km)

L (km)

25

20

15

10

5

E120583(G

eV)

25

20

15

10

5

E120583(G

eV)

1000 2000 3000 4000 5000 6000

L (km)








9F + 119890+ + ]

119890) and ]

119890from 6He (6

2He rarr

6

3Li+119890minus+]


5B rarr 8

4Be+119890++]

119890) and

8Li (83Li rarr 8

4Be + 119890minus + ]










18

10Ne 241 392 82037 921 ]

119890

6

2He 117 402 93453 100 ]

119890

8

5B 111 1443 60087207 100 ]

119890

8

3Li 120 1347 42535516 100 ]

119890



119890) and 29 times 1018 (]

119890) useful














Acknowledgments


References

































































119871times 119880(1)








































































21Δm231

and sin 12057913



13rdquo


















































































13phase and CP-
















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




012

01

008

006

004

002

01 2 3 4 5 6 7

E (GeV)

012

01

008

006

004

002

01 2 3 4 5 6 7


P120583e()

L = 1300 km sin2212057913 = 0089 sin212057923 = 05

(a)

NHIH

120575CP = minus90∘

120575CP = +90∘

012

01

008

006

004

002

01 2 3 4 5 6 7 8 9 10

E (GeV)

NHIH

120575CP = minus90∘

120575CP = +90∘

1 2 3 4 5 6 7 8 9 10

E (GeV)

012

01

008

006

004

002

0

L = 2290 km sin2212057913 = 0089 sin212057923 = 05

P120583e(anti-)

P120583e()

(b)





13= 0089 and sin2120579

23= 05




012

01

008

006

004

002

002 04 06 08 1 12

E (GeV)02 04 06 08 1 12

E (GeV)

01

009

008

007

006

005

004

003

002

001

0

L = 295 km sin2212057913 = 0089 NH

P120583e(anti-)

P120583e()

(a)

LOHO

120575CP = minus90∘

120575CP = +90∘

012

01

008

006

004

002

005 15 25 351 2 3 4

E (GeV)

009

008

007

006

005

004

003

002

001

005 15 25 351 2 3 4

E (GeV)

LOHO

120575CP = minus90∘

120575CP = +90∘

L = 810 km sin2212057913 = 0089 NH

P120583e(anti-)

P120583e()

(b)




23= 059




E (GeV)

012

01

008

006

004

002

1 2 3 4 5 6 70

E (GeV)1 2 3 4 5 6 7

009

008

007

006

005

004

003

002

001

0

L = 1300 km sin2212057913 = 0089 NH

P120583e(anti-)

P120583e()

(a)

E (GeV)

LOHO

120575CP = minus90∘

120575CP = +90∘

1 2 3 4 5 6 7 8 9 10

012

014

01

008

006

004

002

0

E (GeV)

LOHO

120575CP = minus90∘

120575CP = +90∘

012

01

008

006

004

002

01 2 3 4 5 6 7 8 9 10

P120583e(anti-)

P120583e()

L = 2290 km sin2212057913 = 0089 NH

(b)




23= 059









10038161003816100381610038161003816Δ1198982

eff10038161003816100381610038161003816= 24 sdot 10

minus3 eV2 sin2212057923= 10 (17)


120583rarr ]

120583disap-





Δ1198982

eff = Δ1198982

31minus Δ119898

2

21


(18)






13=


13) = 13 [25] 120590(|Δ1198982eff|) = 4 and 120590(sin22120579

23) =


Δ1198982

21= 762 sdot 10

minus5 eV2 sin212057912= 032 (19)



120583








23[04ndash06]





120575CP (true)

95 CL

90 CL



12

10

8

6

4

2

0

Δ1205942


(a)

120575CP (true)

95 CL

90 CL



12

10

8

6

4

2

0

Δ1205942


(b)]


120575CP (true)

95 CL

90 CL



8

6

5

7

4

2

1

3

0

Δ1205942


(a)

120575CP (true)

95 CL

90 CL



8

6

5

7

4

2

1

3

0

Δ1205942


(b)




13= 0026 and sin2120579





NO]A (3 + 3) 048 (043) 046 (041) 016 (0) 021 (004)NO]A (3 + 3) + T2K (5 + 0) 055 (045) 054 (043) 038 (011) 049 (023)



23 the




NO]A (3 + 3) 039 (033) 037 (031) 02 (01) 022 (013)NO]A (3 + 3) + T2K (5 + 0) 041 (034) 039 (031) 028 (022) 03 (025)




13[146]



23


13= 0023 (the best-







23or not





23in the HO (LO)




13 and




20

18

16

14

12

10

8

620 25 30 35 40 45 50 55 60 65 70 75

LO-IH

HO-IH

HO-NH

LO-NH

minus90∘

090∘

180∘

T2K (25 + 25)A

nti-

app

even

ts

app events

(a)

minus90∘

0

90∘

180∘

LO-IH

HO-IH

HO-NH

LO-NH

50

45

40

35

30

25

20

15

1020 30 40 50 60 70 80 90 100 110

NOA (3 + 3)

Ant

i-ap

pev

ents

app events

(b)


13= 0089 For LO (HO) sin2120579




15

10

5

0


NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

Δ1205942

(a)


15

10

5

0


NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

Δ1205942

(b)




15

10

5

0


NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

(a)


15

10

5

0


Δ1205942

NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

(b)




of sin212057923






23le 043 or ge 058




23at 2120590 using






035 04 045 05 055 06 065

2120590

3120590 MINOS

sin212057923 (true)

120575CP

(true

) (de

g)

minus180

minus90

0

90


Global best-fit

(a)

035 04 045 05 055 06 065

2120590

3120590 MINOS

sin212057923 (true)

120575CP

(true

) (de

g)

minus180

minus90

0

90


Global best-fit

(b)
















13also allows












119890





∘ 180∘]



23= 041 is






119890and ]

119890events




NC

101

100

10minus11 2 3 4 5

2nd OSC max

1st OSC max

Even

ts pe

r0125

GeV

bin

in5

yrs




(a)

101

100

10minus1

1 2 3 4 5 6 7 8



NCEv

ents

per0125

GeV

bin

in5

yrs



(b)




100

80

60

40

20

00 50 100 150 200 250

minus90∘

0

90∘

180∘

HO-IHHO-IH

HO-NH

HO-NHLO-NH

LO-NH

LO-IHLO-IH

LBNE10

Ant

i-ap

pev

ents

app events

05lowastLBNO





13= 0089 For


[41]





23-hierarchy LO-NH



and sin2212057913


31(120590 = 4) and












101

102

103

LO-NH true


LO-IH true

LBNO

LBNE10


101

100

100

101

102

103

100

102

103

101

100

102

103

MM-NH true

LBNO

LBNE10


MM-IH true

Δ1205942

Δ1205942

Δ1205942

Δ1205942





combinations





23values






∘ sim 150

∘)






LO-NH true


LO-IH true

LBNO

LBNE10


HO-NH true

LBNO

LBNE10


HO-IH true

20

25

10

15

5

0

20

25

10

15

5

0

20

25

10

15

5

0

20

25

10

15

5

0

Δ1205942

Δ1205942

Δ1205942

Δ1205942


120575CP(true) (deg) 120575

CP(true) (deg)








119890and









LBNE10LBNO

12

10

8

2

4

6

0

2120590

3120590

Δ1205942

120575CP (true)

(a)



LBNE10LBNO

12

10

8

2

4

6

0

2120590

3120590

Δ1205942

120575CP (true)

(b)








120583 The most















sin2212057913 = 10minus1 sin

2212057913 = 10minus2

sin2212057913 = 10minus3 sin

2212057913 = 10minus4

065

065

07

07

07

04

03 035

07

08

075

055

065

045

045

075

25

25

20

15

10

5

5

20

15

10

E120583(G

eV)

E120583(G

eV)

1000 10002000 3000 4000 5000 6000

1000 2000 3000 4000 5000 6000

2000 3000 4000 5000 6000

L (km)L (km)

L (km)

25

20

15

10

5

E120583(G

eV)

25

20

15

10

5

E120583(G

eV)

1000 2000 3000 4000 5000 6000

L (km)








9F + 119890+ + ]

119890) and ]

119890from 6He (6

2He rarr

6

3Li+119890minus+]


5B rarr 8

4Be+119890++]

119890) and

8Li (83Li rarr 8

4Be + 119890minus + ]










18

10Ne 241 392 82037 921 ]

119890

6

2He 117 402 93453 100 ]

119890

8

5B 111 1443 60087207 100 ]

119890

8

3Li 120 1347 42535516 100 ]

119890



119890) and 29 times 1018 (]

119890) useful














Acknowledgments


References

































































119871times 119880(1)








































































21Δm231

and sin 12057913



13rdquo


















































































13phase and CP-
















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




012

01

008

006

004

002

002 04 06 08 1 12

E (GeV)02 04 06 08 1 12

E (GeV)

01

009

008

007

006

005

004

003

002

001

0

L = 295 km sin2212057913 = 0089 NH

P120583e(anti-)

P120583e()

(a)

LOHO

120575CP = minus90∘

120575CP = +90∘

012

01

008

006

004

002

005 15 25 351 2 3 4

E (GeV)

009

008

007

006

005

004

003

002

001

005 15 25 351 2 3 4

E (GeV)

LOHO

120575CP = minus90∘

120575CP = +90∘

L = 810 km sin2212057913 = 0089 NH

P120583e(anti-)

P120583e()

(b)




23= 059




E (GeV)

012

01

008

006

004

002

1 2 3 4 5 6 70

E (GeV)1 2 3 4 5 6 7

009

008

007

006

005

004

003

002

001

0

L = 1300 km sin2212057913 = 0089 NH

P120583e(anti-)

P120583e()

(a)

E (GeV)

LOHO

120575CP = minus90∘

120575CP = +90∘

1 2 3 4 5 6 7 8 9 10

012

014

01

008

006

004

002

0

E (GeV)

LOHO

120575CP = minus90∘

120575CP = +90∘

012

01

008

006

004

002

01 2 3 4 5 6 7 8 9 10

P120583e(anti-)

P120583e()

L = 2290 km sin2212057913 = 0089 NH

(b)




23= 059









10038161003816100381610038161003816Δ1198982

eff10038161003816100381610038161003816= 24 sdot 10

minus3 eV2 sin2212057923= 10 (17)


120583rarr ]

120583disap-





Δ1198982

eff = Δ1198982

31minus Δ119898

2

21


(18)






13=


13) = 13 [25] 120590(|Δ1198982eff|) = 4 and 120590(sin22120579

23) =


Δ1198982

21= 762 sdot 10

minus5 eV2 sin212057912= 032 (19)



120583








23[04ndash06]





120575CP (true)

95 CL

90 CL



12

10

8

6

4

2

0

Δ1205942


(a)

120575CP (true)

95 CL

90 CL



12

10

8

6

4

2

0

Δ1205942


(b)]


120575CP (true)

95 CL

90 CL



8

6

5

7

4

2

1

3

0

Δ1205942


(a)

120575CP (true)

95 CL

90 CL



8

6

5

7

4

2

1

3

0

Δ1205942


(b)




13= 0026 and sin2120579





NO]A (3 + 3) 048 (043) 046 (041) 016 (0) 021 (004)NO]A (3 + 3) + T2K (5 + 0) 055 (045) 054 (043) 038 (011) 049 (023)



23 the




NO]A (3 + 3) 039 (033) 037 (031) 02 (01) 022 (013)NO]A (3 + 3) + T2K (5 + 0) 041 (034) 039 (031) 028 (022) 03 (025)




13[146]



23


13= 0023 (the best-







23or not





23in the HO (LO)




13 and




20

18

16

14

12

10

8

620 25 30 35 40 45 50 55 60 65 70 75

LO-IH

HO-IH

HO-NH

LO-NH

minus90∘

090∘

180∘

T2K (25 + 25)A

nti-

app

even

ts

app events

(a)

minus90∘

0

90∘

180∘

LO-IH

HO-IH

HO-NH

LO-NH

50

45

40

35

30

25

20

15

1020 30 40 50 60 70 80 90 100 110

NOA (3 + 3)

Ant

i-ap

pev

ents

app events

(b)


13= 0089 For LO (HO) sin2120579




15

10

5

0


NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

Δ1205942

(a)


15

10

5

0


NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

Δ1205942

(b)




15

10

5

0


NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

(a)


15

10

5

0


Δ1205942

NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

(b)




of sin212057923






23le 043 or ge 058




23at 2120590 using






035 04 045 05 055 06 065

2120590

3120590 MINOS

sin212057923 (true)

120575CP

(true

) (de

g)

minus180

minus90

0

90


Global best-fit

(a)

035 04 045 05 055 06 065

2120590

3120590 MINOS

sin212057923 (true)

120575CP

(true

) (de

g)

minus180

minus90

0

90


Global best-fit

(b)
















13also allows












119890





∘ 180∘]



23= 041 is






119890and ]

119890events




NC

101

100

10minus11 2 3 4 5

2nd OSC max

1st OSC max

Even

ts pe

r0125

GeV

bin

in5

yrs




(a)

101

100

10minus1

1 2 3 4 5 6 7 8



NCEv

ents

per0125

GeV

bin

in5

yrs



(b)




100

80

60

40

20

00 50 100 150 200 250

minus90∘

0

90∘

180∘

HO-IHHO-IH

HO-NH

HO-NHLO-NH

LO-NH

LO-IHLO-IH

LBNE10

Ant

i-ap

pev

ents

app events

05lowastLBNO





13= 0089 For


[41]





23-hierarchy LO-NH



and sin2212057913


31(120590 = 4) and












101

102

103

LO-NH true


LO-IH true

LBNO

LBNE10


101

100

100

101

102

103

100

102

103

101

100

102

103

MM-NH true

LBNO

LBNE10


MM-IH true

Δ1205942

Δ1205942

Δ1205942

Δ1205942





combinations





23values






∘ sim 150

∘)






LO-NH true


LO-IH true

LBNO

LBNE10


HO-NH true

LBNO

LBNE10


HO-IH true

20

25

10

15

5

0

20

25

10

15

5

0

20

25

10

15

5

0

20

25

10

15

5

0

Δ1205942

Δ1205942

Δ1205942

Δ1205942


120575CP(true) (deg) 120575

CP(true) (deg)








119890and









LBNE10LBNO

12

10

8

2

4

6

0

2120590

3120590

Δ1205942

120575CP (true)

(a)



LBNE10LBNO

12

10

8

2

4

6

0

2120590

3120590

Δ1205942

120575CP (true)

(b)








120583 The most















sin2212057913 = 10minus1 sin

2212057913 = 10minus2

sin2212057913 = 10minus3 sin

2212057913 = 10minus4

065

065

07

07

07

04

03 035

07

08

075

055

065

045

045

075

25

25

20

15

10

5

5

20

15

10

E120583(G

eV)

E120583(G

eV)

1000 10002000 3000 4000 5000 6000

1000 2000 3000 4000 5000 6000

2000 3000 4000 5000 6000

L (km)L (km)

L (km)

25

20

15

10

5

E120583(G

eV)

25

20

15

10

5

E120583(G

eV)

1000 2000 3000 4000 5000 6000

L (km)








9F + 119890+ + ]

119890) and ]

119890from 6He (6

2He rarr

6

3Li+119890minus+]


5B rarr 8

4Be+119890++]

119890) and

8Li (83Li rarr 8

4Be + 119890minus + ]










18

10Ne 241 392 82037 921 ]

119890

6

2He 117 402 93453 100 ]

119890

8

5B 111 1443 60087207 100 ]

119890

8

3Li 120 1347 42535516 100 ]

119890



119890) and 29 times 1018 (]

119890) useful














Acknowledgments


References

































































119871times 119880(1)








































































21Δm231

and sin 12057913



13rdquo


















































































13phase and CP-
















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




E (GeV)

012

01

008

006

004

002

1 2 3 4 5 6 70

E (GeV)1 2 3 4 5 6 7

009

008

007

006

005

004

003

002

001

0

L = 1300 km sin2212057913 = 0089 NH

P120583e(anti-)

P120583e()

(a)

E (GeV)

LOHO

120575CP = minus90∘

120575CP = +90∘

1 2 3 4 5 6 7 8 9 10

012

014

01

008

006

004

002

0

E (GeV)

LOHO

120575CP = minus90∘

120575CP = +90∘

012

01

008

006

004

002

01 2 3 4 5 6 7 8 9 10

P120583e(anti-)

P120583e()

L = 2290 km sin2212057913 = 0089 NH

(b)




23= 059









10038161003816100381610038161003816Δ1198982

eff10038161003816100381610038161003816= 24 sdot 10

minus3 eV2 sin2212057923= 10 (17)


120583rarr ]

120583disap-





Δ1198982

eff = Δ1198982

31minus Δ119898

2

21


(18)






13=


13) = 13 [25] 120590(|Δ1198982eff|) = 4 and 120590(sin22120579

23) =


Δ1198982

21= 762 sdot 10

minus5 eV2 sin212057912= 032 (19)



120583








23[04ndash06]





120575CP (true)

95 CL

90 CL



12

10

8

6

4

2

0

Δ1205942


(a)

120575CP (true)

95 CL

90 CL



12

10

8

6

4

2

0

Δ1205942


(b)]


120575CP (true)

95 CL

90 CL



8

6

5

7

4

2

1

3

0

Δ1205942


(a)

120575CP (true)

95 CL

90 CL



8

6

5

7

4

2

1

3

0

Δ1205942


(b)




13= 0026 and sin2120579





NO]A (3 + 3) 048 (043) 046 (041) 016 (0) 021 (004)NO]A (3 + 3) + T2K (5 + 0) 055 (045) 054 (043) 038 (011) 049 (023)



23 the




NO]A (3 + 3) 039 (033) 037 (031) 02 (01) 022 (013)NO]A (3 + 3) + T2K (5 + 0) 041 (034) 039 (031) 028 (022) 03 (025)




13[146]



23


13= 0023 (the best-







23or not





23in the HO (LO)




13 and




20

18

16

14

12

10

8

620 25 30 35 40 45 50 55 60 65 70 75

LO-IH

HO-IH

HO-NH

LO-NH

minus90∘

090∘

180∘

T2K (25 + 25)A

nti-

app

even

ts

app events

(a)

minus90∘

0

90∘

180∘

LO-IH

HO-IH

HO-NH

LO-NH

50

45

40

35

30

25

20

15

1020 30 40 50 60 70 80 90 100 110

NOA (3 + 3)

Ant

i-ap

pev

ents

app events

(b)


13= 0089 For LO (HO) sin2120579




15

10

5

0


NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

Δ1205942

(a)


15

10

5

0


NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

Δ1205942

(b)




15

10

5

0


NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

(a)


15

10

5

0


Δ1205942

NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

(b)




of sin212057923






23le 043 or ge 058




23at 2120590 using






035 04 045 05 055 06 065

2120590

3120590 MINOS

sin212057923 (true)

120575CP

(true

) (de

g)

minus180

minus90

0

90


Global best-fit

(a)

035 04 045 05 055 06 065

2120590

3120590 MINOS

sin212057923 (true)

120575CP

(true

) (de

g)

minus180

minus90

0

90


Global best-fit

(b)
















13also allows












119890





∘ 180∘]



23= 041 is






119890and ]

119890events




NC

101

100

10minus11 2 3 4 5

2nd OSC max

1st OSC max

Even

ts pe

r0125

GeV

bin

in5

yrs




(a)

101

100

10minus1

1 2 3 4 5 6 7 8



NCEv

ents

per0125

GeV

bin

in5

yrs



(b)




100

80

60

40

20

00 50 100 150 200 250

minus90∘

0

90∘

180∘

HO-IHHO-IH

HO-NH

HO-NHLO-NH

LO-NH

LO-IHLO-IH

LBNE10

Ant

i-ap

pev

ents

app events

05lowastLBNO





13= 0089 For


[41]





23-hierarchy LO-NH



and sin2212057913


31(120590 = 4) and












101

102

103

LO-NH true


LO-IH true

LBNO

LBNE10


101

100

100

101

102

103

100

102

103

101

100

102

103

MM-NH true

LBNO

LBNE10


MM-IH true

Δ1205942

Δ1205942

Δ1205942

Δ1205942





combinations





23values






∘ sim 150

∘)






LO-NH true


LO-IH true

LBNO

LBNE10


HO-NH true

LBNO

LBNE10


HO-IH true

20

25

10

15

5

0

20

25

10

15

5

0

20

25

10

15

5

0

20

25

10

15

5

0

Δ1205942

Δ1205942

Δ1205942

Δ1205942


120575CP(true) (deg) 120575

CP(true) (deg)








119890and









LBNE10LBNO

12

10

8

2

4

6

0

2120590

3120590

Δ1205942

120575CP (true)

(a)



LBNE10LBNO

12

10

8

2

4

6

0

2120590

3120590

Δ1205942

120575CP (true)

(b)








120583 The most















sin2212057913 = 10minus1 sin

2212057913 = 10minus2

sin2212057913 = 10minus3 sin

2212057913 = 10minus4

065

065

07

07

07

04

03 035

07

08

075

055

065

045

045

075

25

25

20

15

10

5

5

20

15

10

E120583(G

eV)

E120583(G

eV)

1000 10002000 3000 4000 5000 6000

1000 2000 3000 4000 5000 6000

2000 3000 4000 5000 6000

L (km)L (km)

L (km)

25

20

15

10

5

E120583(G

eV)

25

20

15

10

5

E120583(G

eV)

1000 2000 3000 4000 5000 6000

L (km)








9F + 119890+ + ]

119890) and ]

119890from 6He (6

2He rarr

6

3Li+119890minus+]


5B rarr 8

4Be+119890++]

119890) and

8Li (83Li rarr 8

4Be + 119890minus + ]










18

10Ne 241 392 82037 921 ]

119890

6

2He 117 402 93453 100 ]

119890

8

5B 111 1443 60087207 100 ]

119890

8

3Li 120 1347 42535516 100 ]

119890



119890) and 29 times 1018 (]

119890) useful














Acknowledgments


References

































































119871times 119880(1)








































































21Δm231

and sin 12057913



13rdquo


















































































13phase and CP-
















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics





10038161003816100381610038161003816Δ1198982

eff10038161003816100381610038161003816= 24 sdot 10

minus3 eV2 sin2212057923= 10 (17)


120583rarr ]

120583disap-





Δ1198982

eff = Δ1198982

31minus Δ119898

2

21


(18)






13=


13) = 13 [25] 120590(|Δ1198982eff|) = 4 and 120590(sin22120579

23) =


Δ1198982

21= 762 sdot 10

minus5 eV2 sin212057912= 032 (19)



120583








23[04ndash06]





120575CP (true)

95 CL

90 CL



12

10

8

6

4

2

0

Δ1205942


(a)

120575CP (true)

95 CL

90 CL



12

10

8

6

4

2

0

Δ1205942


(b)]


120575CP (true)

95 CL

90 CL



8

6

5

7

4

2

1

3

0

Δ1205942


(a)

120575CP (true)

95 CL

90 CL



8

6

5

7

4

2

1

3

0

Δ1205942


(b)




13= 0026 and sin2120579





NO]A (3 + 3) 048 (043) 046 (041) 016 (0) 021 (004)NO]A (3 + 3) + T2K (5 + 0) 055 (045) 054 (043) 038 (011) 049 (023)



23 the




NO]A (3 + 3) 039 (033) 037 (031) 02 (01) 022 (013)NO]A (3 + 3) + T2K (5 + 0) 041 (034) 039 (031) 028 (022) 03 (025)




13[146]



23


13= 0023 (the best-







23or not





23in the HO (LO)




13 and




20

18

16

14

12

10

8

620 25 30 35 40 45 50 55 60 65 70 75

LO-IH

HO-IH

HO-NH

LO-NH

minus90∘

090∘

180∘

T2K (25 + 25)A

nti-

app

even

ts

app events

(a)

minus90∘

0

90∘

180∘

LO-IH

HO-IH

HO-NH

LO-NH

50

45

40

35

30

25

20

15

1020 30 40 50 60 70 80 90 100 110

NOA (3 + 3)

Ant

i-ap

pev

ents

app events

(b)


13= 0089 For LO (HO) sin2120579




15

10

5

0


NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

Δ1205942

(a)


15

10

5

0


NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

Δ1205942

(b)




15

10

5

0


NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

(a)


15

10

5

0


Δ1205942

NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

(b)




of sin212057923






23le 043 or ge 058




23at 2120590 using






035 04 045 05 055 06 065

2120590

3120590 MINOS

sin212057923 (true)

120575CP

(true

) (de

g)

minus180

minus90

0

90


Global best-fit

(a)

035 04 045 05 055 06 065

2120590

3120590 MINOS

sin212057923 (true)

120575CP

(true

) (de

g)

minus180

minus90

0

90


Global best-fit

(b)
















13also allows












119890





∘ 180∘]



23= 041 is






119890and ]

119890events




NC

101

100

10minus11 2 3 4 5

2nd OSC max

1st OSC max

Even

ts pe

r0125

GeV

bin

in5

yrs




(a)

101

100

10minus1

1 2 3 4 5 6 7 8



NCEv

ents

per0125

GeV

bin

in5

yrs



(b)




100

80

60

40

20

00 50 100 150 200 250

minus90∘

0

90∘

180∘

HO-IHHO-IH

HO-NH

HO-NHLO-NH

LO-NH

LO-IHLO-IH

LBNE10

Ant

i-ap

pev

ents

app events

05lowastLBNO





13= 0089 For


[41]





23-hierarchy LO-NH



and sin2212057913


31(120590 = 4) and












101

102

103

LO-NH true


LO-IH true

LBNO

LBNE10


101

100

100

101

102

103

100

102

103

101

100

102

103

MM-NH true

LBNO

LBNE10


MM-IH true

Δ1205942

Δ1205942

Δ1205942

Δ1205942





combinations





23values






∘ sim 150

∘)






LO-NH true


LO-IH true

LBNO

LBNE10


HO-NH true

LBNO

LBNE10


HO-IH true

20

25

10

15

5

0

20

25

10

15

5

0

20

25

10

15

5

0

20

25

10

15

5

0

Δ1205942

Δ1205942

Δ1205942

Δ1205942


120575CP(true) (deg) 120575

CP(true) (deg)








119890and









LBNE10LBNO

12

10

8

2

4

6

0

2120590

3120590

Δ1205942

120575CP (true)

(a)



LBNE10LBNO

12

10

8

2

4

6

0

2120590

3120590

Δ1205942

120575CP (true)

(b)








120583 The most















sin2212057913 = 10minus1 sin

2212057913 = 10minus2

sin2212057913 = 10minus3 sin

2212057913 = 10minus4

065

065

07

07

07

04

03 035

07

08

075

055

065

045

045

075

25

25

20

15

10

5

5

20

15

10

E120583(G

eV)

E120583(G

eV)

1000 10002000 3000 4000 5000 6000

1000 2000 3000 4000 5000 6000

2000 3000 4000 5000 6000

L (km)L (km)

L (km)

25

20

15

10

5

E120583(G

eV)

25

20

15

10

5

E120583(G

eV)

1000 2000 3000 4000 5000 6000

L (km)








9F + 119890+ + ]

119890) and ]

119890from 6He (6

2He rarr

6

3Li+119890minus+]


5B rarr 8

4Be+119890++]

119890) and

8Li (83Li rarr 8

4Be + 119890minus + ]










18

10Ne 241 392 82037 921 ]

119890

6

2He 117 402 93453 100 ]

119890

8

5B 111 1443 60087207 100 ]

119890

8

3Li 120 1347 42535516 100 ]

119890



119890) and 29 times 1018 (]

119890) useful














Acknowledgments


References

































































119871times 119880(1)








































































21Δm231

and sin 12057913



13rdquo


















































































13phase and CP-
















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




120575CP (true)

95 CL

90 CL



12

10

8

6

4

2

0

Δ1205942


(a)

120575CP (true)

95 CL

90 CL



12

10

8

6

4

2

0

Δ1205942


(b)]


120575CP (true)

95 CL

90 CL



8

6

5

7

4

2

1

3

0

Δ1205942


(a)

120575CP (true)

95 CL

90 CL



8

6

5

7

4

2

1

3

0

Δ1205942


(b)




13= 0026 and sin2120579





NO]A (3 + 3) 048 (043) 046 (041) 016 (0) 021 (004)NO]A (3 + 3) + T2K (5 + 0) 055 (045) 054 (043) 038 (011) 049 (023)



23 the




NO]A (3 + 3) 039 (033) 037 (031) 02 (01) 022 (013)NO]A (3 + 3) + T2K (5 + 0) 041 (034) 039 (031) 028 (022) 03 (025)




13[146]



23


13= 0023 (the best-







23or not





23in the HO (LO)




13 and




20

18

16

14

12

10

8

620 25 30 35 40 45 50 55 60 65 70 75

LO-IH

HO-IH

HO-NH

LO-NH

minus90∘

090∘

180∘

T2K (25 + 25)A

nti-

app

even

ts

app events

(a)

minus90∘

0

90∘

180∘

LO-IH

HO-IH

HO-NH

LO-NH

50

45

40

35

30

25

20

15

1020 30 40 50 60 70 80 90 100 110

NOA (3 + 3)

Ant

i-ap

pev

ents

app events

(b)


13= 0089 For LO (HO) sin2120579




15

10

5

0


NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

Δ1205942

(a)


15

10

5

0


NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

Δ1205942

(b)




15

10

5

0


NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

(a)


15

10

5

0


Δ1205942

NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

(b)




of sin212057923






23le 043 or ge 058




23at 2120590 using






035 04 045 05 055 06 065

2120590

3120590 MINOS

sin212057923 (true)

120575CP

(true

) (de

g)

minus180

minus90

0

90


Global best-fit

(a)

035 04 045 05 055 06 065

2120590

3120590 MINOS

sin212057923 (true)

120575CP

(true

) (de

g)

minus180

minus90

0

90


Global best-fit

(b)
















13also allows












119890





∘ 180∘]



23= 041 is






119890and ]

119890events




NC

101

100

10minus11 2 3 4 5

2nd OSC max

1st OSC max

Even

ts pe

r0125

GeV

bin

in5

yrs




(a)

101

100

10minus1

1 2 3 4 5 6 7 8



NCEv

ents

per0125

GeV

bin

in5

yrs



(b)




100

80

60

40

20

00 50 100 150 200 250

minus90∘

0

90∘

180∘

HO-IHHO-IH

HO-NH

HO-NHLO-NH

LO-NH

LO-IHLO-IH

LBNE10

Ant

i-ap

pev

ents

app events

05lowastLBNO





13= 0089 For


[41]





23-hierarchy LO-NH



and sin2212057913


31(120590 = 4) and












101

102

103

LO-NH true


LO-IH true

LBNO

LBNE10


101

100

100

101

102

103

100

102

103

101

100

102

103

MM-NH true

LBNO

LBNE10


MM-IH true

Δ1205942

Δ1205942

Δ1205942

Δ1205942





combinations





23values






∘ sim 150

∘)






LO-NH true


LO-IH true

LBNO

LBNE10


HO-NH true

LBNO

LBNE10


HO-IH true

20

25

10

15

5

0

20

25

10

15

5

0

20

25

10

15

5

0

20

25

10

15

5

0

Δ1205942

Δ1205942

Δ1205942

Δ1205942


120575CP(true) (deg) 120575

CP(true) (deg)








119890and









LBNE10LBNO

12

10

8

2

4

6

0

2120590

3120590

Δ1205942

120575CP (true)

(a)



LBNE10LBNO

12

10

8

2

4

6

0

2120590

3120590

Δ1205942

120575CP (true)

(b)








120583 The most















sin2212057913 = 10minus1 sin

2212057913 = 10minus2

sin2212057913 = 10minus3 sin

2212057913 = 10minus4

065

065

07

07

07

04

03 035

07

08

075

055

065

045

045

075

25

25

20

15

10

5

5

20

15

10

E120583(G

eV)

E120583(G

eV)

1000 10002000 3000 4000 5000 6000

1000 2000 3000 4000 5000 6000

2000 3000 4000 5000 6000

L (km)L (km)

L (km)

25

20

15

10

5

E120583(G

eV)

25

20

15

10

5

E120583(G

eV)

1000 2000 3000 4000 5000 6000

L (km)








9F + 119890+ + ]

119890) and ]

119890from 6He (6

2He rarr

6

3Li+119890minus+]


5B rarr 8

4Be+119890++]

119890) and

8Li (83Li rarr 8

4Be + 119890minus + ]










18

10Ne 241 392 82037 921 ]

119890

6

2He 117 402 93453 100 ]

119890

8

5B 111 1443 60087207 100 ]

119890

8

3Li 120 1347 42535516 100 ]

119890



119890) and 29 times 1018 (]

119890) useful














Acknowledgments


References

































































119871times 119880(1)








































































21Δm231

and sin 12057913



13rdquo


















































































13phase and CP-
















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics





13= 0026 and sin2120579





NO]A (3 + 3) 048 (043) 046 (041) 016 (0) 021 (004)NO]A (3 + 3) + T2K (5 + 0) 055 (045) 054 (043) 038 (011) 049 (023)



23 the




NO]A (3 + 3) 039 (033) 037 (031) 02 (01) 022 (013)NO]A (3 + 3) + T2K (5 + 0) 041 (034) 039 (031) 028 (022) 03 (025)




13[146]



23


13= 0023 (the best-







23or not





23in the HO (LO)




13 and




20

18

16

14

12

10

8

620 25 30 35 40 45 50 55 60 65 70 75

LO-IH

HO-IH

HO-NH

LO-NH

minus90∘

090∘

180∘

T2K (25 + 25)A

nti-

app

even

ts

app events

(a)

minus90∘

0

90∘

180∘

LO-IH

HO-IH

HO-NH

LO-NH

50

45

40

35

30

25

20

15

1020 30 40 50 60 70 80 90 100 110

NOA (3 + 3)

Ant

i-ap

pev

ents

app events

(b)


13= 0089 For LO (HO) sin2120579




15

10

5

0


NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

Δ1205942

(a)


15

10

5

0


NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

Δ1205942

(b)




15

10

5

0


NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

(a)


15

10

5

0


Δ1205942

NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

(b)




of sin212057923






23le 043 or ge 058




23at 2120590 using






035 04 045 05 055 06 065

2120590

3120590 MINOS

sin212057923 (true)

120575CP

(true

) (de

g)

minus180

minus90

0

90


Global best-fit

(a)

035 04 045 05 055 06 065

2120590

3120590 MINOS

sin212057923 (true)

120575CP

(true

) (de

g)

minus180

minus90

0

90


Global best-fit

(b)
















13also allows












119890





∘ 180∘]



23= 041 is






119890and ]

119890events




NC

101

100

10minus11 2 3 4 5

2nd OSC max

1st OSC max

Even

ts pe

r0125

GeV

bin

in5

yrs




(a)

101

100

10minus1

1 2 3 4 5 6 7 8



NCEv

ents

per0125

GeV

bin

in5

yrs



(b)




100

80

60

40

20

00 50 100 150 200 250

minus90∘

0

90∘

180∘

HO-IHHO-IH

HO-NH

HO-NHLO-NH

LO-NH

LO-IHLO-IH

LBNE10

Ant

i-ap

pev

ents

app events

05lowastLBNO





13= 0089 For


[41]





23-hierarchy LO-NH



and sin2212057913


31(120590 = 4) and












101

102

103

LO-NH true


LO-IH true

LBNO

LBNE10


101

100

100

101

102

103

100

102

103

101

100

102

103

MM-NH true

LBNO

LBNE10


MM-IH true

Δ1205942

Δ1205942

Δ1205942

Δ1205942





combinations





23values






∘ sim 150

∘)






LO-NH true


LO-IH true

LBNO

LBNE10


HO-NH true

LBNO

LBNE10


HO-IH true

20

25

10

15

5

0

20

25

10

15

5

0

20

25

10

15

5

0

20

25

10

15

5

0

Δ1205942

Δ1205942

Δ1205942

Δ1205942


120575CP(true) (deg) 120575

CP(true) (deg)








119890and









LBNE10LBNO

12

10

8

2

4

6

0

2120590

3120590

Δ1205942

120575CP (true)

(a)



LBNE10LBNO

12

10

8

2

4

6

0

2120590

3120590

Δ1205942

120575CP (true)

(b)








120583 The most















sin2212057913 = 10minus1 sin

2212057913 = 10minus2

sin2212057913 = 10minus3 sin

2212057913 = 10minus4

065

065

07

07

07

04

03 035

07

08

075

055

065

045

045

075

25

25

20

15

10

5

5

20

15

10

E120583(G

eV)

E120583(G

eV)

1000 10002000 3000 4000 5000 6000

1000 2000 3000 4000 5000 6000

2000 3000 4000 5000 6000

L (km)L (km)

L (km)

25

20

15

10

5

E120583(G

eV)

25

20

15

10

5

E120583(G

eV)

1000 2000 3000 4000 5000 6000

L (km)








9F + 119890+ + ]

119890) and ]

119890from 6He (6

2He rarr

6

3Li+119890minus+]


5B rarr 8

4Be+119890++]

119890) and

8Li (83Li rarr 8

4Be + 119890minus + ]










18

10Ne 241 392 82037 921 ]

119890

6

2He 117 402 93453 100 ]

119890

8

5B 111 1443 60087207 100 ]

119890

8

3Li 120 1347 42535516 100 ]

119890



119890) and 29 times 1018 (]

119890) useful














Acknowledgments


References

































































119871times 119880(1)








































































21Δm231

and sin 12057913



13rdquo


















































































13phase and CP-
















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




20

18

16

14

12

10

8

620 25 30 35 40 45 50 55 60 65 70 75

LO-IH

HO-IH

HO-NH

LO-NH

minus90∘

090∘

180∘

T2K (25 + 25)A

nti-

app

even

ts

app events

(a)

minus90∘

0

90∘

180∘

LO-IH

HO-IH

HO-NH

LO-NH

50

45

40

35

30

25

20

15

1020 30 40 50 60 70 80 90 100 110

NOA (3 + 3)

Ant

i-ap

pev

ents

app events

(b)


13= 0089 For LO (HO) sin2120579




15

10

5

0


NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

Δ1205942

(a)


15

10

5

0


NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

Δ1205942

(b)




15

10

5

0


NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

(a)


15

10

5

0


Δ1205942

NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

(b)




of sin212057923






23le 043 or ge 058




23at 2120590 using






035 04 045 05 055 06 065

2120590

3120590 MINOS

sin212057923 (true)

120575CP

(true

) (de

g)

minus180

minus90

0

90


Global best-fit

(a)

035 04 045 05 055 06 065

2120590

3120590 MINOS

sin212057923 (true)

120575CP

(true

) (de

g)

minus180

minus90

0

90


Global best-fit

(b)
















13also allows












119890





∘ 180∘]



23= 041 is






119890and ]

119890events




NC

101

100

10minus11 2 3 4 5

2nd OSC max

1st OSC max

Even

ts pe

r0125

GeV

bin

in5

yrs




(a)

101

100

10minus1

1 2 3 4 5 6 7 8



NCEv

ents

per0125

GeV

bin

in5

yrs



(b)




100

80

60

40

20

00 50 100 150 200 250

minus90∘

0

90∘

180∘

HO-IHHO-IH

HO-NH

HO-NHLO-NH

LO-NH

LO-IHLO-IH

LBNE10

Ant

i-ap

pev

ents

app events

05lowastLBNO





13= 0089 For


[41]





23-hierarchy LO-NH



and sin2212057913


31(120590 = 4) and












101

102

103

LO-NH true


LO-IH true

LBNO

LBNE10


101

100

100

101

102

103

100

102

103

101

100

102

103

MM-NH true

LBNO

LBNE10


MM-IH true

Δ1205942

Δ1205942

Δ1205942

Δ1205942





combinations





23values






∘ sim 150

∘)






LO-NH true


LO-IH true

LBNO

LBNE10


HO-NH true

LBNO

LBNE10


HO-IH true

20

25

10

15

5

0

20

25

10

15

5

0

20

25

10

15

5

0

20

25

10

15

5

0

Δ1205942

Δ1205942

Δ1205942

Δ1205942


120575CP(true) (deg) 120575

CP(true) (deg)








119890and









LBNE10LBNO

12

10

8

2

4

6

0

2120590

3120590

Δ1205942

120575CP (true)

(a)



LBNE10LBNO

12

10

8

2

4

6

0

2120590

3120590

Δ1205942

120575CP (true)

(b)








120583 The most















sin2212057913 = 10minus1 sin

2212057913 = 10minus2

sin2212057913 = 10minus3 sin

2212057913 = 10minus4

065

065

07

07

07

04

03 035

07

08

075

055

065

045

045

075

25

25

20

15

10

5

5

20

15

10

E120583(G

eV)

E120583(G

eV)

1000 10002000 3000 4000 5000 6000

1000 2000 3000 4000 5000 6000

2000 3000 4000 5000 6000

L (km)L (km)

L (km)

25

20

15

10

5

E120583(G

eV)

25

20

15

10

5

E120583(G

eV)

1000 2000 3000 4000 5000 6000

L (km)








9F + 119890+ + ]

119890) and ]

119890from 6He (6

2He rarr

6

3Li+119890minus+]


5B rarr 8

4Be+119890++]

119890) and

8Li (83Li rarr 8

4Be + 119890minus + ]










18

10Ne 241 392 82037 921 ]

119890

6

2He 117 402 93453 100 ]

119890

8

5B 111 1443 60087207 100 ]

119890

8

3Li 120 1347 42535516 100 ]

119890



119890) and 29 times 1018 (]

119890) useful














Acknowledgments


References

































































119871times 119880(1)








































































21Δm231

and sin 12057913



13rdquo


















































































13phase and CP-
















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics





15

10

5

0


NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

(a)


15

10

5

0


Δ1205942

NOANOA + T2K (5 + 0)NOA + T2K (25 + 25)

(b)




of sin212057923






23le 043 or ge 058




23at 2120590 using






035 04 045 05 055 06 065

2120590

3120590 MINOS

sin212057923 (true)

120575CP

(true

) (de

g)

minus180

minus90

0

90


Global best-fit

(a)

035 04 045 05 055 06 065

2120590

3120590 MINOS

sin212057923 (true)

120575CP

(true

) (de

g)

minus180

minus90

0

90


Global best-fit

(b)
















13also allows












119890





∘ 180∘]



23= 041 is






119890and ]

119890events




NC

101

100

10minus11 2 3 4 5

2nd OSC max

1st OSC max

Even

ts pe

r0125

GeV

bin

in5

yrs




(a)

101

100

10minus1

1 2 3 4 5 6 7 8



NCEv

ents

per0125

GeV

bin

in5

yrs



(b)




100

80

60

40

20

00 50 100 150 200 250

minus90∘

0

90∘

180∘

HO-IHHO-IH

HO-NH

HO-NHLO-NH

LO-NH

LO-IHLO-IH

LBNE10

Ant

i-ap

pev

ents

app events

05lowastLBNO





13= 0089 For


[41]





23-hierarchy LO-NH



and sin2212057913


31(120590 = 4) and












101

102

103

LO-NH true


LO-IH true

LBNO

LBNE10


101

100

100

101

102

103

100

102

103

101

100

102

103

MM-NH true

LBNO

LBNE10


MM-IH true

Δ1205942

Δ1205942

Δ1205942

Δ1205942





combinations





23values






∘ sim 150

∘)






LO-NH true


LO-IH true

LBNO

LBNE10


HO-NH true

LBNO

LBNE10


HO-IH true

20

25

10

15

5

0

20

25

10

15

5

0

20

25

10

15

5

0

20

25

10

15

5

0

Δ1205942

Δ1205942

Δ1205942

Δ1205942


120575CP(true) (deg) 120575

CP(true) (deg)








119890and









LBNE10LBNO

12

10

8

2

4

6

0

2120590

3120590

Δ1205942

120575CP (true)

(a)



LBNE10LBNO

12

10

8

2

4

6

0

2120590

3120590

Δ1205942

120575CP (true)

(b)








120583 The most















sin2212057913 = 10minus1 sin

2212057913 = 10minus2

sin2212057913 = 10minus3 sin

2212057913 = 10minus4

065

065

07

07

07

04

03 035

07

08

075

055

065

045

045

075

25

25

20

15

10

5

5

20

15

10

E120583(G

eV)

E120583(G

eV)

1000 10002000 3000 4000 5000 6000

1000 2000 3000 4000 5000 6000

2000 3000 4000 5000 6000

L (km)L (km)

L (km)

25

20

15

10

5

E120583(G

eV)

25

20

15

10

5

E120583(G

eV)

1000 2000 3000 4000 5000 6000

L (km)








9F + 119890+ + ]

119890) and ]

119890from 6He (6

2He rarr

6

3Li+119890minus+]


5B rarr 8

4Be+119890++]

119890) and

8Li (83Li rarr 8

4Be + 119890minus + ]










18

10Ne 241 392 82037 921 ]

119890

6

2He 117 402 93453 100 ]

119890

8

5B 111 1443 60087207 100 ]

119890

8

3Li 120 1347 42535516 100 ]

119890



119890) and 29 times 1018 (]

119890) useful














Acknowledgments


References

































































119871times 119880(1)








































































21Δm231

and sin 12057913



13rdquo


















































































13phase and CP-
















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




035 04 045 05 055 06 065

2120590

3120590 MINOS

sin212057923 (true)

120575CP

(true

) (de

g)

minus180

minus90

0

90


Global best-fit

(a)

035 04 045 05 055 06 065

2120590

3120590 MINOS

sin212057923 (true)

120575CP

(true

) (de

g)

minus180

minus90

0

90


Global best-fit

(b)
















13also allows












119890





∘ 180∘]



23= 041 is






119890and ]

119890events




NC

101

100

10minus11 2 3 4 5

2nd OSC max

1st OSC max

Even

ts pe

r0125

GeV

bin

in5

yrs




(a)

101

100

10minus1

1 2 3 4 5 6 7 8



NCEv

ents

per0125

GeV

bin

in5

yrs



(b)




100

80

60

40

20

00 50 100 150 200 250

minus90∘

0

90∘

180∘

HO-IHHO-IH

HO-NH

HO-NHLO-NH

LO-NH

LO-IHLO-IH

LBNE10

Ant

i-ap

pev

ents

app events

05lowastLBNO





13= 0089 For


[41]





23-hierarchy LO-NH



and sin2212057913


31(120590 = 4) and












101

102

103

LO-NH true


LO-IH true

LBNO

LBNE10


101

100

100

101

102

103

100

102

103

101

100

102

103

MM-NH true

LBNO

LBNE10


MM-IH true

Δ1205942

Δ1205942

Δ1205942

Δ1205942





combinations





23values






∘ sim 150

∘)






LO-NH true


LO-IH true

LBNO

LBNE10


HO-NH true

LBNO

LBNE10


HO-IH true

20

25

10

15

5

0

20

25

10

15

5

0

20

25

10

15

5

0

20

25

10

15

5

0

Δ1205942

Δ1205942

Δ1205942

Δ1205942


120575CP(true) (deg) 120575

CP(true) (deg)








119890and









LBNE10LBNO

12

10

8

2

4

6

0

2120590

3120590

Δ1205942

120575CP (true)

(a)



LBNE10LBNO

12

10

8

2

4

6

0

2120590

3120590

Δ1205942

120575CP (true)

(b)








120583 The most















sin2212057913 = 10minus1 sin

2212057913 = 10minus2

sin2212057913 = 10minus3 sin

2212057913 = 10minus4

065

065

07

07

07

04

03 035

07

08

075

055

065

045

045

075

25

25

20

15

10

5

5

20

15

10

E120583(G

eV)

E120583(G

eV)

1000 10002000 3000 4000 5000 6000

1000 2000 3000 4000 5000 6000

2000 3000 4000 5000 6000

L (km)L (km)

L (km)

25

20

15

10

5

E120583(G

eV)

25

20

15

10

5

E120583(G

eV)

1000 2000 3000 4000 5000 6000

L (km)








9F + 119890+ + ]

119890) and ]

119890from 6He (6

2He rarr

6

3Li+119890minus+]


5B rarr 8

4Be+119890++]

119890) and

8Li (83Li rarr 8

4Be + 119890minus + ]










18

10Ne 241 392 82037 921 ]

119890

6

2He 117 402 93453 100 ]

119890

8

5B 111 1443 60087207 100 ]

119890

8

3Li 120 1347 42535516 100 ]

119890



119890) and 29 times 1018 (]

119890) useful














Acknowledgments


References

































































119871times 119880(1)








































































21Δm231

and sin 12057913



13rdquo


















































































13phase and CP-
















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics










119890





∘ 180∘]



23= 041 is






119890and ]

119890events




NC

101

100

10minus11 2 3 4 5

2nd OSC max

1st OSC max

Even

ts pe

r0125

GeV

bin

in5

yrs




(a)

101

100

10minus1

1 2 3 4 5 6 7 8



NCEv

ents

per0125

GeV

bin

in5

yrs



(b)




100

80

60

40

20

00 50 100 150 200 250

minus90∘

0

90∘

180∘

HO-IHHO-IH

HO-NH

HO-NHLO-NH

LO-NH

LO-IHLO-IH

LBNE10

Ant

i-ap

pev

ents

app events

05lowastLBNO





13= 0089 For


[41]





23-hierarchy LO-NH



and sin2212057913


31(120590 = 4) and












101

102

103

LO-NH true


LO-IH true

LBNO

LBNE10


101

100

100

101

102

103

100

102

103

101

100

102

103

MM-NH true

LBNO

LBNE10


MM-IH true

Δ1205942

Δ1205942

Δ1205942

Δ1205942





combinations





23values






∘ sim 150

∘)






LO-NH true


LO-IH true

LBNO

LBNE10


HO-NH true

LBNO

LBNE10


HO-IH true

20

25

10

15

5

0

20

25

10

15

5

0

20

25

10

15

5

0

20

25

10

15

5

0

Δ1205942

Δ1205942

Δ1205942

Δ1205942


120575CP(true) (deg) 120575

CP(true) (deg)








119890and









LBNE10LBNO

12

10

8

2

4

6

0

2120590

3120590

Δ1205942

120575CP (true)

(a)



LBNE10LBNO

12

10

8

2

4

6

0

2120590

3120590

Δ1205942

120575CP (true)

(b)








120583 The most















sin2212057913 = 10minus1 sin

2212057913 = 10minus2

sin2212057913 = 10minus3 sin

2212057913 = 10minus4

065

065

07

07

07

04

03 035

07

08

075

055

065

045

045

075

25

25

20

15

10

5

5

20

15

10

E120583(G

eV)

E120583(G

eV)

1000 10002000 3000 4000 5000 6000

1000 2000 3000 4000 5000 6000

2000 3000 4000 5000 6000

L (km)L (km)

L (km)

25

20

15

10

5

E120583(G

eV)

25

20

15

10

5

E120583(G

eV)

1000 2000 3000 4000 5000 6000

L (km)








9F + 119890+ + ]

119890) and ]

119890from 6He (6

2He rarr

6

3Li+119890minus+]


5B rarr 8

4Be+119890++]

119890) and

8Li (83Li rarr 8

4Be + 119890minus + ]










18

10Ne 241 392 82037 921 ]

119890

6

2He 117 402 93453 100 ]

119890

8

5B 111 1443 60087207 100 ]

119890

8

3Li 120 1347 42535516 100 ]

119890



119890) and 29 times 1018 (]

119890) useful














Acknowledgments


References

































































119871times 119880(1)








































































21Δm231

and sin 12057913



13rdquo


















































































13phase and CP-
















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




NC

101

100

10minus11 2 3 4 5

2nd OSC max

1st OSC max

Even

ts pe

r0125

GeV

bin

in5

yrs




(a)

101

100

10minus1

1 2 3 4 5 6 7 8



NCEv

ents

per0125

GeV

bin

in5

yrs



(b)




100

80

60

40

20

00 50 100 150 200 250

minus90∘

0

90∘

180∘

HO-IHHO-IH

HO-NH

HO-NHLO-NH

LO-NH

LO-IHLO-IH

LBNE10

Ant

i-ap

pev

ents

app events

05lowastLBNO





13= 0089 For


[41]





23-hierarchy LO-NH



and sin2212057913


31(120590 = 4) and












101

102

103

LO-NH true


LO-IH true

LBNO

LBNE10


101

100

100

101

102

103

100

102

103

101

100

102

103

MM-NH true

LBNO

LBNE10


MM-IH true

Δ1205942

Δ1205942

Δ1205942

Δ1205942





combinations





23values






∘ sim 150

∘)






LO-NH true


LO-IH true

LBNO

LBNE10


HO-NH true

LBNO

LBNE10


HO-IH true

20

25

10

15

5

0

20

25

10

15

5

0

20

25

10

15

5

0

20

25

10

15

5

0

Δ1205942

Δ1205942

Δ1205942

Δ1205942


120575CP(true) (deg) 120575

CP(true) (deg)








119890and









LBNE10LBNO

12

10

8

2

4

6

0

2120590

3120590

Δ1205942

120575CP (true)

(a)



LBNE10LBNO

12

10

8

2

4

6

0

2120590

3120590

Δ1205942

120575CP (true)

(b)








120583 The most















sin2212057913 = 10minus1 sin

2212057913 = 10minus2

sin2212057913 = 10minus3 sin

2212057913 = 10minus4

065

065

07

07

07

04

03 035

07

08

075

055

065

045

045

075

25

25

20

15

10

5

5

20

15

10

E120583(G

eV)

E120583(G

eV)

1000 10002000 3000 4000 5000 6000

1000 2000 3000 4000 5000 6000

2000 3000 4000 5000 6000

L (km)L (km)

L (km)

25

20

15

10

5

E120583(G

eV)

25

20

15

10

5

E120583(G

eV)

1000 2000 3000 4000 5000 6000

L (km)








9F + 119890+ + ]

119890) and ]

119890from 6He (6

2He rarr

6

3Li+119890minus+]


5B rarr 8

4Be+119890++]

119890) and

8Li (83Li rarr 8

4Be + 119890minus + ]










18

10Ne 241 392 82037 921 ]

119890

6

2He 117 402 93453 100 ]

119890

8

5B 111 1443 60087207 100 ]

119890

8

3Li 120 1347 42535516 100 ]

119890



119890) and 29 times 1018 (]

119890) useful














Acknowledgments


References

































































119871times 119880(1)








































































21Δm231

and sin 12057913



13rdquo


















































































13phase and CP-
















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics







101

102

103

LO-NH true


LO-IH true

LBNO

LBNE10


101

100

100

101

102

103

100

102

103

101

100

102

103

MM-NH true

LBNO

LBNE10


MM-IH true

Δ1205942

Δ1205942

Δ1205942

Δ1205942





combinations





23values






∘ sim 150

∘)






LO-NH true


LO-IH true

LBNO

LBNE10


HO-NH true

LBNO

LBNE10


HO-IH true

20

25

10

15

5

0

20

25

10

15

5

0

20

25

10

15

5

0

20

25

10

15

5

0

Δ1205942

Δ1205942

Δ1205942

Δ1205942


120575CP(true) (deg) 120575

CP(true) (deg)








119890and









LBNE10LBNO

12

10

8

2

4

6

0

2120590

3120590

Δ1205942

120575CP (true)

(a)



LBNE10LBNO

12

10

8

2

4

6

0

2120590

3120590

Δ1205942

120575CP (true)

(b)








120583 The most















sin2212057913 = 10minus1 sin

2212057913 = 10minus2

sin2212057913 = 10minus3 sin

2212057913 = 10minus4

065

065

07

07

07

04

03 035

07

08

075

055

065

045

045

075

25

25

20

15

10

5

5

20

15

10

E120583(G

eV)

E120583(G

eV)

1000 10002000 3000 4000 5000 6000

1000 2000 3000 4000 5000 6000

2000 3000 4000 5000 6000

L (km)L (km)

L (km)

25

20

15

10

5

E120583(G

eV)

25

20

15

10

5

E120583(G

eV)

1000 2000 3000 4000 5000 6000

L (km)








9F + 119890+ + ]

119890) and ]

119890from 6He (6

2He rarr

6

3Li+119890minus+]


5B rarr 8

4Be+119890++]

119890) and

8Li (83Li rarr 8

4Be + 119890minus + ]










18

10Ne 241 392 82037 921 ]

119890

6

2He 117 402 93453 100 ]

119890

8

5B 111 1443 60087207 100 ]

119890

8

3Li 120 1347 42535516 100 ]

119890



119890) and 29 times 1018 (]

119890) useful














Acknowledgments


References

































































119871times 119880(1)








































































21Δm231

and sin 12057913



13rdquo


















































































13phase and CP-
















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics







LO-NH true


LO-IH true

LBNO

LBNE10


HO-NH true

LBNO

LBNE10


HO-IH true

20

25

10

15

5

0

20

25

10

15

5

0

20

25

10

15

5

0

20

25

10

15

5

0

Δ1205942

Δ1205942

Δ1205942

Δ1205942


120575CP(true) (deg) 120575

CP(true) (deg)








119890and









LBNE10LBNO

12

10

8

2

4

6

0

2120590

3120590

Δ1205942

120575CP (true)

(a)



LBNE10LBNO

12

10

8

2

4

6

0

2120590

3120590

Δ1205942

120575CP (true)

(b)








120583 The most















sin2212057913 = 10minus1 sin

2212057913 = 10minus2

sin2212057913 = 10minus3 sin

2212057913 = 10minus4

065

065

07

07

07

04

03 035

07

08

075

055

065

045

045

075

25

25

20

15

10

5

5

20

15

10

E120583(G

eV)

E120583(G

eV)

1000 10002000 3000 4000 5000 6000

1000 2000 3000 4000 5000 6000

2000 3000 4000 5000 6000

L (km)L (km)

L (km)

25

20

15

10

5

E120583(G

eV)

25

20

15

10

5

E120583(G

eV)

1000 2000 3000 4000 5000 6000

L (km)








9F + 119890+ + ]

119890) and ]

119890from 6He (6

2He rarr

6

3Li+119890minus+]


5B rarr 8

4Be+119890++]

119890) and

8Li (83Li rarr 8

4Be + 119890minus + ]










18

10Ne 241 392 82037 921 ]

119890

6

2He 117 402 93453 100 ]

119890

8

5B 111 1443 60087207 100 ]

119890

8

3Li 120 1347 42535516 100 ]

119890



119890) and 29 times 1018 (]

119890) useful














Acknowledgments


References

































































119871times 119880(1)








































































21Δm231

and sin 12057913



13rdquo


















































































13phase and CP-
















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics






LBNE10LBNO

12

10

8

2

4

6

0

2120590

3120590

Δ1205942

120575CP (true)

(a)



LBNE10LBNO

12

10

8

2

4

6

0

2120590

3120590

Δ1205942

120575CP (true)

(b)








120583 The most















sin2212057913 = 10minus1 sin

2212057913 = 10minus2

sin2212057913 = 10minus3 sin

2212057913 = 10minus4

065

065

07

07

07

04

03 035

07

08

075

055

065

045

045

075

25

25

20

15

10

5

5

20

15

10

E120583(G

eV)

E120583(G

eV)

1000 10002000 3000 4000 5000 6000

1000 2000 3000 4000 5000 6000

2000 3000 4000 5000 6000

L (km)L (km)

L (km)

25

20

15

10

5

E120583(G

eV)

25

20

15

10

5

E120583(G

eV)

1000 2000 3000 4000 5000 6000

L (km)








9F + 119890+ + ]

119890) and ]

119890from 6He (6

2He rarr

6

3Li+119890minus+]


5B rarr 8

4Be+119890++]

119890) and

8Li (83Li rarr 8

4Be + 119890minus + ]










18

10Ne 241 392 82037 921 ]

119890

6

2He 117 402 93453 100 ]

119890

8

5B 111 1443 60087207 100 ]

119890

8

3Li 120 1347 42535516 100 ]

119890



119890) and 29 times 1018 (]

119890) useful














Acknowledgments


References

































































119871times 119880(1)








































































21Δm231

and sin 12057913



13rdquo


















































































13phase and CP-
















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




sin2212057913 = 10minus1 sin

2212057913 = 10minus2

sin2212057913 = 10minus3 sin

2212057913 = 10minus4

065

065

07

07

07

04

03 035

07

08

075

055

065

045

045

075

25

25

20

15

10

5

5

20

15

10

E120583(G

eV)

E120583(G

eV)

1000 10002000 3000 4000 5000 6000

1000 2000 3000 4000 5000 6000

2000 3000 4000 5000 6000

L (km)L (km)

L (km)

25

20

15

10

5

E120583(G

eV)

25

20

15

10

5

E120583(G

eV)

1000 2000 3000 4000 5000 6000

L (km)








9F + 119890+ + ]

119890) and ]

119890from 6He (6

2He rarr

6

3Li+119890minus+]


5B rarr 8

4Be+119890++]

119890) and

8Li (83Li rarr 8

4Be + 119890minus + ]










18

10Ne 241 392 82037 921 ]

119890

6

2He 117 402 93453 100 ]

119890

8

5B 111 1443 60087207 100 ]

119890

8

3Li 120 1347 42535516 100 ]

119890



119890) and 29 times 1018 (]

119890) useful














Acknowledgments


References

































































119871times 119880(1)








































































21Δm231

and sin 12057913



13rdquo


















































































13phase and CP-
















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics








18

10Ne 241 392 82037 921 ]

119890

6

2He 117 402 93453 100 ]

119890

8

5B 111 1443 60087207 100 ]

119890

8

3Li 120 1347 42535516 100 ]

119890



119890) and 29 times 1018 (]

119890) useful














Acknowledgments


References

































































119871times 119880(1)








































































21Δm231

and sin 12057913



13rdquo


















































































13phase and CP-
















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics



review article physics potential of long-baseline experiments

Documents