Status of neutrino oscillations 2018: 3 sigma hint for normal mass ordering and improved CP sensitivity

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https://www.sciencedirect.com/science/article/pii/S0370269318304672

DOI: 10.1016/j.physletb.2018.06.019

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©2018

by Elsevier. All rights reserved.

DIRETORIA DE TRATAMENTO DA INFORMAÇÃO

Cidade Universitária Zeferino Vaz Barão Geraldo

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Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Status

of

neutrino

oscillations

2018:

3

σ

hint

for

normal

mass

ordering

and

improved

CP

sensitivity

✩

P.F. de Salas

a

,

D.V. Forero

b

,

c

,

C.A. Ternes

a

,

M. Tórtola

a

,

∗

,

J.W.F. Valle

a

a_{AHEPGroup,InstitutdeFísicaCorpuscular–CSIC/UniversitatdeValència,ParcCientificdePaterna,C/CatedraticoJoséBeltrán,2E-46980Paterna(València),}

Spain

b_{InstitutodeFísicaGlebWataghin–UNICAMP,13083-859,Campinas,SP,Brazil} c_{CenterforNeutrinoPhysics,VirginiaTech,Blacksburg,VA24061,USA}

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory:

Received4August2017

Receivedinrevisedform8June2018 Accepted9June2018

Availableonline14June2018 Editor:A.Ringwald

Keywords:

Neutrinomassandmixing Neutrinooscillation

Solarandatmosphericneutrinos Reactorandacceleratorneutrinos Neutrinotelescopes

Wepresentanewglobalfitofneutrinooscillationparameterswithinthesimplestthree-neutrinopicture, includingnewdatawhichappearedsinceourpreviousanalysis [1].Inthisupdateweincludenew long-baselineneutrinodatainvolvingtheantineutrino channelinT2K,as wellasnewdata intheneutrino channel, data from NO

ν

A, as well as new reactor data, such as the Daya Bay 1230 days electron antineutrinodisappearancespectrumdataandthe1500livedayspromptspectrumfromRENO,aswell asnewDoubleChoozdata.WealsoincludeatmosphericneutrinodatafromtheIceCubeDeepCoreand ANTARESneutrinotelescopesandfromSuper-Kamiokande.Finally,wealsoupdateoursolaroscillation analysisbyincludingthe2055-dayday/nightspectrumfromthefourthphaseoftheSuper-Kamiokande experiment.Withthenewdatawefindapreferencefortheatmosphericangleintheupperoctantfor bothneutrinomass orderings,with maximalmixingallowedat

χ

2_{=1.6(3.2)fornormal(inverted)}

ordering.WealsoobtainastrongpreferenceforvaluesoftheCPphaseδintherange_[

π

,2

π

],excluding valuescloseto

π

/2 atmorethan4

σ

.Moreremarkably,ourglobalanalysisshowsahintinfavor ofthe normalmassorderingovertheinvertedoneatmorethan3

σ

.Wediscussindetailthestatusofthemass ordering,CPviolationandoctantsensitivities,analyzingtheinterplayamongthedifferentneutrinodata samples.

©2018TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3_.

1. Introduction

Thediscoveryofneutrinooscillationsconstitutesamajor mile-stoneinastroandparticlephysicsoverthelastfewdecades.Solar and atmospheric neutrino studies were the first to give a con-vincing evidence for neutrino conversion [2,3]. By studying the distortionintheneutrinospectra,laboratoryexperimentsbasedat reactorsandacceleratorshaveplayeda keyroleinselecting neu-trino oscillations as the conversion mechanism at work. Reactor andaccelerator experiments havenow brought the field of neu-trinooscillationstotheprecision era,contributingsignificantlyto sharpenthedeterminationoftheoscillationparameters [4–9]. Par-ticularly relevant was the input of the KamLAND experiment in

✩ _{https://globalfit.astroparticles.es/.}

*

Correspondingauthor.

E-mailaddresses:pabferde@ific.uv.es(P.F. de Salas),dvanegas@ifi.unicamp.br (D.V. Forero),chternes@ific.uv.es(C.A. Ternes),mariam@ific.uv.es(M. Tórtola), valle@ific.uv.es(J.W.F. Valle).

elucidating the nature of the solutionto the solar neutrino puz-zle [10,11]. Indeed, KamLAND measurements have ruled out al-ternative mechanisms involving spin flavor precession [12,13] as wellasnonstandardneutrinointeraction(NSI)solutionstothe so-larneutrino problem [14]. Such NSI-only scenarios aswell asall othermoreexotichypothesesareallruledoutbyKamLAND [15,5]. Precisiontestsoftheoscillationpicturehavealreadyalong his-tory,andremainastimelyasever.Indeed,onecanprobeneutrino NSIwithatmospheric [16] aswell assolarneutrinodata [17,18], wheretherobustness ofthe solarneutrinooscillationdescription hasbeenquestioned [19,20].Therehavebeena varietyofstudies scrutinizingthepossibleroleofNSIinvariousneutrinooscillation setups [21–35]. Likewise, although already constrainedby exper-iment, the effect of neutrino non-unitarity of the lepton mixing matrix,expectedifneutrinomassesarisealaseesaw [36–38],could leadto importantambiguitiesinprobingCPviolationinneutrino oscillations [39],aswellasopportunitiesforprobingnoveleffects. These need to be taken up seriously in the design of future os-cillationexperiments [40–42].Oneexampleareneutrinofactories,

https://doi.org/10.1016/j.physletb.2018.06.019

0370-2693/©2018TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3_.

634 P.F. de Salas et al. / Physics Letters B 782 (2018) 633–640

whichalsoprovideapotentialtestinggroundforthenon-unitarity oftheneutrinomixingmatrix [43,44].

Similarly, neutrinomagneticmoment interactions inturbulent convective-zone magnetic fields would induce an enhanced so-larantineutrino flux, to whichKamLAND observations are sensi-tive [12,13]. Likewise, radiative-zone randommagnetic fields [45] would induce sizeable density fluctuations, capable of affecting neutrinopropagationinasignificantmanner [46,47].However, un-der thehypothesis of CPTconservation,KamLAND constrains the effectofpotentiallylargedensityfluctuationsonsolarneutrino os-cillations [48,49].

Here we reconsider the determination of neutrino oscillation parameterswithinthesimplestthree-neutrinopicture,inthelight of new data that appeared since our previous published global analysis [1]. These include new long-baseline disappearance and appearancedatainvolvingtheantineutrinochannelinT2K[50,51], an updated dataset in the neutrino mode [52], as well as dis-appearance and appearance neutrino data from NO

ν

A [53–55]. Turning to reactors, we have included the electron antineutrino disappearance spectrumof DayaBay corresponding to1230days of data [56], the 1500 live days prompt reactor spectra from RENO [57,58] aswell astheDoubleChoozeventenergyspectrum fromthefar-Iandfar-IIdataperiods [59].Concerningatmospheric neutrinos,we haveincludeddatafromtheIceCube DeepCore [60] and ANTARES [61] neutrino telescopes, properly taking into ac-count therelevant matter effectsin theneutrinopropagation in-side the Earth. Given the difficulties to analyze the mostrecent atmosphericneutrinodatafromSuper-Kamiokandewiththepublic informationavailable, we directly includethe

χ

2_{-tablesprovided}

bytheSuper-KamiokandeCollaboration,correspondingtothe com-binationofthefourrunperiodsoftheexperiment [62].Finally,we have also updated our solar oscillation analysisby includingthe 2055-dayday/nightspectrumfromthefourthphaseofthe Super-Kamiokandeexperiment [63].

2. Newexperiments

InthissectionwepresentabriefdescriptionoftheNO

ν

A long-baseline accelerator neutrinoexperiment aswell as the neutrino telescopes ANTARES and IceCube DeepCore which were not in-cludedinthepreviousglobalfit [1].

2.1. TheANTARESneutrinotelescope

ANTARES is a deep sea neutrino telescope located at the

Mediterranean Sea, near Toulon (France). It consists of 12 lines with 75 optical modules each, covering a height of 350 m and anchored at the sea floor at a depth of about 2

.

5 km, with a separation of around 70 m between neighboring modules. The neutrinodetectionis basedontheCherenkovlightemittedwhen the chargedleptons produced by the neutrino interactions move through the water. AlthoughANTARES was not designed to con-tributeto thedetermination ofthe oscillationparameters, it was the first large volume Cherenkov-based neutrino telescope per-formingsuch analysiswithatmosphericneutrinos.Theymanaged to do it asa result ofan importantreduction oftheir threshold energy,from50GeV,whenonlymulti-lineeventsareconsidered, to20GeVforsingle-lineevents.

2.2. IceCubeDeepCore

IceCubeisa1km3multipurposeneutrinotelescopeplacednear the Amundsen–ScottSouth Pole Station, buried beneath the sur-faceandextendinguptoadepthofabout2500 meters.Similarly

to ANTARES, it uses Cherenkovlight to detect highenergy neu-trinos, withthe differencethat IceCube uses the polariceasthe medium where this light is produced. It has 86 strings with 60 digital opticalmodules (DOMs) each, placedata depththat goes from1450m to2450m into theice. Inthisanalysiswe usethe datafromDeepCore,adenserregionofstringsinsideIceCube, de-signed tomeasuretheatmosphericneutrinofluxatlow energies. Theobservedenergyliesbetween6.3 GeVand56.2 GeV,way be-lowtheenergythresholdofIceCube,whichisabout100 GeV. 2.3. TheNO

ν

Aexperiment

The NO

ν

A experiment is a long-baseline neutrino oscillation facility, with a 810 km baseline, which makes it the biggest long baseline experiment to date. It was designed to observe

ν

μ-disappearanceas well as

ν

e-appearancein both neutrinoand

antineutrino channels. In order toaccomplish this, it uses an in-tense and(nearly)purebeamof

ν

μ generatedattheFermilab ac-celeratorcomplex.TheseneutrinosgothroughtheEarthto north-ern Minnesota, 810 km away, to be detected at the Ash River fardetector.The NO

ν

Aexperimenthascollected anequivalent of 8

.

85

×

1020 protons on target of datain the neutrinomode and is now taking data with the antineutrino beam. Because of its 810 km baseline, it is more sensitive to matter effects than the T2K experiment.Withfurtherdata taking,thismaytranslateinto a better sensitivity to the neutrino massordering. The detectors are 14 mrad off-axis, which results in a narrowneutrino energy spectrum,peakedaround2 GeV,whichcoincideswiththe oscilla-tionmaximumfor

ν

μ

→

ν

e oscillations.

3. Newdata

We now describe thenew datasamples usedin thisupdated globalneutrinooscillationanalysis.

3.1. Updatedsolarneutrinodatasample

We have updated our solar oscillation analysis including the 2055-day D/N(day/night)spectrum fromthefourthphase ofthe Super-Kamiokande experiment, according to Ref. [63]. This new sample includes the D/N energy spectrum above 3.5 MeV col-lected along 2055 days, from September 2008 to April 2015. The signal observed corresponds to a 8_{B solar neutrino flux}

of 2

.

314

±

0

.

018(stat)

±

0

.

039(syst)

×

106 cm−2s−1. The mea-suredD/Nasymmetryduring thisperiodisdetermined as AD N

=

[

−

3

.

1

±

1

.

6

(

stat

)

±

1

.

4

(

syst

)

] %, at1.5

σ

fromzero.Thanks to the increasing accuracy, thisresult combined withthe observed D/N asymmetry inthe three previous phasesof Super-K,provides an indirect indication for matter-enhanced neutrino oscillations in-side the Earth. Apart fromsmall differencesin the valuesof the oscillation parameters, the main results concerning the neutrino oscillation parametersremain intactwithrespect toourprevious analysis in[1], inparticular thefact that maximal solarneutrino mixingishighlydisfavored.1

3.2. NewdatafromDayaBay

Daya Bayis a multi-core andmulti-detector experiment, with eight 20 ton Gd-doped liquid scintillator antineutrino detectors (ADs)located atthreeexperimental halls(EHs).At EH1andEH2,

1 _{ThereanalysisofKamLANDdatainthelightoftherecentlyobserved“bump”}

inthereactorantineutrinospectrummightproducesmalldeviationsofthesolar oscillationparameters,asobtainedinRef. [64].

twoADsweredeployedwhiletheremainingADswereassignedto thefarsite, EH3. The thermalpowerofeach reactor is2

.

9 GWth

andthebaselinetothenearandfarsites(EH1andEH2)areinthe range0

.

35–0

.

6 kmand1

.

5–1

.

9 km,respectively.After1230 days ofdatataking,DayaBayhasmeasuredapproximatelytwohundred thousandinverse betadecayeventsatthefar site. Thanksto the largestatisticsandthereductionofsystematicalerrors,dueto hav-ingseveral functionallyidenticalADs,Daya Bayhasprovided the mostprecisedeterminationofthereactormixingangletodate.

Inthisanalysis,wehaveincludedtheantineutrinoeventenergy spectrafromthethreeEHs.Systematicalerrorsaccountingfortotal anddetectornormalization,aswell ascore-relatederrorsand en-ergyscaleerrorswereincludedintheanalysis.Systematicalerrors accountingforthebackgroundnormalizationineachexperimental hallhavebeenalsoincludedintheanalysis, wherewehaveused thebackgroundexpectationsfromtheancillaryfilesfromRef. [56]. 3.3.NewdatafromRENO

TheRENO experimenthasrecently reported1500 livedaysof data from antineutrinos produced at six reactor cores each one witha

∼

2

.

8 GWth thermalpower. The experimentdetects

neu-trinosat anearand atafar detector(eachdetectorwith 16ton offiducialmass)locatedat0

.

294 kmand1

.

383 kmfromtheline joiningthesixreactorcores,respectively.2Thankstotheimproved precision,thespectralfitanalysisofRENOdataisnowsensitiveto theneutrinooscillationphase,asreportedinRefs. [57,58].Inour analysis, wehave consideredthe nearandfar detectorevent en-ergydistribution.Wehavefittedthemeasuredenergyspectrumat eachdetectorafterthesubtractionofthebackground,normalizing oursimulationtotheexpectedspectrareportedbytheRENO Col-laboration.Systematicalerrorsaccountingforcore-related(0

.

9% for eachcore)anddetectoruncertainties(0

.

2% foreachdetector) [66], havebeenincludedinouranalysisintheformofnuisance param-eters.We havealsoincludedanuisanceparameteraccountingfor thetotalnormalizationuncertainty,that hasbeenleft completely freeintheanalysis.

3.4.NewdatafromDoubleChooz

The Double Chooz experimentdetects antineutrinos produced attwo reactor cores with a 2

×

4

.

27 GWth total thermal power

withanearandfar detectorof8 ton fiducialmasseach, located at0

.

4 km and1

.

05 km, respectively. The data set considered in this analysis corresponds to 461 days of data with far detector only(far-I)plus 212 days offardetector datawitha near detec-tor (far-II), asreported in Ref. [59].3 _{The eventenergy spectrum}

fromthefar-Iandfar-IIdataperiodswereincludedintheanalysis. Systematical errors considered in our simulation account for the signalandbackgroundnormalizationaswell asforthetotal nor-malization.Thetotalbackgroundhasbeenextractedfromthedata reportedinRef. [59].Theresultsoftheanalysisofthethree reac-torexperimentsaregiveninFig.1andwillbediscussedindetail inthenextsection.

3.5.AtmosphericdatafromANTARES

Weanalyzeatmosphericdatafromthe ANTARESCollaboration followingRef. [61],takingalsointoaccountmattereffects,and

in-2 _{TheexactdetectortoreactordistancesfromRef. [65] wereusedinour}

simula-tion.

3 _{Even though more recentdata has been presented at the Moriond}

confer-ence [67],thecollaborationisstilltryingtounderstand bettertheirsystematics. Forthisreasonwehaveonlyincludedthepreviousdatafrom [59] inouranalysis.

Fig. 1. 90and99%C.L.(2d.o.f.)allowedregionsatthesin2

θ13–m231planefrom

in-dividualreactorneutrinoexperiments(dashedandsolidlines)andfromthe combi-nationofthethreeexperiments(colored regions).Theleft(right)panelscorrespond tonormal(inverted)massordering.

Fig. 2. 90and99%C.L.(2d.o.f.)allowedregionsatthesin2θ23–m231planeobtained

fromtheatmosphericneutrinoexperimentsfornormal(left)andinvertedordering (right).

cluding electron neutrino and neutral current interaction events. Inordertocalibrate oursimulationwehavefirstreproducedvery well the analysis performed by the collaboration using their as-sumptionsandapproximations.Afterwardswehaveincluded neu-tral current interactions and matter effects to our simulation.In Fig.2weplottheallowed regionsintheatmosphericparameters at90 and99% C.L. fromouranalysis ofANTARES data.One sees theregions arestill verylargeandthereforethesensitivityisnot competitivewiththeotherexperiments,describedinthefollowing sections.ItisexpectedthattheANTARESCollaboration willupdate theiranalysiswithmoredata,hopefullyimprovingtheirsensitivity totheatmosphericneutrinooscillationparameters.

3.6. AtmosphericdatafromIceCubeDeepCore

Inordertodeterminetheatmosphericneutrinooscillation pa-rameters, in this simulation we use data published by IceCube DeepCoreinRef. [60],analyzedfollowingalltheupdatespresented bythecollaboration.Neutrinodataarepresentedin64bins,with 8 energy-bins and 8 bins in zenith-angle, see [68]. Tables with systematic detector uncertainties, optical efficiencies and uncer-tainties produced through scattering at holes opened in the ice for the depletion of the DOMs are also provided. The fluxes for atmosphericneutrinosaretakenfrom[69,70].Weperformthe nu-mericalintegrationinmatterusingthePreliminaryReferenceEarth Model (PREM) [71]. In Fig.2 we comparethe allowed regions in theatmosphericneutrinooscillationparameterssin2

θ

23and



m231

obtainedfromANTARES,DeepCoreandSuper-Kamiokandephases I–IVat90and99%confidencelevel.Asdiscussedinthenext sec-tion,withsuchnewanalysis,DeepCoredataarebecoming

compet-636 P.F. de Salas et al. / Physics Letters B 782 (2018) 633–640

itivewiththoseoflong-baselineexperimentsNO

ν

AorT2Kinthe determinationoftheatmosphericneutrinooscillationparameters.4 3.7. AtmosphericdatafromSuper-Kamiokande

Inthiswork weincludethemostrecentatmosphericneutrino resultsfrom theSuper-Kamiokande experiment [62], correspond-ingto thecombinedanalysisofphasesItoIVoftheexperiment, witha total of 328kton-year exposure ofthe detector. The data analysisperformedbytheSuper-KCollaboration,optimizedto en-hancethe sensitivityto theneutrino massordering, includesthe impactoftheatmosphericoscillationparametersaswellasthe re-actorangleandtheCPphase.Asstressedin [73],themostrecent atmosphericneutrinoSuper-Kdatasamplesarenotpresentedina formthatallowsareliableuseoutsidethecollaboration.Therefore, herewe followthesame procedureadopted inprevious publica-tions (Refs. [1,74,75]) which consists of directly incorporating to ourglobalneutrinoanalysisthe

χ

2_{-tablesprovidedbythe}

Super-KCollaboration [76],obtainedinRef. [62]. 3.8. Newlong-baselinedatafromT2K

Inaddition to thedata usedin theneutrinooscillation global fit published in Ref. [1], the T2K Collaboration has new results in the neutrino mode. Therefore, this updated analysis includes thelatest T2Kantineutrino sample aswell astheir updated neu-trino data, as published in Refs. [50–52]. With an accumulated statistics of 14.6

×

1020 POT in theneutrino run, the T2K Collab-oration now observes 240 disappearance and 74

+

15 appearance (chargedcurrentquasi-elasticandchargedcurrentsingle-pion, re-spectively) neutrino events. Note, however, that the CC-1

π

ap-pearanceeventshavenotbeenincludedinoursimulation.Inthe antineutrinochannel,with7.6

×

1020 POT,atotalof68 disappear-ance

ν

¯

μ eventsand7appearance

ν

¯

e eventswererecorded.Inthe

presentanalysis we have includedthe newest neutrino fluxesin Super-KprovidedbytheT2Kwebpage [77].Thesimulationofthe experiment andthe statistical analysis were performed withthe GLoBES package [78,79],includingall systematicuncertainties re-portedinRef. [52].

Notice that T2K has already achieved some CP sensitivity, as seeninFig.4.Indeed,thankstothecombinationoftheresultsin theneutrinoandthe antineutrinochannel,T2K isthefirst exper-imentable to excludeon its own certain valuesof the CPphase at more than 2

σ

for normal ordering (NO), and even at 3

σ

for invertedordering(IO).Theallowedregionsforotheroscillation pa-rameters,such as

θ

13and



m231,are foundto beconsistent with

thereactorexperiments.

3.9. Newlong-baselinedatafromNO

ν

A

Inour globalfit we alsoinclude thelatest results for

ν

μ-dis-appearance and

ν

e-appearance of the NO

ν

A experiment. NO

ν

A

has recentlypublished the results of their neutrino run with an accumulated statistics of 8.85

×

1020 _{POT [55]. In the}

disappear-ancechannel,atotalof126eventshavebeenobserved,while763 eventswere expectedunder theno-oscillation hypothesis. Inthe appearancechannel, atotalof66 eventshavebeendetected.The neutrino oscillationanalysis reported by the NO

ν

ACollaboration imposinga prioron

θ

13 slightlydisfavorsinvertedmassordering,

with a significance of approximately 2

σ

. Our simulation of the

4 _{TherecentreanalysisofDeepCoredataperformedbytheIceCubeCollaboration}

inRef. [72] showsimprovedsensitivitytotheatmosphericneutrinooscillation pa-rameters.However,thedetailsofthisreanalysisarenotyetpubliclyavailable,so thisimprovementcannotbeincorporatedinourglobalfit.

Fig. 3. 90and99%C.L.(2d.o.f.) allowedregions atthe sin2θ23–m231 plane for

normal(left)andinvertedmassordering(right)asrestrictedfromthelong-baseline experiments.

NO

ν

Aexperiment hasbeen performedusing GLoBES [78,79], in-cluding allthe systematicerrorsreported in[53,54] andupdated inRef. [55].

InFig.3we comparetherestrictionsontheatmospheric neu-trinoparametersderivedfromlong-baselineacceleratordata com-ing fromthe T2K,NO

ν

AandMINOSexperiments,at90 and99% confidencelevel.FurtherresultsaresummarizedinFigs.4,5,6,7 and8anddiscussedinthefollowingsection.

4. Globalfitresults

We now describe the global results of our updated neutrino oscillation fit. There are no significant changes derived from the new solar neutrino data, hence we move directly to the re-sults for atmospheric neutrinos. Here there are new data from the ANTARES andIceCube Collaborations as well asfrom Super-Kamiokandephase IV.As seeninFig.2,the863-dayatmospheric

data from ANTARES and the 3-year data from IceCube

Deep-Core are enough to provide a determination of the atmospheric oscillation parameters. Note, however, that the determination of

θ

23 from atmospheric data is still dominated by the analysis of

Super-Kamiokande. In any case, the neutrino telescope results are in complete consistency with what follows from the Super-Kamiokandeatmosphericdata,leadingtoaclearglobalpicturefor theall-atmosphericdatafit,showninFig.2.

Concerningthelong-baselineacceleratordata,Fig.3showsthe allowed regions by thelatest NO

ν

AandT2K neutrino results,as well asthe olderMINOSdatasample. Incomparison withFig.2, one sees that atmosphericparameters are mainly constrainedby long-baseline data,andthatnow allthe resultsarein agreement withmaximalatmosphericmixing.Ontheotherhand,Fig.1shows howthenewreactordata,clearlydominatedbyDayaBay,provide asignificantlyimproveddeterminationof

θ

13.Italsoillustratesthe

importantroleofreactorneutrinodatainmappingouttheallowed regionoftheatmosphericsquaredmasssplittingparameter.

In what follows we highlight the main features of our neu-trino oscillation global fit results, focusing upon the main open challengesofthethree-neutrinopicture:CPviolation,theneutrino massorderingandthe

θ

23octantproblem.

4.1. SensitivitytoCPviolation

Long-baseline neutrinooscillationdata play an importantrole indeterminingtheCPviolatingphase,

δ

.Inordertohighlightthis pointwepresentthe



χ

2_{-profilefortheCPphase,asdetermined}

from T2K,NO

ν

AandSuper-K atmosphericdata alone,aswell as bytheglobaloscillationdatasample,asshownintherightpanels inFig. 4.Note thatherethe



χ

2_{-profilehasbeenobtainedfrom}

Fig. 4. Left:90and99%C.L.(2d.o.f.)regionsfromT2K(bluelines)andNOνA(red) data,fromtheatmosphericSuper-Kresults(green)andfromtheglobalfitofallthe oscillationexperiments(colored regions).Thestarindicatesthebestfitpointfrom ourglobalanalysis,foundfornormalmassordering,whiletheblackdotindicates thelocalminimumfor invertedmass ordering.Right:



χ2_{-profileasafunction}

oftheCPphase

δ

fromT2K,NOνAandSuper-Katmospheric(withthesamecolor codeasintheleftpanel)andfromtheglobalfit(magenta).Inbothcases,theupper (lower)panelscorrespondtonormal(inverted)massordering.(Forinterpretationof thecolorsinthefigure(s),thereaderisreferredtothewebversionofthisarticle.)

This result shows how the current global sensitivity to the CP phase is dominated by the T2K experiment, with added re-jectionagainst

δ

=

π

/

2 obtained after combiningwith the other experiments. Indeed, we find that the combination with reactor dataiscrucialto enhancethe rejectionagainst

δ

=

π

/

2.As a re-sult, we find that in the global analysis,

δ

=

π

/

2 is disfavored with



χ

2

₌

₂₂

_.

_{9 (4.8}

_σ

_{)fornormalordering.Therejectionagainst}

δ

=

π

/

2 isfoundtobestrongerforinvertedmassspectrum,where itisexcluded with



χ

2

₌

₃₇

_.

_{3 (6.1}

_σ

_{), withrespecttothe}

mini-mum forthis ordering. As can also be seen fromthe figure, the currentpreferredvalueof

δ

dependson themassordering, lying closerto 3

π

/

2 for inverted ordering. The currentbest fit values fortheCPviolatingphasearelocatedat

δ

=

1

.

32

π

forNOandat

δ

=

1

.

56

π

forIO.

4.2.Neutrinomassordering

Concerningthe sensitivity to the neutrinomass ordering, our globalfitshowsforthefirsttimeahintinfavor ofnormalneutrino massordering,withinvertedorderingdisfavored with



χ

2

₌

₁₁

_.

₇

(3.4

σ

).InordertodisentangletheoriginofthepreferenceforNO in our global analysis, we display in Figs. 5 and 6 the allowed regionsfor

θ

23,

θ

13and

δ

forNOandIOfordifferentdataset

com-binations:long-baselinedataonly,long-baselineplusatmospheric, long-baseline plus reactors andthe combination of all data sets. Down-trianglesindicate thebestfit pointsobtainedinthe analy-sisoflong-baselinedata,squarescorrespondtothebestfitpoints derived fromthe combination oflong-baseline plus atmospheric, whileup-triangles arethebestfitpointforlong-baseline plus re-actordata.Thestar andblack dotfollowthe sameconvention as inFig.4.

The black lines in these figures delimit the allowed regions from the combination of all long-baseline data discussed above. Inprinciple,given thesmallimpact ofmattereffects inthe neu-trino propagation at such baselines, one would expect a limited sensitivity of the current long-baseline experiments to the neu-trinomassordering.Indeed,thisisconfirmedbyourindependent

Fig. 5. 90 and 99% C.L. (2 d.o.f.) allowed regions in the sin2

θ23–δ (left) and

sin2

θ13–δ(right)planesfromlong-baselinedataonly(blacklines),long-baseline

plusatmospheric (blue), long-baselineplus reactors(cyan) and from the global fit ofallexperiments(colored regions).Upper(lower)panelscorrespondto nor-mal(inverted)mass ordering.The best fit points areindicated byblack down-triangles(long-baselinedata),bluesquares(long-baselineplusatmospheric),cyan up-triangles(long-baselineplusreactors),aswellasstarsandblackdots,following thesameconventionasinFig.4.

Fig. 6. 90and99%C.L.(2d.o.f.)regionsfromthecombinationofdifferentneutrino datasamples.Theconventionusedtoindicatetheregionsandbestfitpointsisthe sameasinFig.5.

analysisofT2KandNO

ν

Adata,thatshowonlyaslightpreference fornormalmass orderingatthe levelof



χ

2

_∼

_{1.However, the}

combinedanalysisoflong-baselineandreactordata(seecyanlines inthefigures)resultsinanenhancedsensitivitytothemass order-ingwhich,inallcases,favors normaloverinvertedmassordering. Thishappensduetothemismatchbetweenthevaluesof

θ

13

pre-ferred by reactor and long-baseline experiments, which is larger fortheinvertedmassordering,asshowninFigs.5and6.Whilein normalordering the bestfit forlong-baseline experiments alone, sin2

θ

13

=

0

.

026, is relatively close to the global one, sin2

θ

13



0.022, mainlyconstrainedby reactors,thisis notthe casefor in-verted ordering,where long-baselinedata prefersin2

θ

13

=

0

.

031.

Asaresult,thecombinedanalysisofreactorandlong-baselinedata showsbetteragreementunderthenormalmassordering hypoth-esis. Forinstance,acombinedanalysisofthe latestNO

ν

A results withreactordataindicatesapreferencefornormalorderingwith



χ

2

₌

₃

_.

_{7.InthecaseofT2K,thecombinationwithreactordata}

resultsinastrongerpreferencefornormaloverinvertedmass or-dering, with



χ

2

₌

₅

_.

_{3. This enhanced sensitivity to the mass}

ordering is due to the tension that exists between the value of the atmosphericmass splittingpreferredby reactor, mainlyDaya Bay, andT2K.One findsthat Daya Bayprefersa highervalue for



m2

638 P.F. de Salas et al. / Physics Letters B 782 (2018) 633–640

islargerforinverted massordering.The combinedanalysisofall long-baselineandreactordatayieldsapreferencefornormalmass orderingwith



χ

2

₌

₇

_.

_5.

Bycombining thesedata samples withatmospheric data,one gets the final global results indicated by the colored regions in Figs. 5 and 6. In principle, one may expect the largest sensitiv-ityto theneutrino mass ordering to come from the observation of matter effects in the atmosphericneutrino flux. However, we find that the neutrino telescope experiments IceCube DeepCore and ANTARES are not yet very sensitive to the mass ordering. In fact, the difference betweennormal andinverted mass order-ingfromthecombinedanalysisofDeepCoreandANTARESisonly



χ

2

₌

₀

_.

_{4,obtainedmainlyfromIceCube DeepCoredata.Onthe}

other hand,themostrecent analysisofatmosphericdata sample of theSuper-K experiment showsan enhanced sensitivityto the mass ordering compared to previous ones. Indeed, Super-K data alone disfavors the inverted mass ordering with



χ

2

₌

₃

_.

_{5. Ifa}

prior onthe reactor mixingangleis imposed inthe atmospheric data analysis, the sensitivityrises up to



χ

2

₌

₄

_.

_{3 [62]. The}

ef-fect of addingthe atmosphericdata to theglobal analysisis not very noticeableinFigs. 5 and6,wherethe allowed regions with andwithoutatmosphericdataaresimilar. However,theimpactof atmosphericdataintheglobalsensitivitytothemassordering al-lowsone todisfavor inverted mass ordering at



χ

2

₌

₁₁

_.

_{7. This}

resultisveryrelevant,sincefromthecombinationofthedifferent typesof neutrinoexperimentswe can obtain forthefirst time a preferencefornormalneutrinomassorderingslightlyabove3

σ

. 4.3. The

θ

23octantproblem

Theroleoflong-baseline,atmosphericandreactorexperiments inselectingthe

θ

23-octantisillustratedinFigs.5and6.Theystress

the complementary role of the different oscillation datasamples onthepossiblediscriminationofthe

θ

23octant.Infact,asnoticed

in Ref. [80] andrecently in Ref. [81], an improved measurement ofthereactoranglehelpsresolvingtheatmosphericoctant.From thefigures,weseethattheanalysisoflong-baselinedataonly (in-dicated byblacklines) showsapreferenceforvaluesof

θ

23 close

to maximal mixingforthe two massorderings, withthe bestfit points indicated by adown-triangle.For bothmass orderings we find a preferred value of sin2

θ

23

=

0

.

508. The combination with

theatmosphericdatasets (illustratedby thebluelinesinthe fig-ures)provides a furtherconstraintonthe allowed regionfor

θ

23.

Moreover, the inclusion of atmospheric datain the analysis pro-ducesashiftofthe bestfitvalue of

θ

23 tolargervaluesforboth

massorderings(sin2

θ

23

=

0

.

54 forNOandsin2

θ

23

=

0

.

53 forIO),

although values of

θ

23 in the first octant are still allowed with



χ

2

_≥

₀

_.

₈

₍

₂

_.

₀

₎

_{forNO (IO).Thecombinationwithreactor}

exper-iments in the globalneutrino fit (colored regions in the figures) movesthebestfitvalue of

θ

23 tolargervaluesforbothmass

or-derings,leadingtosin2

θ

23



0

.

55 asthepreferredvalue.Moreover,

reactor dataalso modify the preferredvalues of

θ

13 and

δ

, from

the values fixed by the combination of long-baseline and atmo-sphericdata,asshowninFigs.5and6.Forbothmassorderings

δ

ispushedtowards3

π

/

2,whilethereactormixingangleisslightly shiftedtowardssmallervalues.Oneshouldstressthatreactordata, speciallyDayaBay andRENO,are crucialto thedetermination of the allowed region for

θ

13. Goingback to the octant preference,

wewouldliketoremarkthattheindicationsdescribed aboveare stillfarfromrobust.Indeed,valuesoftheatmosphericmixing an-gle below 45◦ are allowed at



χ

2

_≥

₁

_.

_{6 forthe case of normal}

ordering andat



χ

2

_≥

₃

_.

_{2 for inverted orderingwith respectto}

theminimuminthismassspectrum.

Despitetherecentprogressonthismatter,theoctant discrim-ination problem lies far beyond the current generation of

neu-Table 1

Neutrinooscillationparameterssummarydeterminedfromthisglobal analysis.Therangesforinvertedorderingrefertothelocalminimum forthisneutrinomassordering.

Parameter Best fit±1σ 2σrange 3σrange m2 21[10−5eV 2_] 7.55+₋00..2016 7.20–7.94 7.05–8.14 |m2 31| [10−3eV2](NO) 2.50±0.03 2.44–2.57 2.41–2.60 |m2 31| [10−3eV2](IO) 2.42+ 0.03 −0.04 2.34–2.47 2.31-2.51 sin2θ12/10−1 3.20₋+00..2016 2.89–3.59 2.73–3.79 θ12/◦ 34.5+₋11..20 32.5–36.8 31.5–38.0 sin2 θ23/10−1(NO) 5.47₋+00..2030 4.67–5.83 4.45–5.99 θ23/◦ 47.7+−11..27 43.1–49.8 41.8–50.7 sin2θ23/10−1(IO) 5.51₋+00..1830 4.91–5.84 4.53–5.98 θ23/◦ 47.9+₋11..07 44.5–48.9 42.3–50.7 sin2θ13/10−2(NO) 2.160₋+00..083069 2.03–2.34 1.96–2.41 θ13/◦ 8.45+₋00..1614 8.2–8.8 8.0–8.9 sin2 θ13/10−2(IO) 2.220₋+00..074076 2.07–2.36 1.99–2.44 θ13/◦ 8.53+₋00..1415 8.3–8.8 8.1–9.0 δ/π(NO) 1.32+₋00..2115 1.01–1.75 0.87–1.94 δ/◦ 238+₋3827 182–315 157–349 δ/π(IO) 1.56+₋00..1315 1.27–1.82 1.12–1.94 δ/◦ 281+23 −27 229–328 202–349

trino oscillation experiments,and will be a particularlystubborn problem in the years to come. On the positive side, however, it has been notedthat the taskof octantdiscrimination and prob-ing for leptonic CP violation in current andfuture long-baseline experiments can be facilitatedby prior model-specific theoretical knowledge ofthepredictedpatternofleptonicmixing. See,asan example,Figure1givenin [82] andtheassociateddiscussion.

5. Summaryanddiscussion

Wehavediscussedindetailthestatusofthemassordering,CP violationandoctantdiscrimination,analyzingtheinterplayamong the different neutrino oscillation data samples. The results ob-tainedinourglobalfitaresummarizedinTable1aswellasFigs.7 and8fornormalandinvertedmassordering.Somecommentsare inorder.

Firstwenotethattheimprovedprecisionon

θ

13followsmainly

fromtheDaya BayandRENO data.Thanks tothecombinationof T2K neutrino and antineutrino data, we have now an improved sensitivity to CP violation. Indeed, T2K is the first experiment showingasensitivityonitsown,excludingsomevaluesof

δ

before combiningwithreactordata.Inthisanalysis,we haveobtaineda strongpreferenceforvaluesoftheCPphaseintherange

[

π

,

2

π

]

, excludingvaluescloseto

π

/

2 atmorethan4

σ

.Concerningthe oc-tant of

θ

23,thisglobalanalysisprefersthesecond octantslightly,

inagreementwiththepreviousoneinRef. [1].Wehavefoundthat fornormalneutrinomassorderingtheupperatmosphericoctantis nowpreferredwith



χ

2

₌

₁

_.

_{6,whileforthecaseofinverted}

or-dering,valuesoftheatmosphericmixingangleintheloweroctant are allowed with



χ

2

_≥

₃

_.

_{2. More remarkably, our global}

anal-ysis favors for the first time the normalmass ordering over the invertedoneat3.4

σ

.Asdiscussedintheprevioussection,partof the sensitivityto themass orderingcomes fromthe mostrecent atmosphericanalysis ofSuper-K.Thisnewanalysisshowsa pref-erencefornormaloverinversemassorderingwith



χ

2

₌

₃

_.

_5.On

the other hand, a mismatchbetweenthe values of

θ

13 preferred

by long-baseline andreactor data(largerfor IO)alsogives a rel-evant contribution to theglobal sensitivityto themass ordering.

Fig. 7. Summaryofneutrinooscillationparameters,2018.Bluelinescorrespondto NOand magentalinestoIO.The



χ2_{-profilesfor invertedorderingareplotted}

withrespecttotheminimumforthisneutrinomassordering(dashed)aswellas withrespecttotheglobalminimum(solidlines).

This effect is also enhanced due to a tension between the pre-ferredvaluesoftheatmosphericmasssplittingbyT2Kandreactor experiments.

Inshort,wehaveseenhowtheprecision inthedetermination ofthebest-knownoscillationparameters hasimprovedthanks to therecentlong-baselineneutrinooscillationandreactordata.Also thesensitivitytomassordering,CPviolationandtheoctantofthe atmospheric angle has improved, although we are still quite far fromarobustmeasurement,especiallyoftheoctant.Thepresence ofnewphysicsbeyondtheStandardModelmayaffectsignificantly the results obtained within the current neutrino oscillation pic-ture. Forexample,nonstandard neutrinointeractions withmatter andnon-unitary neutrino mixing, expected in seesaw models of neutrino mass generation, may significantly reduce the sensitiv-ities. Conversely, however, such well-motivated beyond-standard scenarioscan alsobringinnewopportunitiesforcurrentand fu-turelong-baselineneutrinooscillationexperiments.

Noteadded

During the peer review of the present work, a new neutrino oscillationsglobalfitappearedinRef. [83].Althoughthereare dif-ferencesinthedatasamplesconsidered,aswellasintheapproach followed to incorporate IceCube and short-baseline reactor data, thereisageneralagreementbetweentheresultsofthetwo anal-yses.

Acknowledgements

The authors would like to thank Jason Koskinen of the Ice-Cube Collaboration, Juande Zornoza of the ANTARES Collabora-tion, Federico Sánchez of T2K and Prof. Soo-Bong Kim of RENO forvaluableinformationregardingtheirexperiments.Likewise,we are gratefulto Jordi Salvado andThomas Schwetzfor useful dis-cussions. Work supported by MINECO grants FPA2014-58183-P, FPA2017-85216-P,Multidark-CSD2009-00064,SEV-2014-0398,and

the PROMETEOII/2014/084 and GV2016-142 grants from

Gener-alitat Valenciana. MT is also supported a Ramón y Cajal con-tractRYC-2013-12438(MINECO).PFdSissupportedbytheSpanish grant FPU13/03729 (MECD). CAT is supported by the FPI fellow-shipBES-2015-073593 (MINECO).DVF isthankful forthesupport

Fig. 8. Globalfitsummary2018.Inthetwofour-panelfigures,theupperones cor-respondtonormalorderingandtheloweronestoinvertedmassordering.Globalfit regionscorrespondto90,95and99%C.L.(2d.o.f.).AsinFig.7,regionsforinverted orderingareplottedwithrespecttotheminimumforthisneutrinomassordering.

of FAPESP Grants No. 2014/19164-6 and 2017/01749-6, and also to FAEPEX Grant No. 2391/17 for partial support. DVF was also supported by theU.S. DepartmentofEnergy undercontracts DE-SC0013632andDE-SC0009973.

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