Constraint on 13 from the Super-Kamiokande atmospheric neutrino data

Kimihiro Okumura 　 (ICRR)

for the Super-Kamiokande collaboration

December 9, 2004

RCCN workshop @ Kashiwa ICRR

Outline

In this talk, 3-flavor oscillation analysis results, assuming one mass scale dominance (m12

2=0), will be presented.

We will have two more talks on: Effect of solar oscillation term (m12

2≠0) in atmospheric neutrino sample

Future possibilities M. Shiozawa’s talk

S. Nakayama’s talk

Observation of Atmospheric Neutrinos in Super-Kamiokande

Fully Contained (E ~1GeV, e )

Stopping (E~10GeV, )

Partially Contained (E ~10GeV, )

Through-going (E~100GeV, )

1000 m underground 50,000 ton (22,500 ton fid.) 11,146 20 inch PMTs (SK-I) 1,885 anti-counter PMTs

Water Cherenkov detector Event classification

Neutrino oscillation with m12=0

iiU Neutrino Mixing : Weak eigenstates

: Mass eigenstates

100

0

0

0

010

0

0

0

001

1212

1212

1313

1313

2323

2323

111

111

321

cs

sc

ces

esc

cs

sc

UUU

UUU

UUU

Ui

ieee

cij=cosij sij=sinijMixing Matrix :

i

E

LmP e

22

132

232 27.1

sin2sinsin)(

E

LmP ee

22

132 27.1

sin2sin1)(

E

LmP

22

232

132

232

132 27.1

sin)sincos1(sincos41)(

In the approximation ofm2=0

(We know m122~8.3×10-5eV2 )

expressed with three parameters (m23

2, 23, 13)

13=0

E

LmP

22

232 27.1

sin2sin1)(

0)( eP

2-flavor oscillation (↔

six parameters (m12

2, m232,

12, 23, 13,)

in case of vacuum oscillation

3-flavor oscillation

with m122=0

two parameters (m23

2, 23)

Search for non-zero 13

Electron appearance expected in the 2 -10GeV

upward going events.

E

LmP m

e

22

132

232 27.1

sin2sinsin)(

E(GeV)

cos

)( eP

matter effect

vacuum oscillation

s213=0.05 s213=0.00 null oscillation

Electron appearance

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

0.45 Mtonyr

(Super-K 20yrs)

)( eP oscillation w/ matter

constraint on 13 given by reacter experiment; sin213<0.05

SuperK-I atmosheric neutrino data

special sample: Multi-Ring electron to increase multi-GeV e sensitivity

CC e CC

1489day FC+PC + 1646day upward going muon data

Selection criteria for Multi-GeV Multi-Rring electrons

• FC, Evis>1.33GeV• Most energetic ring is electron-like• Log(electron likelihood) > 0 defined by following variables;

1. PID likelihood2. Momemtum fraction of most energetic ring3. Number of decay-electrons4. Distance btw decay-e and primary vertex considering energy dependence

We used Likelihood method to discriminate multi-G multi-R electrons;

Total electron-likelihood

CCeCC

NC

w/ L cut w/o L cut

e CC 73.5 52.0

CC 11.4 26.7

NC 15.1 21.3

e CC events are enhanced by Likelihood cut

52% → 74%

(percentage %)

select

Binning for 3flavor analysis

single-R muon

multi-R muon

Up-stop

Up-thru

All zenith angle is 10bins 37 momentum bins x 10 zenith bins = 370 bins in total

multi-R electron

single-R electron

PC-stop PC-thru

1GeV

10GeV

zenith angle 10 bin

PP

2 definition for 3-flavor analysis

errorsystematicofsigma

tcoefficienerrorsystematicf

termerrorsystematic

eventsectedofN

binnthineventsobservedofN

fN

NNNfN

i

ni

i

n

nobs

i in

i

ni

n

nobsn

obsnobs

i

ni

n i

ii

1:

:

:

exp:#

:#

) 1(

ln2) 1(2

exp

2

exp

exp2

n

ni

nnobsij

in

nj

ni

nobs fNNfffN exp

2j2

2mini

2

...))(1( 1

@ 0

• 2 was calculated with Poisson probability

• Effect of systematic error was considered for calculating expectation

• Systematic error terms were obtained by solving linear equation : Mij

×j=vj

(G.L.Gogli et al. hep-ph/0206162)

a. Combined overall normalization relative norm. FC/PC relative norm. upstop/upthru

b. Neutrino flux• /e below 5GeV• /e above 5GeV• anti-e/e below 10GeV• anti-e/e above 10GeV• anti-/ below 10GeV• anti-/ above 10GeV• UP/DOWN ratio• Horizontal-vertical in FC/PC• Neutrino flight length • Energy spectrum• K/pi ratio• Sample-by-sample normalization (FC multi-GeV ) Sample-by-sample normalization (PC and upstop)

c. Neutrino interactions• QE• Single-production• DIS• DIS Bodek• Coherent production• NC/CC• Low energy QE• Axial vector mass (MA)• Hadron simulator• Nuclear effect

d. SK 1. Event selection

FC reduction PC reduction Upmu efficiency Upmu 1.6GeV cut Flasher BG Cosmic mu BG

2. Event reconstruction Ring-counting Single-R PID Multi-R PID Energy calibration Up/down asymmetry of energy

3. Othersa. Tau

4. 3flavor analysis Upthru BG in horizontal bin Upstop BG in horizontal bin Non eCC in multi-G single-R electron Non eCC in multi-G multi-R electron Normalization of multi-R electron

List of systematic errors

Total number of errors: 44

Analysis details

100yr Monte Carlo data was generated for expectation

4 step constant function was used for matter density in Earth

Averaging technique of oscillation probability was used to compensate small MC statistics

2 was calculated in oscillation parameter space of (m2, sin223, sin213)

Log10(E GeV)

P(e)

P(ee)

Earth radius (km)

Mat

ter

dens

ity

averaged

m2=2.0x10-3 eV2

sin223=0.5 sin213=0.05

coszenith=-0.6

Best-fit zenith angle distributions

Null oscillation 2min/ndf = 376.82/368 @(2.5x10-3, 0.5, 0.0)

CC e CC

multi-GeV electronsUP/DOWN asymmetryZenith angle

No significant excess due to matter effect was seen in upward-going multi-GeV electron sample

single-R electron

multi-R electron

Allowed region by 3 flavor analysis

2min/ndf = 376.82/368 @(2.5x10-3, 0.5, 0.0)

sin

2

sin2

Normal hierarchy

sin213<0.14 was allowed in 90% C.L. with SK data only

Allowed region by 3 flavor analysis

sin2 sin2

m2

(eV

2)

Normal hierarchy

0.36<sin223<0.65 was allowed in 90% C.L.

Normal (m2>0) or inverse (m2<0) mass hierarchy ?

Matter effect is different btwn normal / inverse mass hierarchy:

Basically, water Cherenkov detector cannot discriminate neutrino/anti-neutrino event-by-event basis, but small effect can be obtained in multi-GeV electron sample due to the difference of cross section, etc..

3

2

13

2

1m2>0

m2<0

Normal Inverse

neutrino anti-neutrino

m2>0 enhanced suppressed

m2<0 suppressed enhanced

Normal vs Inverse hierarchy

Normal (m2>0)

Inverse (m2<0)

2min/ndf = 376.82/368 @(2.5x10-3, 0.5, 0.0)

2min/ndf = 376.76/368 @(2.5x10-3, 0.525, 0.00625)

Summary

3-flavor oscillation analysis with m122=0 assumption was

performed using SK-I combined (FC+PC+Up) dataset. No significance excess in upward-going multi-GeV electr

on was seen With this oscillation scheme and normal hierarchy assum

ption, 90% C.L. allowed region was obtained ; sin213<0.14

0.36<sin223<0.65

Both normal and inverse mass hierarchy hypothesis are consistent with Super-K data

End