Probing atmospheric mixing and leptonic CP violation in current and future long baseline oscillation experiments

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DOI: 10.1016/j.physletb.2017.05.080

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DIRETORIA DE TRATAMENTO DA INFORMAÇÃO

Cidade Universitária Zeferino Vaz Barão Geraldo

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http://www.repositorio.unicamp.br

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Probing

atmospheric

mixing

and

leptonic

CP

violation

in

current

and

future

long

baseline

oscillation

experiments

Sabya Sachi Chatterjee

a

,

b

,

Pedro Pasquini

c

,

J.W.F. Valle

d

,

∗

a_{InstituteofPhysics,SachivalayaMarg,SainikSchoolPost,Bhubaneswar751005,India}

b_{HomiBhabhaNationalInstitute,TrainingSchoolComplex,AnushaktiNagar,Mumbai400085,India} c_{InstitutodeFísicaGlebWataghin–UNICAMP,13083-859,CampinasSP,Brazil}

d_{AHEPGroup,InstitutdeFísicaCorpuscular–C.S.I.C./UniversitatdeValència,ParcCientificdePaterna,C/CatedraticoJoséBeltrán,2E-46980Paterna(València),} Spain

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory:

Received13February2017 Accepted28May2017 Availableonline31May2017 Editor:A.Ringwald

WeperformrealisticsimulationsofthecurrentandfuturelongbaselineexperimentssuchasT2K,NO

ν

A, DUNEandT2HKinordertodeterminetheirultimatepotentialinprobingneutrinooscillationparameters. We quantify the potential ofthese experimentsto underpinthe octant ofthe atmosphericangle θ23

as well as the value and sign of the CP phase δC P.We do this both in general, as well as within

thepredictiveframeworkofapreviouslyproposed[1]benchmarktheoryofneutrinooscillationswhich tightlycorrelatesθ23andδC P.

©2017TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.

1. Preliminaries:aminimalbenchmarktheoryofneutrino oscillations

Thediscoveryofneutrinooscillationsconstitutesamajor mile-stoneinparticlephysics[2,3].Whileoscillationsarea generic ex-pectationintheoriesofneutrinomass,thecorrespondingsetof os-cillationparameterscanbeextremelyrich[4],precludingthe pos-sibilityof making detailedpredictions for thenext generation of oscillationexperiments [5]. Despitethetremendous experimental progresswehavehadandwhichhasbroughtneutrinooscillation physics to the precision age, one still lacks reliable information, forinstance,ontheoctantoftheatmosphericangleaswellasthe valueof(Dirac-type)CPphase[6–8],whosedeterminationremains ambiguous.Agenericneutrinooscillationpatternwouldinvolvein additiona setofnon-unitarity parameters[9,10],knowntobring inapotentially seriousambiguity inprobingCPviolationin neu-trinooscillations[11].

Hereweassumethestandardthreeneutrinoparadigm[12]and performrealistic simulationsofthecurrentandfuturelong base-lineoscillationexperimentssuchasT2K,NO

ν

A,DUNEandT2HKin orderto determinetheir potentialin probingneutrino oscillation

*

Correspondingauthor.

E-mailaddresses:sabya@iopb.res.in(S.S. Chatterjee),pasquini@ifi.unicamp.br (P. Pasquini),valle@ific.uv.es(J.W.F. Valle).

URL:http://astroparticles.es/(J.W.F. Valle).

parameters.Fordefinitenesswefocusontheleastwell-determined ones,namelytheatmosphericangleandthe(Dirac-type)CPphase. Firstwequantifythesensitivityoftheseexperimentsto

θ

23and

δ

C P ingeneral. We also posethe question within theframework ofasimplebenchmarktheoryofneutrinooscillationsproposedin Ref.[1].Suchtheoryhasbeenproposedfromfirstprinciples,based on a warpedflavor modelnaturally predicting light Dirac neutri-nos, so that the lepton mixing matrixhas the samestructure as the CKM matrix describing quark mixing. A beautiful feature of the modelconsistsinthe integrationofitsextra-dimensional na-ture,whichaccountsforthestandardmodelmasshierarchies,with the implementation ofa predictive non-Abelianflavor symmetry, inourcase

(

27

)

⊗

Z

4

⊗

Z

4.Thelatterleadstothedescriptionof

allthefourneutrinooscillationparameters

θ

i j and JCP,wherethe

latteristhe leptonicCPinvariant, intermsofjusttwo angles:

θ

ν and

φ

ν accordingtothefollowingequations,

sin2

θ

12

=

1 2

−

sin 2

θ

νcos

φ

ν sin2

θ

13

=

1 3

(

1

+

sin 2

θ

νcos

φ

ν

)

sin2

θ

23

=

1

−

sin 2

θ

νsin

(

π

/

6

− φ

ν

)

2

−

sin 2

θ

νcos

φ

ν JCP

= −

1 6

√

3cos 2

θ

ν (1) http://dx.doi.org/10.1016/j.physletb.2017.05.080

0370-2693/©2017TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3_.

Giventhegooddetermination of

θ

13by reactorexperiments, this

modelisinasense effectivelyaone-parameter theory,hencewe callita“minimal”benchmarktheoryofneutrinooscillations.

Here we explore the potential of current and planned long

baseline oscillationexperiments intesting thepredictions of this model.Weperformstate-of-the-artsimulationsoftherelevant ex-perimentsT2K,NO

ν

A,DUNEandT2HKinordertoascertainhow welltheycanprobethemodelandcomparewiththesituationin ageneralunconstrainedoscillationscenario.

2. Numericalanalysisandexperimentalsetups

Inordertoquantifythesensitivitiesofthevariousexperimental setupsintestingourbenchmarkoscillationmodel,weuseGLoBES

[13,14]asa numericalsimulator. Theglobal(unconstrained) best fitvaluesof theoscillation parametersin thethree flavor frame-work, taken from [6], are given as: sin2

θ

12

=

0

.

323, sin2

θ

13

=

0

.

0234,sin2

θ

23

=

0

.

567

(

0

.

573

)

forNH(IH),

δ

C P

=

1

.

34

π

,



m221

=

7

.

5

×

10−5 _eV2_,



m2

31

=

2

.

48

×

10−3

(

−

2

.

38

×

10−3

)

eV 2 _forNH

(IH).Ifspecificallynotmentionedsomethingelse,allthetruedata have been generated using the unconstrained best values of the oscillationparameters. Also,we haveconsidered afixedhierarchy bothintrueandtestdata.Weare notusinganyprioronthe os-cillationparametersbecauseourtestoscillationparameterswillbe predictedbythemodel[1].Inordertofindthesensitivityofthis model at a certain confidence level, we are using the following Poissionian

χ

2_function

_[15,16]

_:

χ

2

=

min {ξa,ξb}



2 n



i=1

(

yi

−

xi

−

xiln yi xi

)

+ ξ

_a2

+ ξ

_b2



(2) where,n isthetotalnumberofbinsand

yi

( ˜

f

, ξ

a

, ξ

b

)

=

Nipre

( ˜

f

)



1

+

π

a

_ξ

a



+

Nb_i

( ˜

f

)



1

+

π

b

_ξ

b



(3)

where

˜

f denotes the oscillation parameters predicted by the

modeland

π

a_,

_π

b_{denotethesystematicerrorsonsignaland} back-groundrespectively,assumedtobeuncorrelatedbetweendifferent channels. Onthe other hand

ξ

a and

ξ

b are the pullsdueto sys-tematicerrors,while N_ipre isthetotalnumberofpredictedsignal events in the ith energy bin and Nb

i is the background events, where the charged current (CC) background depends on

˜

f . The truedatameasuredbyanexperimententerinEq.(2)through xi

(

f

)

=

Nobsi

(

f

)

+

Nbi

(

f

)

(4)

Nobs_i isthenumberofobservedCCsignaleventsinthei-thenergy binand f denotes thestandard unconstrainedoscillation param-eterswhosethebestfitvaluesare takenfromRef. [6].Individual contributionscomingfromthevariousrelevantchannelsareadded togetherinordertogetthetotal

χ

2 _as

χ

_total2

=

χ

2 νμ→νe

+

χ

2 ¯ νμ→¯νe

+

χ

2 νμ→νμ

+

χ

2 ¯ νμ→¯νμ (5) Finally, this total

χ

2 _{is minimized over the free oscillation}

parameters. The simulation runs over four possible experimental scenarios, the“current” T2K, NOvAexperiments andthe “future”

T2HK and DUNE proposalsetups and this encompass the list of

the experiments aimed at improving the

θ

23 measurements and

thedeterminationoftheCPphase

δ

CP.Forthelatterthepredicted

correlation between

θ

23 and

δ

CP [1] can be used to significantly

shrink down the parameter space of the benchmark model as

shownin [17].In order to sharpen andextend those results we firstbriefly summarizetheprocedureusedineach ofthefour se-tups.

1. T2K: Tosimulatethe T2K(Tokaito Kamiokande)experiment,

we assumed the configuration in [18] with a full exposure

of 7

.

8

×

1021 protonson target (POT) whichproduce an off-axis(angle of 2

.

50) neutrino beamwithenergypeak around

0.6 GeV hitting a 50 kt (fiducial volume 22.5 Kt) water

Cerenkov Super-K far detector at Kamioka at a distance of

295 kmfromthe target.Inthiswork,halfofthetotalexposure

has been assumed in the neutrino mode and the remaining

half ofthe exposure inthe antineutrino mode. We have fol-lowed reference[18] in great detail, reproducing their event spectrainall themodesratherwell. Followingthesame ref-erence, weare usinganuncorrelated5%signal normalization error and10% background normalizationerrorfor both neu-trinoandantineutrinoappearanceanddisappearancechannels respectively.

2. T2HK: T2HK (Tokai to Hyper-Kamiokande) is also a

super-beamacceleratorbasedoff-axisexperimentwhichisexpected tobe operationalaround2025[19].Ituses thesameoff-axis setupandthesamebaseline asT2K. Itissupposed tobethe

upgraded version of T2K which also uses a 30 GeV proton

beamacceleratedby theJ-PARCfacility,whichhitsthetarget

and produces an intense neutrino beam. The produced

neu-trinos at the target will be collected by a 560 kt (fiducial) waterCerenkovfardetectorplacedatHyper-Kamiokande. Fol-lowingRef. [20],we assume an integratedbeamwith power 7

.

5 MW

×

107 _{sec which correspondsto 1}

_.

₅₃

_×

₁₀21 _POT.To

make the event numberalmost equal for both neutrino and

antineutrino modes, we have assumed a run time ratio of

1:3for

ν

:

ν

¯

that is2.5 yrsforneutrinomode and7.5yrsfor

antineutrino mode. As a simplified case, we assume an

un-correlated5% signal normalizationerrorand10% background normalizationerrorforbothpolaritiesandforbothappearance anddisappearancechannelsrespectively.

3. NO

ν

A: NO

ν

A(NuMIOff-axis

ν

e Appearance)

[21,22]

isan off-axis accelerator based superbeam experiment, consisting of twodetectors,oneisaneardetectoratFermilabandanother one is a 14 Kt TASD far detector placed in Ash river, Min-nesota at an angle 0

.

80 from the beam direction. Neutrinos fromNuMI(NeutrinosattheMainInjector)willpassthrough 810 km of earth matter before they are detected at the far detector. The off-axis is chosen to get peak energy

approxi-mately at 2 GeV. NO

ν

A uses a 120 GeV proton beam with

beampower 700 kWto produce the intense neutrinobeam.

TheexpectedPOTis3

.

6

×

1021dividedin50%neutrinomode and50%anti-neutrinomode,withuncorrelated5%signal nor-malizationerrorand10% background normalizationerrorfor bothneutrinoandantineutrinoappearanceanddisappearance channel respectively. All the relevant information has been takenfrom

[23]

.

4. DUNE: DUNEisa longbaseline futuregenerationon-axis

su-perbeamexperimenthaving1300 kmbaseline fromFermilab

to Sanford Underground Research Laboratory in Lead, South

Dakota. DUNE will use a 40 kt LArTPC as its far detector.

We havefollowedthe DUNECDR

[24]

asreference. It usesa

80 GeVprotonbeamwithbeampower1.07MWwitha total

exposureof300kt.MW.yrs havingneutrinomoderunningfor 3.5 yrs andantineutrino mode running for3.5 yrs. All other detailshavebeenmatchedtotheDUNEdesignreport. Beforewe gototheresultsection,itisworthtomentionthat

in the numerical simulation we have used a line-averaged

con-stantmatterdensityof2.8 gm/cm3 _{forT2K,T2HKandNO}

_ν

_A,and

Fig. 1. Allowedregionsofthetwomodelparametersθν andφνat2σ (left)and3σ(right)confidencelevelat1d.o.f.thatis(χ2=4,9 respectively).Theplotsassume NormalHierarchy (NH)astrue.ThedarkgreenbandrepresentsthesensitivityofT2K,whilethebluebandcorrespondstoNOνA.Theredandcyanbandsgivetheexpected sensitivitiesoftheDUNEandT2HKexperiments.(Forinterpretationofthereferencestocolorinthisfigurelegend,thereaderisreferredtothewebversionofthisarticle.)

Table 1

Valuesoftheneutrinooscillationparameterscorrespondingtotheχ2_{minimaobtainedfromthebenchmarkmodel.Thesixthcolumndenotes}

thestandard“unconstrained”three-neutrinobestfitvaluesforNHtakenfrom[6].Thenumberwithintheparenthesisindicatestheminimum valueoftheχ2_{predictedfromthebenchmarkmodelforthecorrespondingexperiment.}

Parameter DUNE (χ2

min=0.14) T2HK (χmin2 =0.637) NOνA (χmin2 =0.016) T2K (χmin2 =0.015) Unconstrained case

s2 12 0.341 0.341 0.341 0.341 0.323(±0.016) s2 13 0.023 0.023 0.024 0.024 0.0234(±0.0020) s2 23 0.567 0.565 0.565 0.566 0.567(+ 0.025 −0.043) δCP/π 1.30 1.30 1.30 1.30 1.34(+₋00..6438)

3. Constrainingthebenchmarkmodelparameters

θ

ν and

φ

ν

fromexperiment

Equations

(1)

,expressedintermsoftwofreeparameters

θ

ν and

φ

ν suggest that our benchmark model can be tested directly in lowenergylongbaseline(LBL)neutrinooscillationexperimentsby obtainingtheoscillationprobabilityasafunctionofthesetwo pa-rametersandcomparingto experimentaldata.Thiswilllead toa restrictionatacertainconfidencelevel.Inthissection,wepresent theallowedregionofthetwomodelparameters

θ

ν and

φ

ν implied bythecurrentandfutureLBLexperiments.

Fig. 1representstherestrictedregionofthetwoparameters

θ

ν and

φ

ν at2

σ

(leftpanel)and3

σ

(rightpanel)confidencelevelat 1degreeoffreedom assumingnormalhierarchy(NH)asourtrue choice. Thedark green band representsthe allowed region given by T2K, the blue band is obtained from NO

ν

A, the red band is thesensitivityregionexpectedforDUNEandtheCyanband corre-spondstothesensitivityregionoftheproposedT2HKexperiment. Truedata sethasbeen generatedusingthe unconstrained values oftheoscillationparametersasmentionedinsec. 2andthen fit-tedto thetest data setobtainedfromeach pairof

θ

ν and

φ

ν in

order to calculate the minimum



χ

2_{. Now the same procedure}

hasbeen followedforall allowed1 _valuesof

_θ

ν and

φ

ν .In order toobtainthesesensitivitybands,weonlyconsiderthosevaluesof thenewparametersforwhichmodelcanbetestedatcertain con-fidencelevelthatis



χ

2

_≤

_n

_σ

_(here,n

₌

₂

_,

_3).

From

Fig. 1

,itisquiteevidentthattheT2HKexperimentis ex-pected to provide the best sensitivity on the model parameters,

followed by DUNE. The performance of T2HK is best because of

lowbaselineandhugestatisticswhichimpliesaveryprecise

mea-1 _{Aspointedoutby[1],themodelallowsbothNH(forθ}

ν∈ [0,π/2]∪[3π/2,2π]) andIH(θν∈ [π/2,3π/2]).FordefinitenesshereweconsideronlyNHintheregion θν∈ [0,π/2].Theangleφνcanassumeanyvalueinbetween0to2π.

surementof

δ

C P,anessentialingredienttoconstrainourreference benchmarkmodel.NotethatforDUNE,theCPsensitivityis

some-what less than T2HK. On the other hand NO

ν

Agives somewhat

bettersensitivitythanT2K.

In

Table 1

,weshow afaircomparisonbetweenthemodel in-dependent(unconstrained)oscillationparametersandtheone pre-dicted by our simple benchmarkmodel in differentexperiments.

The minimum value of the



χ

2 _{coming from different}

exper-iments is also shown within parenthesis for the corresponding

experiment. Oneshould keep in mindthat this analysisassumes that the truevalues is the minimum of the current global neu-trino oscillation fit. Since the latter assumes the unconstrained scenario with its 4 free parameters, it follows that the true val-uesinthesimulationcannotbereproducedbytheourbenchmark modelwhichhasonly2parameters,lying2

σ

awayfromthe min-imum[1].

4. Sensitivitiesonoscillationparameters

Herewe examinethesensitivitiesonneutrinomixing parame-tersandCPphase,speciallyfocusingto

θ

23and

δ

C P,currentlythe two most poorly determined oscillation parameters. Before pre-senting ourresults notice that oscillation studies can be used to probeoscillationparametersintwoways:eitherinthegeneral un-constrained three-neutrinoscenario orwithin the aboveminimal benchmarkpicture ofneutrinooscillations.Inotherwords,by as-sumingthegeneraloscillationpictureasthetruth,weexpectthat our availableoscillation parameterspacewillbe highly restricted byfutureexperimentsinthebenchmarkscenario.Alternatively,by takingourminimalbenchmarkpictureastrue,therealminimum oftheoscillationparameters differsfromtheoneobtainedbythe globaloscillationfit,whichassumesgeneral

χ

2 _{minimizationwith}

Fig. 2. Precision“measurement”ofsin2θ23andδC PatT2KandNOνAaspredictedbythebenchmarkmodelwhenNHisthetruehierarchy.Thestardenotestheunconstrained valuesfromthefifthcolumnofTable 1andthebandscorrespondtothe2σ,3σ,and4σ C.Luncertainties.(Forinterpretationofthereferencestocolorinthisfigure,the readerisreferredtothewebversionofthisarticle.)

carefulanalysis. Inordertodothatone shouldanalyzeand com-parebothschemesinthesamefootingforeachexperiment. 4.1.SensitivityofT2KandNO

ν

Ato

θ

23and

δ

C Pintheminimal

benchmarkoscillationmodel

TheresultsfromSection 3canbetranslatedfromthetwo pa-rametersofourbenchmarkmodelintothefourfree parameters

θ

i j and

δ

CPdescribingoscillations,throughEq.(1),obtaininga

χ

₀2,

χ

₀2

≡

χ

2

(θ

i j

(θ

ν

, φ

ν

), δ

CP

(θ

ν

, φ

ν

))

(6)

which is the

χ

2 _{function relevant if one assumes the standard}

pictureastrue.Fordefiniteness weassumeNHtobethetrue hi-erarchy.Thecorrespondingtwo-dimensional2

,

3 and4

σ

contours fortheT2K andNO

ν

Aexperimentsarepresentedin

Fig. 2

.These arethevaluesofthe parameters

θ

23and

δ

C P whichactually con-tribute to delimit the bands indicated in Fig. 1. The left panels give the sin2

θ

23 vs

δ

C P contour plot,while the right panels are thesin2

θ

23 versus JC P contourplots,where JC P istheCP invari-ant.Theupper(lower)panelsof

Fig. 2

correspondtoT2K(NO

ν

A). Theredbandineachplotof

Fig. 2

correspondstothe2

σ

C.L. al-lowedregion,thebluebandcorrespondsto3

σ

C.L.andthegreen corresponds to the 4

σ

C.L. allowed region. The star denotes the unconstrainedvaluestakenfromthefifthcolumnof

Table 1

.

Notice the clear correlation between

θ

23 and

δ

C P which is a consequenceof

Fig. 1

.Notealso,thatamaximalchoiceof

θ

23

cor-responds to the maximal CP violation (up to sign) for T2K and

NO

ν

A which is a very important prediction of the benchmark

model. Moreover, for non-maximal values of

θ

23,there is a four

folddegeneracyintheCPphasedeterminationinT2K andNO

ν

A. Apartfromthe

θ

23–

δ

C P four-folddegeneracy,thereisalso degen-eracy betweenthelower octant(sin2

θ

23

<

0

.

5) andhigheroctant

(sin2

θ

23

>

0

.

5),sothat,thistwoparametermodelcannot

distin-guishtheoctantoftheatmosphericangle

θ

23.Asexpected,inthe

JC P plotsthedegeneracyisclearlyreduced.

4.2. SensitivityofT2KandNO

ν

Ato

θ

23and

δ

C Pinthegeneral

3-neutrinooscillationpicture

Here we summarize our model independent results for the

oscillation parameters

θ

23 and

δ

C P. They hold in the general 3-neutrino oscillation picture assuming again NH to be the true hierarchy.Theprecision“measurements”oftheoscillation param-eterssin2

θ

23and

δ

C P intheT2KandNO

ν

Aexperimentsaregiven in

Fig. 3

.ThestarsymbolcorrespondstotheunconstrainedGlobal best-fitvaluesoftheoscillationparametersasgivenin

Table 1

.The red,blueanddarkgreenbandsineachplotcorrespondtothe2

σ

, 3

σ

and 4

σ

uncertainties respectively in sin2

θ

23 and

δ

C P plane.

Fig. 3clearlyreflectsthephysicspotentialofT2KandNO

ν

Ain re-constructingthe CPphase

δ

C P andatmosphericmixingangle

θ

23

Fig. 3. Precision“measurement”ofsin2θ23andδC P atT2KandNOνAforgenericunconstrained3-neutrinooscillationswhenNHisthetruehierarchy.Thestardenotesthe unconstrainedvaluestakenfromthefifthcolumnofTable 1andthebandscorrespondtothe2σ,3σ,and4σC.Luncertainties.(Forinterpretationofthereferencestocolor inthisfigure,thereaderisreferredtothewebversionofthisarticle.)

corresponding tothe pointdenoted bythe symbol“star”. Evenif forafixed phase,there isadegeneracy betweenthe twooctants oftheatmosphericangle

θ

23at2

σ

C.L.forbothexperiments.

Notice that the unconstrained best fit doesnot coincide with theminimumpredictedbythemodelbecausethetruevalue can-not be reproduced perfectly within the model.This implies that ourbenchmarkoscillationschemefindsdifferentminimumvalues forthecurrent/expectedoscillationparametersthanobtainedinan unconstrainedfit.

4.3. Sensitivityoffutureexperiments

We now turn to the sensitivity of the future generation of plannedlongbaselineacceleratorneutrinooscillationexperiments suchasDUNE[24]andT2HK[19],fordefiniteness.Ourresultsare depictedin

Figs. 4 and 5

.Theupper(lower)panelof

Fig. 4

corre-spondstoDUNE(T2HK).Noticethatinall plotsof

Fig. 4

,there is anextracyanbandat5

σ

C.L.Oneseesthattheywillhavethe po-tentialofseverelyconstraining theparameterspaceofthemodel. Themostimportantpointtonoteisthattheyhelptoremovethe four-folddegeneracytotwo-folddegeneracy,duetotheir fantastic sensitivityto

δ

CP.It excludesalargepartofthe parameterspace.

The allowed region at 4

σ

corresponds to the 1

.

10

π

(

−

162◦) to 1

.

75

π

(

−

45◦)forDUNEandformaximalvalueof

θ

23,model

pre-dicts maximal CP violation that

δ

C P

= −

90◦. This is a very nice predictionofthebenchmark model[1]. Noticethat T2HKplays a crucialroleinremoving thefour-folddegeneracyoftheCPphase completelyformostoftheparameterspace(forexample,if

θ

23lies

intheupperoctant) anditimprovesthesensitivitytremendously whichcanbeattributedtothefactthat T2HKhasvery good sen-sitivitytotheCPphase.Forafixed CPphase,italsoremovesthe octantdegeneracybutnotat5

σ

C.L.andthatcanbeeasilyverified byplacingahorizontallinearoundthestarsymbolontheleftplot ofthelowerpanelof

Fig. 4

.

Fig. 5

displaysthesensitivityregionin

δ

C P versussin2

θ

23,clearlyindicatingthecapabilityofT2HK

(sim-ilar holdsfor DUNE)in establishingCP violationby rejecting the CPconservationscenario atmorethan5

σ

C.L.The figuregivesa quantitativeestimateoftheprecise“measurement”ofsin2

θ

23and

δ

C P forthe generic unconstrained3-neutrinooscillationscenario, whenNHisthe truehierarchy.The stardenotesthebest-fit (un-constrained)valuesofthetwoparameters.Thetruedatahavebeen generatedwithallthebest-fitvaluesoftheoscillationparameters

mentioned in sec. 2 andin the fit we have marginalized on

so-larandreactormixingangles

θ

12and

θ

13respectivelykeepingNH

fixed. The red,blue anddarkgreen bandscorrespond tothe 2

σ

, 3

σ

and4

σ

C.L uncertainty respectivelyat 1 d.o.f. Notice that in thiscasealsotheoctantwouldremainunresolvedevenat2

σ

C.L. Before concludingletusalsoshow thecorresponding

χ

2

pro-files. The plotsin

Fig. 6

quantifythereconstruction capabilityfor the oscillation parameters

θ

23 (

δ

C P). The green dot indicates the unconstrainedbestfitvaluefrom[6].Theblackdashedcurve indi-catesthecurrentglobalfitmeasurement,whiletheredsolidcurve givestheT2HKexpectationforthegeneraloscillationschemeand the blue solid curve represents the precise measurement by the model.

5. Summaryandoutlook

We have performed realistic simulations of the current long

baseline experiments T2K andNOvA aswell as futureonessuch

asDUNEandT2HKinordertodeterminetheir potentialin prob-ing neutrinooscillation parameters in general, aswell astesting our“minimal”benchmarktheoryofneutrinooscillations.Wehave seen that the standard unconstrained three-neutrino picture and ourbenchmarkscenariopredictdifferentminimafortheneutrino oscillation parameters. Nevertheless, current neutrino oscillation

experiments cannot exclude our benchmark scenario. In all our

considerations wehavehadtoassumea“true”valueofthe oscil-lationparametersinordertodeterminetheexpectedprecisionof afuture“measurement”.This“true”valuehasbeentakenfrom[6]. Howeverwecouldwellhavetakenitfromanyoftheotherrecent globaloscillationfits,namelythosein[7,8].

An obvious question arises, namely, what isthe sensitivity of the model for any pair of unconstrained value of

θ

23 and

δ

C P? In other words, what are the values of

θ

23 and

δ

C P “true” for

which the model can be confirmedor excluded at a given

con-fidence?Withthisinmind,wefixthetruevaluesofthecurrently “bestdetermined”oscillationparameters



m2

i j,

θ

12and

θ

13.Given theircurrenterrorstheircentralvaluesarenotexpectedtochange significantly in upcoming experiments. We now vary both

θ

₂₃TRUE

and

δ

_CPTRUE,finding the corresponding minimumof

χ

2 _{within the}

benchmark scheme by varying the modelparameters

θ

ν and

φ

ν . Thiswayweobtainafunction

χ

2

min

(θ

TRUE 23

,

δ

CPTRUE

)

,

χ

_min2

(θ

₂₃TRUE

, δ

_CPTRUE

)

Fig. 4. Precision“measurement”ofsin2θ23andδC P atfutureLBLexperimentsDUNEandT2HKwhenNHisthetruehierarchy.Thestardenotestheunconstrainedvalues takenfromthefifthcolumnofTable 1.Thebandscorrespondtothe2, 3, 4and5σC.Luncertainty.(Forinterpretationofthereferencestocolorinthisfigure,thereaderis referredtothewebversionofthisarticle.)

Fig. 5. Precision“measurement”ofsin2θ23 andδC P forgenericunconstrained3-neutrinooscillationswhenNHisthetruehierarchy.Thestardenotestheunconstrained valuestakenfromthefifthcolumnofTable 1.Thebandscorrespondtothe2σ,3σand4σ C.Luncertainty.Noticethatinthiscasetheoctantwouldremainunresolvedeven at2σ C.L..(Forinterpretationofthereferencestocolorinthisfigure,thereaderisreferredtothewebversionofthisarticle.)

Fig. 6. Theleft(right)panelindicatesthereconstructionofoscillationparametersθ23(δC P).Thegreendotindicatesthebestfitvalueintheunconstrainedoscillationpicture, takenfrom[6].Theblackdashedcurveindicatesthecurrentglobalfitmeasurement,theredsolidcurveindicatestheT2HKexpectationforthemeasurementinthegeneric oscillationscheme,whilebluesolidcurverepresentstheprecisemeasurementbythemodel.(Forinterpretationofthereferencestocolorinthisfigurelegend,thereaderis referredtothewebversionofthisarticle.)

Fig. 7. Probingthemodelthroughthetruevaluesofsin2θ23andδC Pfornormalneutrinomassordering(NH).TheshadedregionsdenotetheconfidencelevelatwhichDUNE (left)orT2HK(right)wouldconfirmourminimalbenchmarkoscillationmodel.Theredbandcorrespondsto90%C.L.,thebluebandcorrespondsto2σ C.L.andthedark greenbandcorrespondstothe3σ C.L.allowedregion.Theconfidencelevelsaregivenfor1d.o.f.(χ2₌₂

.71,4 and 9 respectively).Thestardenotestheunconstrained valuestakenfromthefifthcolumnofTable 1.(Forinterpretationofthereferencestocolorinthisfigurelegend,thereaderisreferredtothewebversionofthisarticle.)

Now foreach truedatasetthe newparameters are marginal-izedwithintheirallowedvaluescomingfrom

Fig. 1

.Theresulting

χ

2 _{representstheabilityoftheexperimenttoprobethemodelif}

itmeasures agivenvalue of

θ

₂₃TRUE and

δ

TRUE_CP andithasbeen ad-dressed very nicely in Fig. 7. The light red band corresponds to the90%C.L.region,thelightbluebandcorrespondsto2

σ

C.L. re-gion and the green band corresponds to the 3

σ

C.L region. The blankregion indicates the unconstrained parameter space of

θ

23

and

δ

C P for whichthe model can be excluded at more than 3

σ

C.L..Inshort,our“minimal”benchmarkoscillationmodelservesto highlighttheincreasedsensitivityof thenewplannedgeneration oflongbaselineoscillationexperiments.

Acknowledgements

This research is supported by the Spanish grants

FPA2014-58183-P,MultidarkCSD2009-00064,SEV-2014-0398(MINECO)and

PROMETEOII/2014/084 (Generalitat Valenciana). P. S. P.

acknowl-edges the support of FAPESP grant 2014/05133-1, 2015/16809-9

and2014/19164-6.

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