Takaaki Kajita (ICRR, U.of Tokyo)

• Production of atmospheric neutrinos• Some early history (Discovery of atmospheric

neutrinos, Atmospheric neutrino anomaly)• Discovery of neutrino oscillations• Studies of atmospheric neutrino oscillations• Sub-dominant oscillations –present and future-

III International Pontecorvo Neutrino Physics SchoolAlushta, Ukraine, Sep. 2007

IntroductionIntroduction

3

2

1

UeWe know that neutrinos have mass:

e

3

21

e

3

21

23=45±8 12=34±313 < 11

Small 13 and m122 << m23

2 OK to interpret the present data with 2 flavor oscillation framework: P( )=1-sin22ij ・ sin2(1.27mij

2 ・ L/E)

Atmospheric LBL Solar

KamLAND

Future experiments

Event statistics in atmospheric Event statistics in atmospheric neutrino experimentsneutrino experiments

TK and Y.Totsuka, RMP73, 85 (2001) Sorry: MINOS not included yet. More than 20,000 now.

Super-Kamiokande: history and planSuper-Kamiokande: history and plan

1996

97

98

99

2000

01

02

03

04

05

06

07

08

09

2010

11

accident

SK full reconstruction

SK-I SK-II SK-III

today

The following discussion: based on the SK-I+II (or SK-I) data

((mm22, sin, sin2222) )

SK-I+II atmospheric neutrino data SK-I+II atmospheric neutrino data CC e CC

SK-I: hep-ex/0501064 + SK-II 800 days

Osc.

No osc.

SK-I: 92 kton ・ yr SK-II: 49 kton ・ yr

Total: 141 kton ・yr

Estimating the oscillation parametersEstimating the oscillation parametersDown-going

Up-going

2sin1 2DownUp

Transition point (as a function of

energy) m2

Confirmation of non-oscillated flux

Accurate measurement possible due to small syst.

in up/down (2% or less)

2-flavor oscillation analysis 2-flavor oscillation analysis (SK-I + SK-II combined analysis)(SK-I + SK-II combined analysis)

FC1ringe-like

FCmulti-re-like

FC1ring-like

FCmulti-r-like

PCstop

PCthru

UPstop

Plep

Sub-

GeV

Mul

ti-Ge

V

CC e CC

38 event type andmomentum bins

x10 zenith bins

380 bins

Various detector related systematic errors are different between SK-I and SK-II. SK-I and SK-II data bins are not combined.

380 bins for SK-I + 380 bins for SK-II 760 bins in total

UP throughnon-showering

UP throughshowering

Each box has 10 zenith-angle bins

Poisson with systematic errors

Nobs : observed number of eventsNexp : expectation from MCi : systematic error termi: sigma of systematic error

Definition of Definition of 22

270

1

760

1 expexp

exp2

70

12i

2760

1

expexpexp

ln2)(2),(),(

ln2

2exp

!))(exp(

),(

i i

i

nn

nobsn

obsnobs

n

obsobs

obs

i

i

nnobs

Nnn

obs

NNNNN

NNLNNL

NNN

NNLnobs

Number of data bins

Number of syst error terms

)1())((70

1exp j

jjMC fCCforPNN

2 minimization at each parameter point (m2, sin22, …). Method (2 version): G.L.Fogli et al., PRD 66, 053010 (2002).

70 systematic error terms 70 systematic error terms ● (Free parameter) flux absolute normalization● Flux; (nu_mu + anti-nu_mu) / (nu_e + anti-nu_e) ratio ( E_nu < 5GeV )● Flux; (nu_mu + anti-nu_mu) / (nu_e + anti-nu_e) ratio ( E_nu > 5GeV )● Flux; anti-nu_e / nu_e ratio ( E_nu < 10GeV )● Flux; anti-nu_e / nu_e ratio ( E_nu > 10GeV )● Flux; anti-nu_mu / nu_mu ratio ( E_nu < 10GeV )● Flux; anti-nu_mu / nu_mu ratio ( E_nu > 10GeV )● Flux; up/down ratio● Flux; horizontal/vertical ratio● Flux; K/pi ratio● Flux; flight length of neutrinos● Flux; spectral index of primary cosmic ray above 100GeV● Flux; sample-by-sample relative normalization ( FC Multi-GeV )● Flux; sample-by-sample relative normalization ( PC + Up-stop mu )● Solar activity during SK1● Solar activity during SK-II

● MA in QE and single-● QE models (Fermi-gas vs. Oset's)● QE cross-section ● Single-meson cross-section ● DIS models (GRV vs. Bodek's model)● DIS cross-section ● Coherent- cross-section ● NC/CC ratio● nuclear effect in 16O● pion spectrum● CC cross-section

● Reduction for FC● Reduction for PC● Reduction for upward-going muon● FC/PC separation● Hadron simulation (contamination of NC in 1-ring -like)● Non- BG ( flasher for e-like )● Non- BG ( cosmic ray muon for mu-like )● Upward stopping/through-going mu separation● Ring separation● Particle identification for 1-ring samples● Particle identification for multi-ring samples● Energy calibration ● Energy cut for upward stopping muon● Up/down symmetry of energy calibration ● BG subtraction of up through ● BG subtraction of up stop ● Non-e contamination for multi-GeV 1-ring electron ● Non-e contamination for multi-GeV multi-ring electron ● Normalization of multi-GeV multi-ring electron● PC stop/through separation

Flux (16)

interaction (12)

Detector, reduction and reconstruction (21×2)(SK-I+SK-II, independent)

2 flavor analysis 2 flavor analysis

Best Fit: m2 = 2.5 x 10-3 eV2

sin2 2 = 1.002 = 839.7 / 755 dof (18%)

1.9 x 10-3 eV2 < m2 < 3.1 x 10-3 eV2

sin2 2 > 0.93 at 90% CL

1489 days (SK-1)+ 800 days (SK-II)

Preliminary

2 distributions

Allowed Parameter Space from atmospheric Allowed Parameter Space from atmospheric and Accelerator Long Baseline experiments and Accelerator Long Baseline experiments

Accuracy: m2: Atm LBL, sin22: still atm.

L/E analysis L/E analysis

Motivation: Really oscillation ?Motivation: Really oscillation ?Before 2004, what we knew was that neutrinos change flavor if they propagate long enough distances.

Other mechanisms were proposed to change the neutrino flavor. For example, they were neutrino decay or neutrino decoherence models.

-like multi-GeV

+ PC

These models explained the atmospheric neutrino data well.

decoherence

decay

oscillation

oscillation

decoherence decay

Further evidence for oscillations Strong constraint on oscillation parameters, especially m2

Should observe this dip!

SK collab. hep-ex/0404034

L/E analysisL/E analysis

P = (cos2sin2・ exp(– ))2

m2

LE

P = 1 – sin22 ・ (1 – exp(–))

21 L

E

L/E plot in 1998 SK evidence paper…L/E plot in 1998 SK evidence paper…

Due to the bad L/E resolution events, the dip was completely washed out. (Or neutrinos decay….)

Something must be improved….

Selection criteria Selection criteria

Events are not used, if:

★horizontally going events

★low energy events

Select events with high L/E resolution

((L/E) < 70%)

FC single-ring -like

Full oscillation 1/2 oscillation

(L/E)=70%

Similar cut for: FC multi-ring -like,

OD stopping PC, and

OD through-going PC

L/E distributionL/E distribution

MC (no osc.)

SK-I+II, FC+PC, prelim.

The oscillation dip is observed.

Mostly down-going

Mostly up-going

Osc.

MC (osc.)

(Preliminary)

Allowed oscillation parameters from the Allowed oscillation parameters from the SK-I+II L/E analysisSK-I+II L/E analysis

(preliminary)SK-I+II

2.0 x 10-3 eV2 < m2 < 2.8 x 10-3 eV2

sin2 2 > 0.93 at 90% CLConsistent with the zenith-angle analysis

Slightly unphysical region (2=0.5)

SK-I+II L/E analysis and non-oscillation SK-I+II L/E analysis and non-oscillation modelsmodels

(preliminary)SK-I+II

Osc.

Decay Decoh.

Oscillation gives the best fit to the data. 　Decay and decoherence models were disfavored by 4.8 and 5.3 , resp.

decoherencedecay

2(osc)=83.9/83dof

2(decay)=107.1/83dof

2(decoherence)=112.5/83dof

Seach for CC Seach for CC events events

Search for CC Search for CC events (SK-I) events (SK-I)CC events

hadrons

● Many hadrons ．．．． (But no big difference with other (NC) events ． )

BAD - likelihood analysis● Upward going only

GOOD Zenith angle

Only ～ 1.0 CC FC events/kton ・ yr

(BG (other events) ～ 130 ev./kton ・ yr)

hadrons

CC MC

Selection of Selection of events eventsPre-cuts: E(visible) >1,33GeV, most-energetic ring = e-like

E(visible)

Number of ring

candidates

Max. distance between primary

vertex and the decay-electron

vertex

Sphericity in the lab frame

Sphericity in the CM frame

MC

Atm. MC

data

Likelihood / neural-net distributionsLikelihood / neural-net distributions

Likelihood

Neural-net

Down-going (no ) Up-going

Zeni

th-a

ngle

Zenith angle dist. and fit results Zenith angle dist. and fit results Likelihood analysis NN analysis

coszenith

, e, & NC background

Data

scaled MC

coszenith

Num

ber o

f eve

nts

138±48(stat) +15 / -32(syst) 134±48(stat) +16 / -27(syst)

78±26(syst) 78±27 (syst)

Fitted # of eventsExpected # of events

Zero tau neutrino interaction is disfavored at 2.4.

Hep-ex/0607059

Constraints on non-standard Constraints on non-standard oscillationsoscillations

Oscillation to Oscillation to or or sterilesterile ? ? -like data show zenith-angle and energy dependent deficit of

events, while e-like data show no such effect.

sterile or

x

x

sterile

sterile

Propagation

Interaction

Difference in P() and

P(sterile) due to matter effect

Neutral current interaction

Z

Testing Testing vs. vs. sterilesterile

Up through muons

High E PC events

(Evis>5GeV)Multi-ring e-like,

with Evis >400MeV

Neutral current

Matter effect

sterile

sterile

sterile

Pure sterile excluded (PRL85,3999 (2000))

Limit on oscillations to Limit on oscillations to sterilesterile

(sin・ sterile+cos・ )

If pure , sin2=0

If pure sterile, sin2=1

SK collab. draft in preparation

Consistent with pure

SK-1 data

Mass Varying Neutrinos (MaVaN)?Mass Varying Neutrinos (MaVaN)?

Neutrino dark energy scenario Relic neutrinos with their masses varied by ambient neutrino density (A.Nelson et al. 2004) Possibly their masses also varied by matter density or electron density beyond the MSW effect

•m2→m2×(e/0)n (0=1.0mol/cm3) mass varying with electron density • 2 flavor Zenith angle analysis (assuming sin22=1.0)• SK-I dataset

Check the MaVaN model in atmospheric data

Neutrino flight lengthNeutrino flight length

About 350m above see level

Super-K detector: 1000m underground below the top of Mt. Ikenoyama

Down-going neutrinos fly in the air except for the last 1 to (a few) km.

Excluding a pure MaVaN scenarioExcluding a pure MaVaN scenarion vs m2 for MaVaN model 2-2

min (@m2=1.95x10-3)

2-

2 min

n

Tested MaVaN scenario is strongly disfavored

m

2

nBest fit : m2=1.95×10-3eV2

n=-0.03 2=172.2/178 dof

Standard oscillation

m2→m2×(e/0)n

survival probability for oscillation + decoherence

Constraining decoherence parameterConstraining decoherence parameter

Pure decoherence is excluded at about 5.

It might be possible that oscillation and decoherence co-exists.

ELmeP E

Lr

2cos.12sin

211)(

22 0

Constraining the decoherence parameter with SK L/E analysis

2min = 83.8/81 d.o.f

(0,m2,sin22)= (0 GeV,2.4x10-3eV2,1.0)0 <1.4x10-22GeV (90%C.L.)

0 (×10-

21GeV)

New constraint on decoherence New constraint on decoherence parameterparameter

SK collab. Draft in preparation

SK-I+II

More than factor 10 improvement over the previous upper limit (2×10-21GeV) (Lisi et al, PRL 85, 1166 (2000)

UNO

MEMPHYS Hyper-K

INO

Super-K

Present: Study of dominant oscillation channels

Future: Study of sub-dominant oscillations

e

3

21

Solar,

KamLAND

Atmospheric

Long baseline

12, m122

Known: Unknown:

13

Sign of m232

or

(CP)If 23 ≠/4, is it >/4 or </4 ?

23, |m23

2|

Future atmospheric exp’s

Present and future osc. experimentsPresent and future osc. experiments

1313

Search for non-zero Search for non-zero 13 13 in atmospheric in atmospheric neutrino experimentsneutrino experiments

ELmP e

2232

132

232 27.1sin2sinsin)(

(m122=0 and vacuum

oscillation assumed)

Since e is involved, the matter effect

must be taken into account.

Earth model

Simulation

Core Mantle

Search for non-zero Search for non-zero 13 13 in atmospheric in atmospheric neutrino experimentsneutrino experiments

Electron appearance in the multi-GeV upward going events.

ELmP e

2232

132

232 27.1sin2sinsin)(

s213=0.05 s213=0.00 null oscillation

Monte Carlo, SK 20yrs

Electron appearance

1+multi-ring, e-like, 2.5 - 5 GeV

cosE(GeV)

cos

)( eP

Matter effect

(m122=0 and vacuum

oscillation assumed)

Assuming 3 is the heaviest:

SK-I multi-GeV e-like dataSK-I multi-GeV e-like data

Multi-GeV, single-ring e-like Multi-GeV, multi-ring e-like(special)

No evidence for excess of upward-going e-like events No evidence for non-zero 13

1313 analysis from Super-K-I analysis from Super-K-I

Normal

Inverted

3

21

3

21

Hep-ex/0604011

22 distributions distributionsSK-1

If the shape of 2 continues to be like this, (factor ～ 2) more data might constrain the interesting 13 region at 90%CL.

CHOOZ limit

Future sensitivity to non-zero Future sensitivity to non-zero 1313

s2212=0.825 s223=0.40 ~ 0.60 s213=0.00~0.04 cp=45o

m212=8.3e-5 m223=+2.5e-3

Positive signal for nonzero 13 can be seen if 13 is near the CHOOZ limit and sin223 > 0.5

20yrs SK(450kton ・yr)

3

3 for 80yrs SK~4yrs HK(1.8Mton ・ yr)

sin223=0.600.550.50

0.450.40

ELmP e

2232

132

232 27.1sin2sinsin)(

Approximate CHOOZ limit

But probably after T2K/Nova…

Search for non-zero Search for non-zero 13 13 with with disappearance in atmospheric disappearance in atmospheric exp. exp.

But I was unable to fine the sensitivity plots for magnetized iron detectors. Sorry…

INO/2006/01Project report

Sign of Sign of mm22

Sign of Sign of mm22 If m23

2 is positive, resonance for

If m232 is negative, resonance for anti-

Very important to measure the

charge of leptons Magnetized

detector (With resolution)

13

Blue = normalRed = inverted

INO/2006/01Project report

13 (sin213) Significance (1.12Mtonyr)

7 deg (0.015) 1.6

9 (0.025) 2.5

11 (0.036) 3.5

13 (0.05) 4.5

Can we discriminate positive and Can we discriminate positive and negative negative mm22 in water Ch.? in water Ch.?

(total) and d/dy are different between

and anti-.

If m232 is positive,

resonance for If m23

2 is negative, resonance for anti-

+

CC e

CC e

Others

Multi-ring e-like

y=(E-E)/E

d/d

y

)(or

)(

e

e

P

P

CC e

CC e

Others

1-ring e-likeFr

actio

n

E(GeV)

SK atm. MC

Electron appearance for positive and Electron appearance for positive and negative negative mm22

Single-ring e-like Multi-ring e-like

Positive m2

Negative m2

null oscillation

cos cos

Relatively high anti-e fraction

Lower anti-e fraction.

Small (Large) effect for m2 <0 (>0).

22 difference (true – wrong hierarchy) difference (true – wrong hierarchy)m2: fixed, 23: free, 13: free

Exposure: 1.8Mtonyr = 80yr SK = 3.3yr HK

3

True=

3

True= 3

21 3

21

Water Ch. and magnetized muon detectors have similar sensitivity

Octant of Octant of 2323

Solar oscillation effect in Solar oscillation effect in atmospheric neutrinos atmospheric neutrinos

e

3

21

So far, m122 has been

neglected, because m12

2 (8.0×10-5) << m23

2 (2.5×10-3)

m232

m122

However,

Diameter of the Earth (L) = 12,800km,

Typical atmospheric neutrino energy (E) = 1GeV

(L/E)-1 = 8×10-5 (km/GeV)-1

Solar oscillation terms cannot be neglected !

●matter effect must be taken into account

●13 = 0 assumed.

s2212=0.825 m212=8.3×10-5

m223=2.5×10-3

sin213=0

Atmospheric neutrinos oscillation by (12, m12

2).

)( eP

Peres & Smirnov NPB 680 (2004) 479

Solar term effect to atmospheric Solar term effect to atmospheric

w/o matter effect with matter effect

Oscillation probability is different between s223=0.4 and 0.6 discrimination between 23 >/4 and </4 might be possible by studying low energy atmospheric e and events.

)()(oscnofluxoscflux

e

e

However, due to the cancellation between e and ex, the change in the e flux is

small.

Solar term effect to atmospheric Solar term effect to atmospheric

P2 : 2 transition prob. ex by m122

P(e e) = 1 – P2

P(e ) = P( e) = cos223 P2

e flux (osc) = f(e0) ・ (1-P2)+f(0) ・ cos223P2

Effect Effect of the of the solar termssolar terms to the to the sub-GeV sub-GeV /e /e ratioratio (zenith angle dependence) (zenith angle dependence)

Below 1.3GeV P , e < 400 MeV P , e > 400 MeV

m212 = 8.3 x 10-5 eV2

m223 = 2.5 x 10-3 eV2

sin2 212 = 0.82sin213=0

(e

) (3

flavo

r)

(e

) (2

flavo

r ful

l-mix

ing)

sin223 = 0.6

sin223 = 0.4sin223 = 0.5

2 flavor (sin2223=.96)

It could be possible to discriminate the octant of 23, if sin223 is significantly away from 0.5.

Solar terms off : best-fit : sin2 23 = 0.50

Solar terms on :

best-fit : sin2 23 = 0.52 (sin2 223 = 0.9984)

Constraint on sinConstraint on sin222323 with and without with and without the solar termsthe solar terms

w/o solar terms

w/ solar terms

(preliminary)

Still (almost) maximum mixing is most favored.

Future Future 2323 octant determination with the octant determination with the (12) and (13) terms(12) and (13) terms

s223=0.40 ~ 0.60 s213=0.00~0.04 cp=45o

Discrimination between 23>/4 and </4 is possible for all 13.

1.8Mtonyr = SK 80 yrs = 3.3 HK yrs

Discrimination between 23>/4 and </4 is marginally possible only for sin213 >0.04.

sin223 sin223

sin2

13

sin2223=0.96 sin2223=0.99

90%CL 90%CL

Test point

Fit result

2323 octant determination and syst. errors octant determination and syst. errors

m212 = 8.3 x 10-5 eV2

m223 = 2.5 x 10-3 eV2

sin2 212 = 0.82sin213=0

P , e < 400 MeV

sin223 = 0.6

sin223 = 0.4sin223 = 0.5

2 flavor (sin2223=.96)

(e

) (3

flavo

r)

(e

) (2

flavo

r ful

l-mix

ing)

true

0.8 Mtonyr = SK 20yr = HK 0.8yr

S.Nakayama, RCCN Int. Workshop on sub-dom. Atm. Osc. 2004

• Present atmospheric neutrino data are nicely explained by oscillations.

• L/E analysis has shown evidence for “oscillatory” signature.

• The data are consistent with tau neutrino appearance.

• So far, no evidence for sub-dominant oscillations.• Future atmospheric neutrino experiments

(magnetized detector, very large water Cherenkov) are likely to give unique contribution to this field (especially if sin2213 is close to the present limit). Detecting solar oscillation effect is also an interesting possibility.

Summary of atmospheric neutrino-2Summary of atmospheric neutrino-2

End