Takaaki Kajita, ICRR, Univ. of Tokyo

NuFact04, Osaka, July 2004

Outline

• Atmospheric neutrino beam• Atmospheric neutrinos: Present

L/E analysis• Atmospheric neutrinos: Future

sub-dominant oscillations ?• Summary

Only 2 and 3 flavor neutrino oscillations

Atmospheric neutrinos Cosmic Ray

π, K

νµe

νµ νe

Atmosphere μ

Neutrinos from the other side of the Earth.

νµ

νe

Atmospheric neutrino beam

Zenith angle:

10-1

1

10

10 2

10 3

Flu

x×E

ν2(m

-2se

c-1

sr-1

Ge

V)

Honda fluxBartol fluxFluka flux

(a)

0.60.70.80.9

11.11.21.31.4

10-1

1 10 102

103

E (GeV)

Flu

x r

atio

Bartol/HondaFluka /Honda

(b)

10-1

1

10

Flu

x×E

ν2(m

-2s

Honda fluxBartol fluxFluka flux

0.60.70.80.9

11.11.21.31.4

10-1

1 10 102

103

E (GeV)

Flu

x r

atio

Bartol/HondaFluka /Honda

(b)

Flux

×E

ν2

Eν(GeV)

Measured cosmic ray proton flux

νµ

νe

Total νµ+νµ flux

Event classificationFully Contained (FC) (Eν ~1GeV)

Partially Contained (PC) (Eν ~10GeV)

Through-going µ(Eν ~100GeV)

Stopping µ (Eν ~10GeV)

0

200

400

600

800

1000FC νe

FC νµ

PC

020406080

100120140160

10-1

1 10 102

103

104

Eν (GeV)

Eve

nts

/ 100

0 da

ys

Upward stopping µUpward through-going

Super-Kamiokande(50,000ton water

Ch. Detector)

Soudan-2 (1kton tracking detector)

MACRO (large muon detector)

76m

12m

9.3m

Super-K atmospheric neutrino data

0

100

200

300

-1 -0.5 0 0.5 1

Num

ber

of E

vent

s Sub-GeV e-likeP < 400 MeV/c

0

100

200

300

-1 -0.5 0 0.5 1

Sub-GeV µ-likeP < 400 MeV/c

0

100

200

300

-1 -0.5 0 0.5 1

Num

ber

of E

vent

s Sub-GeV e-likeP > 400 MeV/c

0

100

200

300

400

-1 -0.5 0 0.5 1

Sub-GeV µ-likeP > 400 MeV/c

0

50

100

150

-1 -0.5 0 0.5 1cosθ

Num

ber

of E

vent

s Multi-GeV e-like

0

50

100

150

-1 -0.5 0 0.5 1cosθ

Multi-GeV µ-like

0

20

40

60

-1 -0.5 0 0.5 1

multi-ringSub-GeV µ-like

0

25

50

75

100

-1 -0.8 -0.6 -0.4 -0.2 0

Upward stopping µ

0

50

100

-1 -0.5 0 0.5 1

multi-ringMulti-GeV µ-like

0

100

200

300

400

-1 -0.8 -0.6 -0.4 -0.2 0cosθ

Upward through-going µ

0

50

100

150

200

-1 -0.5 0 0.5 1cosθ

PC

1489day FC+PC data + 1646day

upward going muon data

CC νe CC νµ

e μ

120

100

80

60

40

20 0

� 1 � 0.8 � 0.6 � 0.4 � 0.2 0-|cos θ|

120

100

80

60

40

20 0

� 1 � 0.8 � 0.6 � 0.4 � 0.2 0cos θ

Num

ber o

f eve

nts

/ bin

Num

ber o

f eve

nts

/ bin

UGS + ID

IU

0

1

2

3

4

5

6

7

8

-1 -0.8 -0.6 -0.4 -0.2 0cos Θ

µ flu

x (10

-13 cm

-2 s-1 sr-1 )

Data

Bartol flux (GRV94)

∆m2=0.0025eV2

or

MACRO

OscillationΔm2 =2.5×10-3

Upward horizontal

0

0.2

0.4

0.6

0.8

1

1.2

1.5 2 2.5 3 3.5 4

L /E

Multiple scattering

Eµ

Eν

PLB 566 (2003) 35

10-4

10-3

10-2

10-1

0 0.2 0.4 0.6 0.8 1sin22θ

∆m2 (

eV2 )

Neutrino oscillation parameters

Soudan-2

MACRO

Super-K

⎪⎩

⎪⎨⎧

>

×<∆< −

92.02sin)(104.35.1

232

23223

θeVm

νµ ντ

90%CL

0

0.2

0.4

0.6

0.8

1

1 10 102

103

104

L/E (km/GeV)

Pro

b.(ν µ

ν µ)

oscillation

decoherencedecay

Further evidence for oscillationsStrong constraint on oscillation parameters, especially ∆m2

0

50

100

150

200

250

300

350

-1 -0.5 0 0.5 1

cosΘ

Num

ber

of E

vent

s

µ-like multi-GeV+ PC

Should observe this dip!

New !

SK collab. hep-ex/0404034

Selection criteria

Following events are not used:

★horizontally going events

★low energy events

Select events with high L/E resolution

(∆(L/E) < 70%)

0

1

2

3

4

5

6

7

8

9

10

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Selected Selected

Zenith angle (cosθ)

Eν

(GeV

)FC single-ring µ-like

Full oscillation 1/2 oscillation

∆(L/E)=70%

Similar cut for: FC multi-ring µ-like,

OD stopping PC, and

OD through-going PC

2121 FC µ-like and

605 PC

1

10

10 2

10 3

1 10 102

103

104

L/E (km/GeV)

Num

ber

of events

L/E distribution

MC (no osc.)

1489 days FC+PC (Super-K)

Evidence for oscillatory signature

Mostly down-going

Mostly up-going

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

1 10 102

103

104

L/E (km/GeV)D

ata/

Pre

dic

tio

n (

nu

ll o

scill

atio

n)

Osc.

Decay Decoh.

Decay and decoherence disfavored at 3.4 and 3.8σ level, respectively.

10-4

10-3

10-2

10-1

0 0.2 0.4 0.6 0.8 1sin22θ

∆m2 (

eV2 )

Allowed neutrino oscillation parameters

10-3

10-2

0.7 0.8 0.9 1

sin22θ

∆m2 (

eV2 )

68% C.L.90% C.L.99% C.L.

χ2min=37.9/40 d.o.f

@ ∆m2=2.4x10-3,sin22θ=1.00(sin22θ=1.02, χ2min=37.8/40 d.o.f)

1.9x10-3 < ∆m232 < 3.0x10-3 eV2

0.90 < sin22θ23 (90% C.L.)

Stronger constraint on ∆m2

Consistent with that of the standard zenith angle analysis

SK L/E analysis

90% CL

SK Zenith angle analysis

K2K

Soudan2

MACRO

Kam.

Search for non-zero θ13

Electron appearance in the 5 – 10GeV upward going events.

⎟⎟⎠

⎞⎜⎜⎝

⎛ ∆⋅⋅=→

ELmP e

2232

132

232 27.1sinsinsin)( θθνν µ

MM-e 2.5 - 5.0 GeV0

50

100

150

200

250

300

350

400

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

s213=0.05s213=0.00null oscillation

MC, SK 20yrs

Electron appearance

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

cosΘ

0

0.1

0.2

0.3

0.4

0.5

-1

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

1 10Eν (GeV)

co

sΘ

ν

∆m2=0.002eV2, sin2θ23=0.5, sin2θ13=0.05

P(νe → νµ)

Eν(GeV)

cosΘ

)( eP ννµ →

Matter effect

(∆m122=0 assumed)

Super-K e-like data0

100

0

200

0

50

100

Nu

mb

er o

f ev

ents Multi-G e-like

0

50

100

150Multi-G µ-like

50

100

Multi-R e-like

50

100

150Multi-R µ-like

0

50

Nu

mb

e

0

50

0

50

100

-1 -0.5 0 0.5 1

cosθ

Multi-R e-like

0

50

100

150

-1

0

50

Nu

mb

e0

50

0

50

100

-1 -0.5 0 0.5 1

cosθ

Multi-R e-like

0

50

100

150

-1 -0.5 0 0.5 1

cosθ

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

No evidence for excess of upward-going e-like events

3 flavor analysis from Super-K

0

0.1

0.2

0.3

0.4

0.5

0 0 2 0 4 0 6 0 8 1

sin2

θ 13

90% C.L.99% C.L.

0

0.1

0.2

0.3

0.4

0.5

0 0.2 0.4 0.6 0.8 1sin2θ23

sin2 θ 1

3

90% C.L.99% C.L.

0 0.1 0.2 0.3 0.4 0.510-4

10-3

10-2

10-1

sin2 θ13

∆m

2 (eV

2)

SK 90% C.L.SK 99% C.L.CHOOZ 90% CL excludePALO VERDE 90% CL exclude

0 0 1 0 2 0 3 0 4 0 510-4

10-3

10-2

10-1

∆m

2 (eV

2)

SK 90% C.L.SK 99% C.L.CHOOZ 90% CL excludePALO VERDE 90% CL exclude

Normal

Inverted

ν3

ν2ν1

ν3

ν2ν1

prelim.

Present: Study of dominant oscillation channel (νµ ντ)

Future: Study of sub-dominant oscillations

νm

ass

⎩⎨⎧∆

23

2)13(23

θm

⎩⎨⎧ ⋅⋅⋅⋅⋅∆

12

212 (small)

θm

⎩⎨⎧

⋅⋅⋅⋅⋅∆

(small)13

2)23(13

θm

ν3

ν2

ν1

νe νµ ντNormal mass hierarchy is assumed.

★θ13?

★Mass hierarchy?

★Solar oscillation effects?

Possible future atmospheric ν detectors

Magnetized large tracking detector

Hyper-K (1Mton)

Very large water Cherenkov detector

MONOLITH,

INO (India-based Neutrino Observatory, …

Mton class detector at Frejus

UNO

0

5

10

15

20

25

30

35

40

0 0.02 0.04 0.06 0.08sin2θ13

∆χ2 (s

in2 θ 13

- (

no

θ13

))

0

5

10

15

20

25

30

35

40

0 0.02 0.04 0.06 0.08sin2θ13

∆χ2 (s

in2 θ 13

- (

no

θ13

))

0

5

10

15

20

25

30

35

40

0 0.02 0.04 0.06 0.08sin2θ13

∆χ2 (s

in2 θ 13

- (

no

θ13

))

Water Cherenkov detector 450 kton・yr (SK 20 years)

3σ 3σ 3σ

Importance of s2θ23>0.5; S.Pascoli et al., hep-ph/0305152

TK noon2004

(∆χ2 ∝～ exposure) ～ Present bound on sin2θ13

MM-e 2.5 - 5.0 GeV0

50

100

150

200

250

300

350

400

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Multi-GeVelectron appearance

Sensitivity to non-zero θ13

SK 20yr MC

How can we discriminate positive and negative ∆m2 ?Real ∆m23

2 = positiveassumed

(No resonance for anti-neutrinos)

Real ∆m232 = negative

assumed

(No resonance for neutrinos)

0

0.1

0.2

0.3

0.4

0.5

-1

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

1 10Eν (GeV)

cosΘ

ν

∆m2=0.003eV2, sin2θ23=0.5, sin2θ13=0.026

P(νe → νµ)

Eν(GeV)

cosΘ

P(νµ νe)

0

0.1

0.2

0.3

0.4

0.5

-1

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

1 10Eν (GeV)

cosΘ

ν

∆m2=0.003eV2, sin2θ23=0.5, sin2θ13=0.026

P(νe → νµ)

Eν(GeV)

cosΘ

P(νµ νe)

Sign of ∆m23(13)2 ?

ν3

ν2ν1 ν3

ν2ν1

Measurement of sign of ∆m2

in large magnetized detectors

10-4

10-3

10-2

10-2

10-1

1sin2(2Θ13)

∆m

2 (

eV

2)

CHOOZexcluded

SK allowed

MONOLITH 200 ktyMONOLITH 400 kty

Determination of sign of Δm2 at 90%CL.

Δm2=2.5×10-3

sin2θ =0.0213

NPB (proc suppl) 91 (2001) 147, hep-ex/0106252

Measurement of sign of ∆m2

in water Cherenkov detectors ?

0

5

10

15

20

25

30

35

40

0 0.02 0.04 0.06 0.08sin2θ13

∆χ2 (i

nve

rted

-no

rmal

)

0

5

10

15

20

25

30

35

40

0 0.02 0.04 0.06 0.08sin2θ13

∆χ2 (i

nve

rted

-no

rmal

)

0

5

10

15

20

25

30

35

40

0 0.02 0.04 0.06 0.08sin2θ13

∆χ2 (i

nve

rted

-no

rmal

)

3σ 3σ 3σ

∆m2: fixed, θ23: free, θ13: free, positive ∆m2

Exposure: 1.8Mtonyr (SK 80yr or HK ～3.3 yr)

Use differences in σ and dσ/dy

TK NOON2004

Solar oscillation effectsSolar neutrino oscillation: LMA (∆m12

2 = 7×10-5eV2)

1

1.05

1.1

1.15

1.2

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1cos(θe)

No

sc

e /N

0 e

∆m2 21 = 7.3E-05 eV 2

sin2(Θ23)=0.35

sin2(Θ23)=0.4

sin2(Θ23)=0.45

sin2(Θ23)=0.5

sin2(Θ23)=0.55

sin2(Θ23)=0.6

Expected number of sub-GeV e-like events in SK.

Peres, Smirnov NPB 680 (2004) 479

The number of e-like events changes as a function of sin2θ23 (NOT sin22θ23).

Discrimination of >45 and <45 θ23 might be possible. (However, the effect is very small for s22θ23=1.00.)

P.LipariNOON2004

10

1

• Atmospheric neutrinos have been playing major role in the neutrino oscillation studies.

• The present data are nicely explained by νµ ντoscillations with;

∆m2=1.9 – 3.0 × 10-3 eV2

sin22θ > 0.90 (SK L/E analysis)• Recent L/E analysis has shown evidence for “oscillatory”

signature.• Future atmospheric neutrino experiments is likely to

continue to contribute to the neutrino oscillation physics (θ13, sign of ∆m23

2 ….) (If (a) much larger detector, (b) relatively large θ13.)

End

0

20

40

60

80

100

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2OD charge / expectation from OD track length

Num

ber

of e

vent

s

Specials in L/E analysis1.5m from top & bottom

1m from barrel

22.5kt→26.4kt

Expand fiducial volume

More statistics for high energy muons

Classify PC events using OD charge

I. OD stoppingII. OD through going

Different L/E resolution

FC single-ring, multi-ring µ-like

PCobserved charge / expectation from through-going

OD stopping

OD through-going

OD through-going MC

OD stopping MC

Energy and angular resolution of neutrinos

0

10

20

30

40

50

60

70

80

90

10-1

1 10

FC single-ring µ-like

FC multi-ring µ-like

PC OD stopping

PC OD through-going

Observed energy (GeV/c)

Ene

rgy

reso

lutio

n (%

)

20

40

60

80

100

120

10-1

1 10

FC single-ring µ-like

FC multi-ring µ-like

PC OD stopping

PC OD through-going

Observed energy (GeV/c)A

ngul

ar r

esol

utio

n (d

egre

e)

L/E cuts

0123456789

10

-1 -0.5 0 0.5 1

FC single-ring

Selected Selected

(a)

0123456789

10

-1 -0.5 0 0.5 1

FC multi-ring

Selected Selected

(b)

0123456789

10

-1 -0.5 0 0.5 1

PC OD stopping

Selected Selected

(c)

Reconstructed zenith angle (cosΘ)

Rec

onst

ruct

ed E

ν (G

eV)

0123456789

10

-1 -0.5 0 0.5 1

PC OD through-going

Selected Selected

(d)

µ µ

Full osc.

Half osc.

Sensitivity to other models (determination of L/E resolution cut)

70% 80%

80%70%

ν decay ν decay

ν decoherence ν decoherence

ν decay

ν decoherence

L/E resolution cut at 70%

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1 10 102

103

104 0

0.2

0.4

0.6

0.8

1

1.2

1.4

1 10 102

103

104

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1 10 102

103

104

L/E (GeV/km)

S

urvi

val p

roba

bilit

y

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1 10 102

103

104

L/E (GeV/km)

0

2

4

6

8

10

12

14

16

18

20

50 60 70 80 90 100

L/E resolution cut (%)∆χ

2

Event summary of L/E analysis

Fractions of FC and PC samples in L/E distribution

1619 2105.8 (98.3%)

502 813.0 (94.2%)

114 137.0 (95.4%)

491 670.4 (99.1%)

single-ring

multi-ring

stopping

through-going

FC

PC

Data MC CC νµ

1

10

10 2

10 3

1 10 102

103

104

FC + PCFC single + multi-ring

L/E (km/GeV)

Nu

mb

er o

f ev

ents

Check of the observed dip in L/E distribution (1)

Other L/E resolution cuts

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

1 10 102

103

104

L/E (km/GeV)

Dat

a/P

red

icti

on

(n

ull

osc

illat

ion

)

60% cut

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

1 10 102

103

104

L/E (km/GeV)

Dat

a/P

red

icti

on

(n

ull

osc

illat

ion

)

80% cut

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

1 10 102

103

104

L/E (km/GeV)

Dat

a/P

red

icti

on

(n

ull

osc

illat

ion

)

90% cut

Check of the observed dip in L/E distribution (2)

FC e-like

(Flat L/E distribution is expected.)

0

0.5

1

1.5

2

2.5

3

1 10 102

103

104

L/E (km/GeV)

Dat

a/P

red

icti

on

(n

ull

osc

illat

ion

)

0

50

100

150

200

250

300

1 10 102

103

104

L/E (km/GeV)

Nu

mb

er o

f ev

ents

Check of the observed dip in L/E distribution (3)zenith angle : cosθ -cosθ

(Zenith angle of each event is inverted. Because of the wrong assignment of L, no dip is expected.)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

1 10 102

103

104

L/E (km/GeV)

Dat

a/P

red

icti

on

(n

ull

osc

illat

ion

)

Sensitivities to alternative models and the data

0

2

4

6

8

10

12

14

16

18

20

50 60 70 80 90 100L/E resolution cut (%)

∆χ2

ν decay

ν decoherence

L/E resolution cut at 70%

obtained ∆χ2

Neutrino decay and decoherence models ?

OscillationDecayDecoherence

χ2min=37.9/40 d.o.fχ2min=49.1/40 d.o.f ∆χ2 =11.3χ2min=52.4/40 d.o.f ∆χ2 =14.5

ν decay disfavored at 3.4σ

ν decoherence at 3.8σ

First dip observed in the data cannot be explained by alternative hypotheses

Evidence for oscillatory signature

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

1 10 102

103

104

L/E (km/GeV)

Dat

a/P

red

icti

on

(n

ull

osc

illat

ion

)

0

5

10

15

20

25

30

35

40

45

50

0 0.2 0.4 0.6 0.8 1

sin2θ13

χ2-χ

2m

in

4.61

9.21

0

5

10

15

20

25

30

35

40

45

50

0 0.2 0.4 0.6 0.8 1

sin2θ13χ2

-χ2

min

χ2 as a function of sin2θ13

Normal Inverted

How can we discriminate neutrino and anti-neutrino interactions ?

Simple answer: No. It is not possible to discriminate event by event in water Cherenkov experiments.

However, σ(total) and dσ/dy are different.

Try to discriminate positive and negative ∆m2 using these events.

0

0.2

0.4

0.6

0.8

1

10Eν (GeV)

frac

tio

n

0

0.2

0.4

0.6

0.8

1

10Eν (GeV)

frac

tio

nCC νe

CC νe

CC νe

CC νe

Others Others

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

Electron appearance for positive and negative ∆m2 in a

water Chrenkov detector

GeV

GeV Single-ring e-like

0.5 1Mul-e 2.5 - 5.0 GeV

0

50

100

150

200

-1 -0.5 0 0.5 1

30

MM-e 1.0 - 2.5 GeV

Multi-GeV Multi-ring e-like

0

50

100

150

200

-1 -0.5 0 0.5 1MM-e 2.5 - 5.0 GeV

0

50

100

150

200

-1 -0.5 0 0.5 1

100

60

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

Positive ∆m2

Negative ∆m2

null oscillation

cosΘ cosΘ

Relatively high anti-νefraction

Lower anti-νe fraction

∆m2=0.002eV2

s2θ23 = 0.5s2θ13 = 0.05(SK 20yrs)

χ2 difference (inverted-normal)

0

5

10

15

20

25

30

35

40

0 0.02 0.04 0.06 0.08sin2θ13

∆χ2 (i

nve

rted

-no

rmal

)

0

5

10

15

20

25

30

35

40

0 0.02 0.04 0.06 0.08sin2θ13

∆χ2 (i

nve

rted

-no

rmal

)

0

5

10

15

20

25

30

35

40

0 0.02 0.04 0.06 0.08sin2θ13

∆χ2 (i

nve

rted

-no

rmal

)

∆m2: fixed, θ23: free, θ13: freeExposure: 1.8Mtonyr

(SK 80yr or HK ～3.3 yr)

3σ 3σ 3σ

True= normal mass hierarchy assumed.

χ2 difference (normal – inverted)

∆m2: fixed, θ23: free, θ13: freeExposure: 1.8Mtonyr

(SK 80yr or HK ～3.3 yr)

3σ 3σ 3σ

0

5

10

15

20

25

30

35

40

0 0.02 0.04 0.06 0.08sin2θ13

∆χ2 (i

nve

rted

-no

rmal

)

0

5

10

15

20

25

30

35

40

0 0.02 0.04 0.06 0.08sin2θ13

∆χ2 (i

nve

rted

-no

rmal

)

0

5

10

15

20

25

30

35

40

0 0.02 0.04 0.06 0.08sin2θ13

∆χ2 (i

nve

rted

-no

rmal

)

True= inverted mass hierarchy assumed.