Neutrino oscillations Oleg Lychkovskiy ITEP2008. Plan Lecture I Lecture I Introduction Introduction Two-flavor oscillations Two-flavor oscillations Three-

Neutrino oscillationsNeutrino oscillations

Oleg LychkovskiyOleg Lychkovskiy

ITEPITEP20082008

PlanPlan

Lecture ILecture I IntroductionIntroduction Two-flavor oscillationsTwo-flavor oscillations Three-Three- flavor oscillationsflavor oscillations Matter effectMatter effect

Lecture IILecture II Overview of experiments and observations.

Introduction: acquaintance with neutrinosIntroduction: acquaintance with neutrinos

SM interactions:SM interactions:

Low energy (Low energy (E<<100E<<100 GeV) interactions: GeV) interactions:

ββ – decay: – decay:

(Z, A) (Z, A) (Z+1,A) + e (Z+1,A) + e-- + v + vee

vve e – capture:– capture:

vve e + p + p n + e n + e++

π – decay:π – decay: Deep inelasticDeep inelasticscattering:scattering:

… … and so onand so on

Typical energies: MeV-PeV >> m:Typical energies: MeV-PeV >> m:always always ultrarelativisticultrarelativistic!!

Two-flavor oscillationsTwo-flavor oscillations

Key feature: flavor eigenstates, in which neutrinos are created Key feature: flavor eigenstates, in which neutrinos are created

and detected, do not coincide with mass eigenstates!and detected, do not coincide with mass eigenstates!

mm11 and and mm22 - masses of - masses of vv11 and and vv22

Two-flavor oscillations, wave packet formalismTwo-flavor oscillations, wave packet formalism

(at given t only x=Vt ± a/2 are relevant)

Two-flavor oscillations, wave packet formalismTwo-flavor oscillations, wave packet formalism

Two-flavor oscillations, plane wave formalismTwo-flavor oscillations, plane wave formalism

Final oscillation probability does not depend on the specificFinal oscillation probability does not depend on the specificform of the wave packet form of the wave packet F(x)F(x)!!

Thus we may put Thus we may put F(x)=1, x=L F(x)=1, x=L and drop the integration over and drop the integration over xx! !

We get the same final result with less calculations:We get the same final result with less calculations:

Three-flavor mixingThree-flavor mixing

• 3 angles: 3 angles: θθ12 12 ,, θθ13 13 , , θθ2323

νe , νμ , ντ - flavor eigenstatesν1 , ν2 , ν3 - mass eigenstates with masses

mm11, m, m22, m, m33

• 2 CP-violating Majorana phases: 2 CP-violating Majorana phases: αα1 1 , α, α22 (physical only if (physical only if ν’s are Majorana fermions) are Majorana fermions)

• 1 CP-violating Dirac phase: 1 CP-violating Dirac phase: δδ

Three-flavor mixingThree-flavor mixing

Unknown: absolute values of masses, Unknown: absolute values of masses, θθ1313 , , δδ, , αα11 , , αα11 , ,

sign of sign of ΔΔmm223232 , octet of , octet of θθ2323

Three-flavor mixingThree-flavor mixing

e e

normal hierarchynormal hierarchy inverted hierarchyinverted hierarchy

mm2232 32

(Mass)(Mass)22

mm222121}}

mm2232 32

mm222121}}

oror

sinsin221313

sinsin221313

Three-flavor oscillationsThree-flavor oscillations

)1(Re2

)(

2/'''

2/3 3

'''

2

2

EmiL

jijlljillill

EmiL

i jjlljillill

ji

ji

eUUUU

eUUUUP

)1(Re2

)(

2/'''

2/3 3

'''

2

2

EmiL

jijlljillill

EmiL

i jjlljillill

ji

ji

eUUUU

eUUUUP

In particular, one can see that Majorana phases do not enter In particular, one can see that Majorana phases do not enter the oscillation probabilitythe oscillation probability

Three-flavor oscillations: Three-flavor oscillations: ννμμ ννl’l’

L L ΔΔmm222121 /4E<< π, /4E<< π, sinsin221313 neglectedneglected

Assume Assume

Then, neglecting and one obtains Then, neglecting and one obtains

Relevant for the majority Relevant for the majority of of accelerator experiments accelerator experiments

and for and for atmospheric neutrinosatmospheric neutrinos

Example: Example: K2KK2K (E=1GeV, L=250km) (E=1GeV, L=250km)

Three-flavor oscillations: Three-flavor oscillations: ννee ννee ,,

sinsin221313 neglectedneglected

Assume the detector registers only electron neutrinosAssume the detector registers only electron neutrinos

ji

jiejeiee EmLUUP 4/sinRe41)( 2222

ji

jiejeiee EmLUUP 4/sinRe41)( 2222

Neglecting Neglecting |U|Ue3e3||22 = |s = |s1313||22 < 0.05 < 0.05 , one obtains, one obtains

The same result one can get in a more illuminating wayThe same result one can get in a more illuminating way

Three-flavor oscillations: Three-flavor oscillations: ννee ννee ,,

sinsin221313 neglectedneglected

Two-flavor mixing effectively!Two-flavor mixing effectively! ==12 12 mm22mm22

2121

Relevant for Relevant for KamLANDKamLAND

Three-flavor oscillations: Three-flavor oscillations: ννee ννee , ,

small baselines, small baselines, 1313 in play in play

http://dayawane.ihep.ac.cn/docs/experiment.htmlhttp://dayawane.ihep.ac.cn/docs/experiment.html

If one does not neglect If one does not neglect ss13132 2 , ,

oscillationsoscillations with small with small amplitude ~ amplitude ~ ss1313

2 2 and small period and small period

LLoscosc = = 4E/4E/ΔΔmm223131 are superimposed are superimposed

on the on the ΔΔmm2121–related oscillations. –related oscillations.

If in addition

one comes to

Relevant for Relevant for Double Chooz, Daya BayDouble Chooz, Daya Bay

Example: Example: Double ChoozDouble Chooz (E=4 MeV, L=1 km) (E=4 MeV, L=1 km)

Matter (MSW) effect in neutrino Matter (MSW) effect in neutrino oscillationsoscillations

ννee-e-e interaction (through W-boson exchange):interaction (through W-boson exchange):

averaging of this Lagrangian over the matter electronsaveraging of this Lagrangian over the matter electronsgives an effective matter potential:gives an effective matter potential:

ννll-e-e interaction through Z-boson exchange does not depend on interaction through Z-boson exchange does not depend on flavor and thus does not influence oscillationsflavor and thus does not influence oscillations

Matter (MSW) effectMatter (MSW) effect

eeeF

e

iii

i

nGV

miH

2ˆ

:,, basis eigenstateflavor the in diagonal is term ninteractioMatter

)(ˆ

:,, basis eigenstate mass the in diagonal is nHamiltonia Vacuum3

1000

321

mmm

VHH

111

0

,,

ˆˆ

basis eigenstatematter

nHamiltonia total theofation Diagonaliz

for the details see lecture notes by Y.Nir, arXiv:0708.1872

Neutrinos in matter, two-flavor case, Neutrinos in matter, two-flavor case, nnee=const=const

Resonance:Resonance: Overwhelming Overwhelming

matter effect:matter effect:

Oscillations with the maximal amplitude!

No oscillations!

Relevance of matter effectRelevance of matter effect

Supernova coreSupernova core::ρ ~ 1012 g/cm3

E ~10 MeVV ~ 0.1 eV

ΔΔmm212122 /2E /2E ~0.5 · · 1010-11 -11 eVeV

ΔΔmm313122 /2E /2E ~ 10 10-10 -10 eVeV

Overwhelming Overwhelming

matter effect!matter effect!

Key parameter:

Sun core: ~ 100 g/cm3

V ~0.5 ·· 10-11eVE ~ (0.5-20) MeV

ΔΔmm212122 /2E /2E ~(0.2-8)1010-11-11 eVeV

relevantrelevant

ΔΔmm313122 /2E /2E ~ (0.6-24) 10 10-10-10 eVeV

irrelevantirrelevant

EarthEarth:: ρ =(1-10) g/cm3

V = (0.4-4) 10-13 eV

Reactors: E ~ few MeVΔΔmm2121

22 /2E /2E ~ (1-10)1010-11 -11 eVeV

ΔΔmm313122 /2E /2E ~ (3-30)10 (3-30)10-10-10 eVeV

Matter effect is irrelevantMatter effect is irrelevant

Accelerators, atmospheric Accelerators, atmospheric neutrinos:neutrinos: E ~ few GeV

ΔΔmm212122 /2E /2E ~ (0.1-1)1010-13-13 eVeV

ΔΔmm313122 /2E /2E ~ (0.3-3)10 (0.3-3)10-12-12 eVeV

Matter effect may be relevantMatter effect may be relevant

Remarks upon the previous lecture

Misprint: Misprint: tree-flavortree-flavor three-flavorthree-flavor MSW effect = Mikheyev-Smirnov-Wolfenstein MSW effect = Mikheyev-Smirnov-Wolfenstein

effecteffect ““octant”=… = 1/4 of the coordinate plane octant”=… = 1/4 of the coordinate plane

Lecture II.Neutrino oscillations.

Overview of experiments and observations.

Based on the review by O.Lychkovskiy, A.Mamonov, L.Okun, M.Rotaev,

to be published in UFN (УФН).

Three-flavor mixingThree-flavor mixing

• 3 angles: 3 angles: θθ12 12 ,, θθ13 13 , , θθ2323

νe , νμ , ντ - flavor eigenstatesν1 , ν2 , ν3 - mass eigenstates with masses

mm11, m, m22, m, m33

• 2 CP-violating Majorana phases: 2 CP-violating Majorana phases: αα1 1 , α, α22 (physical only if (physical only if ν’s are Majorana fermions) are Majorana fermions)

• 1 CP-violating Dirac phase: 1 CP-violating Dirac phase: δδ

SOURSESOURSEν/ν,

flavorrelevant relevant energyenergy

MSWMSWwhat what waswas (can (can be) extractedbe) extracted

SunSun νe 0.5-19 MeV0.5-19 MeVof major

importanceθθ12 12 m2

21

ReactorsReactors νe 1-6 MeV1-6 MeV irrelevantirrelevantm2

21, , θθ1212

θθ1313

Cosmic raysCosmic rays

(atmospheric(atmospheric

ν’s))

νμ, νμ, minor fraction

of other flavors

0.1 GeV -0.1 GeV -

10 TeV10 TeVrelevant

θθ23 23 m232

octant of octant of θθ23 23

AcceleratorsAcceleratorsνμ, νμ,

minor fraction of other flavors

0.5-50 GeV0.5-50 GeV relevantrelevantm2

32, , θθ2323

θθ1313 , , δ

hierarchy, octanthierarchy, octant

SupernovaSupernova all species 1-40 MeV1-40 MeVof major

importancehierarchy, hierarchy, θθ1313

Solar neutrinos

Neutrino oscillations in the matter of the Sun

We are interested in νe νe oscillations and we neglect θθ1313

ne=ne(r), r is the distance from the center of the Sun

Effectively two-flavor case with 1-2 mixing: θθ =θθ1212 , m2=m2

21

, m=m(r), θθ= = θθ(r)(r)

adiabaticity condition holds:

Neutrino oscillations in the matter of the Sun

At the Earth (r=R)

where averaging over the production point r0 is performed

Neutrino oscillations in the matter of the Sun

Probability weakly depends on m221 , but, nevertheless,

is sensitive to its sign!

Radiochemical experiments

Homestake:

ννee + + 3737ClCl 3737Ar + eAr + e--

3737ArAr 3737Cl + eCl + e++ + + ννee

Eth=0.86 MeV

t1/2=35 days

Result: ~ 4 times less neutrinos, than predicted by the SSM

SAGE, GALLEX/GNO:

ννee + + 7171GaGa 7171Ge + eGe + e--

7171GeGe 7171GaGa + e+ e++ + + ννee

Eth=0.23 MeV

t1/2=11.4 days

Result: ~ 2 times less neutrinos, than predicted by the SSM

Cherenkov detector experiments

Kamiokande ((1-3) kt of H2O) and Super-Kamiokande (50 kt of H2O):

ννll + e + e ννll + e + e

SNOSNO: (1 kt of D: (1 kt of D22O):O):

ννee + d + d p + p + e p + p + e

ννll + d + d p + n + p + n + ννll

ννll + e + e ννll + e + e

EEthth>5 >5 MeVMeV

The total flux was measured, and it coincided with the SSM prediction!The total flux was measured, and it coincided with the SSM prediction!

SSM verified SSM verified the the ννee deficite is due to oscillations! deficite is due to oscillations!

BorexinoMain goal: mono-energetic (E= 862 кэВ) 7Be neutrinos

Scintillation detector: low threshold (Eth= 0.5 MeV),

but no direction measured

!!!First real-time low-energy solar neutrinos:

47 ± 7stat ± 12syst 7Be ν / (day · 100 t)

(arXiv:0708.2251)

Reactor Reactor experiments

νe:• produced in β-decays in nuclear reactors: -decays in nuclear reactors: (A,Z) (A,Z) (A,Z+1) + e(A,Z+1) + e-- + + νe

• detected through νe + p n + n + ee++

• scintillation detectors usedscintillation detectors used• antineutrino energy: few MeVantineutrino energy: few MeV

Long-baseline, Long-baseline, L=O(100) L=O(100) km:km:KamLANDKamLAND

Short-baseline, Short-baseline, L=O(1) L=O(1) km:km:Chooz, Double Chooz,Chooz, Double Chooz,

Daya BayDaya Bay

oscillations

KamLANDKamLAND

• Sources of : 55 Japanese reactorsSources of : 55 Japanese reactors• Baselines: Baselines: L=(140 - 210) L=(140 - 210) kmkm• energies: energies: 1.71.7 MeV MeV < E < 9.3 < E < 9.3 MeVMeV• Probability of survival:Probability of survival:

Sensitive toSensitive to ΔΔmm2221 21 and and θθ1212 Status: runningStatus: running

KamLANDKamLAND!!!The latest result!!!The latest result::

Also 70Also 70±± 2727 geo-neutrinos geo-neutrinos registered!registered!

arXiv: 0801.4589v2 arXiv: 0801.4589v2

ChoozChooz

• Source: Chooz nuclear stationSource: Chooz nuclear station• Baseline: Baseline: L=1.05 L=1.05 kmkm• energies: energies: 33 MeV MeV < E < 9 < E < 9 MeVMeV• Probability of survival:Probability of survival:

The final result: The final result: sinsin222θ2θ13 13 < 0.2< 0.2 90%CL 90%CL Status: finishedStatus: finished

Future experiments:Future experiments: Double Chooz Double Chooz and Daya Bayand Daya Bay

Goal: measuring Goal: measuring θθ1313

Daya BayDaya Bay

sinsin2222θθ13 13 << 0.010.01

by 2013by 2013

Double ChoozDouble Chooz

sinsin2222θθ13 13 << 0.030.03

by 2012by 2012

Double Chooz sensitivity evolutionDouble Chooz sensitivity evolution arXiv:hep-ex/0701020v3

near detectors will be built near detectors will be built

the initial spectrum will be measured, the initial spectrum will be measured, not calculatednot calculated

Double Chooz and Daya Bay sensitivitiesDouble Chooz and Daya Bay sensitivities

Atmospheric neutrinosAtmospheric neutrinos• Source: cosmic rays, interacting with the atmosphere.Source: cosmic rays, interacting with the atmosphere.

Major fraction:Major fraction: Minor fraction: Minor fraction: Negligible fraction: Negligible fraction:

• Detection reactions: deep inelastic scatteringDetection reactions: deep inelastic scattering

νμ + N μ + hadrons

• Experiments:Experiments: Kamiokande, IMB, Super-Kamiokande, Amanda, Baikal, MACRO,Kamiokande, IMB, Super-Kamiokande, Amanda, Baikal, MACRO, Soudan, IceCube, …Soudan, IceCube, …

• “ “Baselines”: Baselines”: L=(0 - 13000) L=(0 - 13000) kmkm• Energies: Energies: 0.1 0.1 GeV GeV < E < 10 < E < 10 TeVTeV

Atmospheric neutrinosAtmospheric neutrinos

Original flux and energy spectrum Original flux and energy spectrum are poorly known are poorly known

large theoretical large theoretical flux uncertaintiesflux uncertainties

MSW-effect and 3-flavor oscillationsMSW-effect and 3-flavor oscillationsin play, extended sourcein play, extended source

no simple precise no simple precise expressions!expressions!

Approximate expressions:

Atmospheric neutrino fluxesAtmospheric neutrino fluxes

SK atmospheric neutrino resultsSK atmospheric neutrino results

Phys.Rev. D71 (2005) 112005Phys.Rev. D71 (2005) 112005, , arXiv:hep-ex/0501064v2

sinsin2222θθ2323 > 0.92 > 0.92

1.5 1.5 · 1010-3-3 < < m232 < 3.4 < 3.4 · 10 10-3-3 eVeV22

90% 90% CLCL

Evidence for appearance!Evidence for appearance!Phys.Rev.Lett.97:171801,2006Phys.Rev.Lett.97:171801,2006,,hep-ex/0607059hep-ex/0607059

Prospects for resolving Prospects for resolving hierarchy ambiguityhierarchy ambiguityarXiv:0707.1218arXiv:0707.1218

Accelerator neutrino experiments

• νμ and νμ are produced in meson decays • energies: few GeVenergies: few GeV• baselines: hundreds of kilometersbaselines: hundreds of kilometers

μ

oscillations

Main goals: appearance observations: search for e or τ

measuring 13

precise measurement of m223 , 23

mass hierarchy CP

Accelerator neutrino experiments К2К

MINOS OPERA

MiniBooNEТ2К

NOVA

LSND

e

m232, sin2223

sterile

13 CP(?)

For К2К, MINOS (?) and OPERA (?)

L L ΔΔmm222121 /4E<< π, /4E<< π, 1313=0=0

approximation is valid

T2К, NOvA and, probably, OPERA and MINOS, will go beyond this approximation!

Next several slides are from the talk by Yury Kudenko at NPD RAS Session

ITEP, 30 November 2007

Accelerator neutrino experiments

L/E 200

L=250 km <E> 1.3 GeV

98.2%e 1.3%

First LBL experiment К2К1999-2005

~1 event/2 days at SK

Predictions of flux and interactions at Far Detector by Far/Near ratio

Signal of oscillation at K2K Reduction of events Distortion of energy spectrum

disappearance

Expected: 158.1 + 9.2 – 8.6Observed: 112

- # Events

Expected shape (no oscillation)

Best fit

Best fit valuessin22 = 1.00m2 [eV2] = (2.80 0.36)10-

3

Kolmogorov-Smirnov testBest fit probability = 37%

Null oscillation probability (shape + # events) = 0.0015% (4.3)

K2K final result

- Shape distortion

PRD74:072003,2006

+

Near Det: 980 tons

Far Det: 5400 tons

735 km

Beam: NuMI beam, 120 GeV Protons - beam

Detectors: ND, FD

Far Det: 5.4 kton magnetized Fe/Sci Tracker/Calorimeter at Soudan, MN (L=735 km)

Near Det: 980 ton version of FD, at FNAL (L 1 km)

Precise study of “atmospheric” neutrino oscillations, using the NUMI beam and two detectors

MINOS

New MINOS result 2.50 POT analyzed ≈ 2x statistics of 2006 result Improved analysis

Comparison of new and old MINOS results

J.Thomas, talk at Lepton-Photon2007

# expected (no osc.) 73830# observed 563

m223 =(2.38 +0.20 -0.16) x 10-3

sin2223=1.00 -0.08

m223 and 23: SK/K2K/MINOS

|m223|| m2

13|= (2.4 0.2)x10-3 eV2 23 ~ 45o

After 5 years running: expected accuracy of m232 and sin2223 10%

chance for first indication of non-zero 13

MINOS: projected sensitivityM.Ishitsuka, talk at NNN07

OPERA

High energy, long baseline beam( E 17 GeV L ~ 730 km )

direct search

pure beam: 2% anti <1% e

P( ) = cos413sin223sin2[1.27m223L(km)/E(GeV) ]

E/L ~ 2.310-2 10m223 (atm)

Pb

Emulsion layers

1 mm

kink

after 5 years data taking:~22000 interactions~120 interactions~12 reconstructed<1 background event

Target mass ~1300t

OPERA: sensitivity

full mixing, 5 years run 4.5 x1019pot/y

M.Spinetti, talk at NNN07

New MINOS

Second generation LBL experiments

T2KNOVA

Off Axis Neutrino Beams

• Increases flux on oscillation maximum• Reduces high-energy tail and NC backgrounds• Reduces e contamination from K and decay

T2K (Tokai to Kamioka)

~1GeV beam (100 of K2K)

JPARC facility

on-axisoff-axis beam

JPARC MINOS Opera K2KE(GeV) 50 120 400 12Int(1012 ppp) 330 40 24 6 Rate (Hz) 0.29 0.53 0.17 0.45Power (MW) 0.77 0.41 0.5 0.0052

Statistics at SK OAB 2.5 deg, 1 yr = 1021 POT, 22.5 kt~ 2200 tot ~ 1600 charged current e < 0.5% at peak

OA3°

TargetHornsDecay Pipe

SuperKOA2°

OA2.5°

T2K off-axis beam

0 deg

0o

Principle Goals of T2K

Background uncertainty 10%CP = 0 CP = /2CP = - /2 CP =

- - Search for e appearance 13 sensitivity 1o (90% c.l.)

-Measurement m223

with accuracy of 1%(sin2223) 0.01 (m2

23) < 110-4 eV2

m2=2.5x10-3

CHOOZ limit

T2K sensitivity to 13

ambiguities: CP - 13 sign m223 23

NOA

Mass hierarchy can be resolved if 13 near to present limitusing both anti- beams andsin2213 from T2K + reactor experiments

matter effects increase (decrease) oscillations for normal (inverted) hierarchy for

P( e) depends on

sin2213 sign m223 CP

13 sensitivities vs time

A.Blondel et al.,hep-ph/0606111

Short baseline reactor experiments Double-Chooz and Daya Bay 13 ( insensitive to CP)

Daya Bay goal

Summary for accelerator experiments

K2K confirmation of atmospheric neutrino oscillations discovered by SK

MINOS confirmed the SK и K2K results high precision measurements of oscillation parameters

MiniBooNe rules out (98% cl) the LSND result as e

oscilations with m2 ~ 1 eV2 new anomaly appears run with anti- beam OPERA data taking begun in 2007

T2K-I neutrino beam in 2009

Main goal for next 5 years: 13

Neutrino production in SNNeutrino production in SN

Matter effect in SupernovaMatter effect in Supernova Adiabaticity almost everywhere, resonant layers are possible Adiabaticity almost everywhere, resonant layers are possible

exeptionsexeptions Three flavors in play, two different resonansesThree flavors in play, two different resonanses

H-H-резонанс: резонанс:

L-L-резонанс:резонанс:

13

231 2cos

2)(2

E

mrnG HeF

12

221 2cos

2)(2

E

mrnG LeF

km 10)158( km 10)53( 44 LH rr

Adiabaticity conditionsAdiabaticity conditions

Adiabaticity ofAdiabaticity of H-resonanceH-resonance depends ondepends on θθ1313 !!

L- resonance is always adiabatical!L- resonance is always adiabatical!

12 ln2tan2sin

dr

nd

E

m e

In resonance layer the adiabaticity parameter reads In resonance layer the adiabaticity parameter reads

1)10(105.2 3/24 EL МэВ/

3/23/4

13

132

3 )10()2(cos

2sin10

EH МэВ/

Level crossing scheme for SNLevel crossing scheme for SN

Mass hierarchy andMass hierarchy and θθ1313

NH=Normal Hierarchy, IH=Inverted HierarchyNH=Normal Hierarchy, IH=Inverted Hierarchy

LL==LLarge arge θθ13 13 : : θθ13 13 >0.03>0.03

SS==SSmall mall θθ13 13 : : θθ13 13 << 0.0030.003

NH, NH, LL IH, IH, LL NH and IH, NH and IH, SS

00 11 11

11 00 11HP

HP

Takahashi, Sato,Takahashi, Sato,hep-ph/0205070hep-ph/0205070R=10 kpcR=10 kpc

Future SN neutrino signal in SK

θθ1313 measurment with SNmeasurment with SNIfIf

and the hierarchy isand the hierarchy isinverted, thaninverted, than

θθ1313 is measurable!is measurable!

015.0003.0 13 )106.0( 13

oo

Takahashi, Sato,Takahashi, Sato, hep-ph/0205070hep-ph/0205070

Conclusions

Present knowledge: central value 2 interval m2

12 (10-5 eV2) 7.6 7.1 - 8.3 m2

31 (10-3eV2) 2.4 2.0 - 2.8 sin212 0.32 0.26 - 0.40sin223 0.50 0.34 - 0.67sin213 0.0 <0.05

5-year goals: • to increase the sensitivity for m2

12 , m231 , sin212 , sin223 up to (1-10)%

• sin213 sensitivity at the level 0.003

• mass hierarchy, (?)