Search for Nucleon DecaySearch for Nucleon Decay 　　 　　in Super-Kamiokande in Super-Kamiokande

M.MiuraM.Miura

Kamioka Observatory, ICRRKamioka Observatory, ICRR

ICRR SeminarICRR Seminar

Nov 26, 2014 in Kashiwa campusNov 26, 2014 in Kashiwa campus

1

ContentsContents1)1) IntroductionIntroduction

2)2) Super-Kamiokande detectorSuper-Kamiokande detector

3)3) p p e e++++00 mode mode

4)4) p p K K++++ mode mode

5)5) pp ++++, n, n ++00

6)6) Other modesOther modes

7)7) Summary of searchesSummary of searches

8)8) Future prospectsFuture prospects

2

1. Introduction

3

The Standard Model

• In July 2012, LHC reported they found Higgs (-like) particle.• It was a missing piece of the Standard Model.• Experimental data of particle physics can be well explained by the Standard Model.• End of explore for particle physics ?

Wait, Wait, Wait, Wait

• There are several important questions which There are several important questions which the Standard Model has not been answered. the Standard Model has not been answered. Why quarks and leptons ?Why quarks and leptons ? Why three generations ?Why three generations ? Why three gauge interactions ?Why three gauge interactions ? Why mass differences ?Why mass differences ? What is the origin of charge ?What is the origin of charge ? ……… ………..

4

Hint of beyond the Standard Model

5

Running Coupling Constants

log E(GeV)

Inve

rse

of c

oupl

ing

Electromagnetic

Weak

Strong (o

nly quark)

• Strength of Electromagnetic, Weak, and strong interaction are function of energy.• By extrapolating to high energy, they seems to meet around ~1015 GeV.• Merging three interactions Grand Unify Theory.• Obviously, this energy is out of range by accelerators.

Not conserve baryon and lepton number: GUTs allowed Proton decay

Examples of proton decay

Model Mode Prediction (years)

Minimal SU(5) pe+0 1028.5 ~ 1031.5 [1]

Minimal SO(10) pe+0 1030 ~ 1040 [2]

Minimal SUSY SU(5) pK+ ≤ 1030 [3]

SUGRA SU(5) pK+ 1032 ~ 1034 [4]

SUSY SO(10) pK+ 1032~1034 [5]

[1] P. Langacker, Phys. Reports 72, 185 (1981)[2] D.G. Lee, M.K. Parida, and M. Rani, Phys. Rev. D51, 229 (1995)[3] H.Murayama and A. Pierce, Phys. Rev. D65, 55009 (2002)[4] T. Goto and T. Nihei, Phys. Rev. D59, 115009 (1999)[5] V. Lucas and S. Ruby, Phys. Rev. D55, 6986 (1997)

Proton lifetime predictions

u

dp

3

~

c~

W

sc

c

~

u uK+

Minimal SU(5) model SUSY SU(5) model

d

u

u e+

d

dc

X

p0

> 1030 years !

How measure proton lifetime?

• Impossible to keep watching a proton for > 10Impossible to keep watching a proton for > 103030 years: Age years: Age of universe~ 1.4x10of universe~ 1.4x101010 years years

• Definition of lifetime Definition of lifetime : N = N: N = N00 exp(-t/ exp(-t/))

• If initial number of proton, NIf initial number of proton, N00 is large, we may observe is large, we may observe

proton decay.proton decay.

• Need massive detectorNeed massive detector, same as neutrino observation., same as neutrino observation. Kamiokande (3kt), IMB (8kt): water cherenkov detectorKamiokande (3kt), IMB (8kt): water cherenkov detector Soudan (963t), NUSEX (150t), Frejus (900t): Iron calorimeterSoudan (963t), NUSEX (150t), Frejus (900t): Iron calorimeter

• Super-Kamiokande (SK): 7.5x10Super-Kamiokande (SK): 7.5x103333 protons in fiducial protons in fiducial volume.volume.

• SK is the most sensitive detector for nucleon SK is the most sensitive detector for nucleon decay search!decay search!

7

2. Super-Kamiokande Detector2. Super-Kamiokande DetectorLocation: Kamioka mine, Japan. ~1000 m under ground.Size: 39 m (diameter) x 42 m (height), 50kton water. Optically separated into inner detector (ID) and outer detector (OD, ~2.5 m layer from tank wall.)Photo device: 20 inch PMT (ID), 8 inch PMT (OD, veto cosmic rays).Mom. resolution: 3.0 % for e 1 GeV/c (4.1%: SK-2).Particle ID: Separate into EM shower type (e-like) and muon type (-like) by Cherenkov ring angle and ring pattern.

-like () e-like (e

Nucleon Decay Experiment

8

K+ paper 2005: > 2.3x1033 years (92kton ・ year)

SK-3Live time: 518 daysExposure: 31.9kton ・ yrID PMT:11146Photo coverage: 40 %

SK-2Livetime:- 798.6 daysExposure:- 49.2 kton·yrInner PMT:5182Photo coverage:19 %

96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13

Accident reconstruction electronics upgrade

SK-4 (~13’Feb)Live Time: 1417 daysExposure: 87.3kton ・ yr

History of Super-Kamiokande

e+0 paper 2007: > 8.2x1033 years (141kton ・year)

This talk: 260 kton ・ year exposure in total

Same

SK-1Livetime: - 1489.2 daysExposure:- 91.7 kton·yrInner PMT: 11146Photo coverage:40 %

9

How to Search 1

Proton decay MC Efficiency, Selection criteria 8 bounded protons in O:

Fermi momentum, binding energy, various nuclear effects are taken into account.

2 free protons: simple two body decay.Atmospheric MC BKG for proton decay Flux : Primary cosmic rays make and e.

M.Honda et .al., Phys.Rev. D75 043006(2007)

interaction: NEUT Y.Hayato, Nucl.Phys.Proc.Suppl. 112,171(2002)

• Analysis method: two typesAnalysis method: two types 1) Select events by cuts (less BKG)1) Select events by cuts (less BKG)

Selection efficiency Selection efficiency Estimated by signal MC. Estimated by signal MC. Number of background Number of background Estimated by BKG MC. Estimated by BKG MC. Criteria are tuned as Sig/Criteria are tuned as Sig/√√BKG becomes max.BKG becomes max. Check agreement between data and BKG in sideband region.Check agreement between data and BKG in sideband region. Open data and calculate lower limit of lifetime.Open data and calculate lower limit of lifetime.

2) Fit data distribution by Signal and BKG MC and 2) Fit data distribution by Signal and BKG MC and estimate lower limit of lifetime.estimate lower limit of lifetime.

11

How to Search 2

Data BKG Sig= x

+ x

3. p3. pee++00 mode mode

0

P

e+

Event features;• e+ and 0 are back-to-back (459 MeV/c) •0 2 s : all particles can be detectable. Reconstruct proton mass and momentum.

Selection;• Fully contained, VTX in fiducial volume.• 2 or 3 ring • all e-like, w/o decay-e• 85 < M0 < 185 MeV (for 3-ring event) .• 800 < MP < 1050 MeV & Ptot < 250 MeV/c

12

e+ 0

Signal MC

13

What causes inefficiency ?

Signal MC

Signal box

• If a proton in oxygen decays, 0 is suffered from nuclear interactions.

Absorption: 1 ring Scatter: Change invariance mass and total momentum. Charge exchange: Change Nring and PID.

• Also nuclear interactions are dominant source of systematic error. •Free protons (H) are free from them (eff.~90%). High efficiency for water cherenkov detector.

Results of pe+0

14

Blue: Signal MC Green: BG MC(ATM Red: Data

Total invariant mass (MeV/c2)

Tot

al m

omen

tum

(M

eV/c

)Total mass vs Total momentum

Total mass (1D)

Dot: DataBlue: Signal MCGreen: BKG MC

• No data found.• Data agrees with BKG (Atm.) MC.

15

Exp.(kt ・yr)

Eff(%)

BKG

b

Data

n

SK1 91.7 39.2±0.7 0.27 0

SK2 49.2 38.5±0.7 0.15 0

SK3 31.9 40.1±0.7 0.07 0

SK4 87.3 39.5±0.7 0.22 0

Total 260.1 0.71 0

Lifetime limit (90%C.L,): > 1.4x1034 years

Error for eff. (%)

-N int. 15

Frmi-mom 8

Correlated decay

7

Other 4

Total 19

Error for BKG (%)

-N int. 8

p-int. water 36

-flux, crs 11

Other 22

Total 44

dbddbPPPPn

be

AnP

nb

)()()()(!

)(1)|(

)(

it

dnPLClim

0)|(..

Life time limit can be calculated based on Bayes’ therem:

P(x): probability function for x: Exposure: Efficiencyb: Expected BKG

: decay rate, lim = 1/lim

• Regarded as a dominant proton decay mode in SUSY-GUTs.Regarded as a dominant proton decay mode in SUSY-GUTs.

• Momentum of KMomentum of K++ is is below Cherenkov thresholdbelow Cherenkov threshold, stop in water , stop in water and decay and decay use decay products from Kuse decay products from K++:: KK++ ++ (63 %) (63 %) KK++ ++ 00 (23 %) (23 %) have monochromatic momentumhave monochromatic momentum..

• Nuclear Nuclear (6 MeV) is emitted from remained nucleus when (6 MeV) is emitted from remained nucleus when deexcitation (41 % in probability).deexcitation (41 % in probability).

• Following three methods are used to search for Following three methods are used to search for pp + K+ K++ . .

• Published to Phys. Rev. D 90, 072005 (2014),Published to Phys. Rev. D 90, 072005 (2014),

16

4. p4. p + K+ K++ mode mode

17

… with Synopsis ( selected by editors).

e+e

16O->15N

6.3MeV

K+

+

Method (A) K+ ++ with nuclear

t

T(dN/dt=max)

Tstart

12ns window

e

Hits

Event features;• K+ is invisible, stops and 2 body decay (P = 236 MeV/c).• Proton in 16O decays and excited nucleus emits 6 MeV (Prob. 41%, not clear ring).

=> Tag to eliminate BKG.

Selection:• 1 -like ring with decay-e.• 215 < P < 260 MeV/c• Proton ring rejection.• Search Max hit cluster by sliding time window (12ns width); - 8 < N < 60 hits for SK-1,3,4 4 < N < 30 hits for SK-2 - T-T < 75 nsec

visibleinvisible

18

19

What causes inefficiency ?

• hit cluster is much smaller than .• hits spread due to PMT time resolution (2.2 nsec @ 1pe). • To avoid tail, time window starts to slide from dN/dt <0 (t0).• As a result, tagging efficiency is low if is close to .

t-t(nsec)

Results of Method (A) Black: DataRed: ATM MCBlue: PDK MC

No candidates have been observed.

Exp.(kton ・ yr)

Eff(%) BKG Data

SK1 91.7 7.9±0.1 0.08 0

SK2 49.2 6.3±0.1 0.14 0

SK3 31.9 7.7±0.1 0.03 0

SK4 87.3 9.1±0.1 0.13 0

Total 260.1 0.38 0

N distributions

20

40% coverage

19% coverage

NOTE• PMT density was half in SK2.• Decay electron tagging has been improved in SK4 by new electronics.

21

Black: DataRed: ATM MCBlue: PDK MC

P

Method (B) K+ ++, spectrum

• Proton decay signal should have monochromatic momentum.• Make momentum distributions of rejected events by cut.• Data agrees with atmospheric MC and cannot see any bump in signal region.• Fitting data by signal and BKG MC to estimate lower limit of lifetime limit with other two method (see later page).

Method (C) K+ ++

K+

+

e+

0

+

e

205 MeV/c

Event features;• Br. 21 %.•and are back-to-back and have 205 MeV/c.•P+ is just above Č thres.(not clear ring).

=> Search for monochromatic 0 with backward activities.

Selection:• 1 or 2 e-like rings with decay-e.• 85 < M0 < 185 MeV.• 175 < P0 < 250 MeV/c.• Ebk: visible energy sum in 140-180 deg. of 0 dir, Eres: in 90-140 deg, Lshape: Likelihood based on charge profile 10 < Ebk < 50 MeV Eres < 12 MeV (20 MeV for 1ring) Lshape > 2.0 (3.0 for 1ring)

Eres

Ebk

visibleinvisible

22

Blue: SignalRed: BKG

Improvement: pImprovement: pKK++,K,K++++00

# of Ring: K++0

Judge as 1 ring (~20%) if opening angle of 2 s is small or momentum of one is small.

Use “0 fitter”• Make likelihood assuming 0 and search for missing ring.• It is used for e appearance analysis of T2K to reduce BKG.

It makes 1 ring sample available It makes 1 ring sample available for this analysis!for this analysis! Efficiency increased.Efficiency increased.

M0

P0

23

1 2 3 4

0 50 100 150 200 250 300

0 50 100 150 200 250 300 350 400

No candidates.

Exp.(kton ・yr)

Eff(%) BKG Data

SK1 91.7 7.8±0.1 0.18 0

SK2 49.2 6.7±0.1 0.17 0

SK3 31.9 7.9±0.1 0.09 0

SK4 87.3 10.0±0.1 0.18 0

Total 260.1 0.62 0

Results of Method (C)

p K+ Lifetime limit (90% CL) combining Method (A) ,(B), and (C): > 5.9 x1033 yrs

-

24

Black: DataRed: ATM MCBlue: PDK MC

Ebk (MeV)

Lshape

• Published to Phys.Rev.Lett. 113, 121802 (2014).Published to Phys.Rev.Lett. 113, 121802 (2014).• Predicted by minimal SUSY SO(10) model;Predicted by minimal SUSY SO(10) model;

(n (n ++00 )=2 )=2(p (p ++++) ) 5.7 ~ 13x10 5.7 ~ 13x103232 years years

25

4. p4. p + + ++, n, n + + 00,,

0

n

+

p

n +0 p ++

Two e-like rings one -like ring

P0 ~ 460 MeV/c P+ ~ 458.8 MeV/c

Affected by nuclear interaction, same as pe+0 case

Large background Fit momentum by Signal and BKG MC

26

n +0 p ++

Data: SK1 ~ SK3, 173 kt ・ year exposure

(n +0 ) > 1.1 x1033 years (p ++) > 3.9x1032 years

Almost ruled out the predicted range.Almost ruled out the predicted range.

5. New modes: |5. New modes: |(B-L)| =2(B-L)| =2

27

★ Decay to trilepton p e+, + Phys.Rev.Lett. 113,101801 (2014) Predicted by SO(10) (Pati and Salam): 1030~1033 years [6] Single charged lepton in final state check excess in P distribution.

Pe P

No significant excesses. : Lifetime limit (90%CL) pe+: > 1.7x1032 years p+: > 2.2x1032 years (IMB-3:1.7x1031 years) (Frejus:2.1x1031 years)

Cross: dataHist: Atm MC : Signal MC

Cross: dataHist: Atm MC : Signal MC

[6] J.C. Pati, Phys.Rev.D29,1549 (1984), P.H. Gu and U. Sarkar (2011), 1110.4581

28

★ Dinucleon decay: pp++, pn+0, nn 00

Search for -pair in back-to back. For nn00, use total mass and momentum cuts. For other modes, difficult to reconstruct total mass and momentum. Use multi-variable analysis (Boosted Decision Tree).

Eff(%) BG(evts) Obs(evts) Limit(yr) (Frejus)

pp++ 5.9 4.5 2 >7.3x1031 7.0 X 1029

pn+0 10.2 0.8 1 >1.8x1032 2.0 X 1030

nn 00 21.1 0.1 0 >4.1x1032 3.4 X 1030

New modes: New modes: B =2B =2

Total invariant mass Total invariant mass

Tot

al m

omen

tum

Tot

al m

omen

tum

Signal MC

BG MC

Data

Consistent with expected backgrounds.

Signal region

6. Summary of searches6. Summary of searches• We have We have not fond any evidencesnot fond any evidences

of nucleon decay, so far.of nucleon decay, so far.• We calculated nucleon lifetime We calculated nucleon lifetime

limits with 90 % C.L.limits with 90 % C.L.

pp e e++00: > 1.4x10: > 1.4x103434 yrs yrs

KK++: > 5.9x10: > 5.9x103333 yrsyrs

• Other new modesOther new modes have also been have also been studied and published in this studied and published in this year.year.

• Those are the most stringent Those are the most stringent limit in the world.limit in the world.

29

nn 0 0pn + 0

pp + +

pp 　K +K +

n 0

n + -

n 　e + -

n + -

n 　e + -

p +

p 　e +

p +K 0

p K +

p +

p +

p 　e +

p + 0

p 　e + 0

p + 0

p 　e + 0p + 0

p 　e + 0

1031

1032

1033

1034

1035

/B　(years)

30

7. Future prospect7. Future prospectOn going project: neutron tagging

pe+0: ATM MC• Backgrounds of proton decay are atmospheric interactions.• Sometimes they are accompanied with neutron.• Fow example, dominant background of pe+0 is Chargted Current 1 production;ep e+n0

en e-n+ +charge exchange• neutron tag is useful to reduce background.

31

n+p d+ (2.2 MeV), =204s (enable for SK4)• Search for hit cluster N>7 in 10 ns window after prompt signal.• Eff. 25 %, BKG 1.4 %.• MC including neutron capture is developing.

How to tag neutron

Agree well!

Preliminaryneutron after all pe+0 cut (SK4)

Almost 50 % BKG can be rejected!

Super-K+Gd option is under study, also.

• Longer exposure = increase expected background. Longer exposure = increase expected background. Any room to improve cut criteria?Any room to improve cut criteria?

• Improvements of systematic errors contribute better Improvements of systematic errors contribute better sensitivities.sensitivities.

• Not all searches use data including SK1-SK4. Should Not all searches use data including SK1-SK4. Should be updated.be updated.

• Any other good decay modes ? Feedback from Any other good decay modes ? Feedback from theorists are welcome!theorists are welcome!

• Model independent analysis ? Look for discrepancies Model independent analysis ? Look for discrepancies between data and atmospheric between data and atmospheric MC. MC.

32

Other items to be studied

33

Further more: Hyper-Kamiokande

1 Mega ton Water Chrenkov Detector

Base design

• Total Volume: 0.99 Mton• Inner Volume: 0.74 Mton• Fiducial volume: 0.56 Mton

(0.056 Mton x 10 compartments)

• Outer volume: 0.2 Mton• Photo-sensors:

99,000 20 inch PMT (ID)(20 % photo coverage)

25,000 8 inch PMT (OD)

34

Hyper-K for Nucleon Decay • Sensitivity (90%CL) with HK

10 years run;

e+0: 1.3x1035 year

K+: 2.5x1034 year

• 33 discovery potential discovery potential

e+0: 5.6x10 5.6x10 3434 years years

K+: 1.2x101.2x103434 year year

(with base design)(with base design)

pe+0

pK+

--

Letter of Intent: Hyper-Kaiokande Experiment arXiv:1109.3262 [hep-ex] 35

-

Photo sensor R&D for Hyper-K

20 inch PMT in baseline design- It is almost hand-made even in electrics parts.- Expensive and not suitable for mass production.- But we need 99,000 PMTs.

Other possibility: Hybrid Photo Detector (HPD), High QE Other possibility: Hybrid Photo Detector (HPD), High QE PMT (box&line)PMT (box&line)

e

DynodeDynode

~2kV

e

~8kV

Avalanche Diode (AD)Avalanche Diode (AD)

e

Avalanche Gain ~100@250V

Bombardment Gain ~400 @8kV

PMT HPD36

Advantage of HPD• Avalanche Diode is suitable for mass production.

lower cost.• Better photon counting.• Better collection efficiency .

(20 inch PMT~75 %HPD ~95%)• Better timing resolution

(20 inch PMT ~2.2 nsec HPD ~1.1 ns in TTS)

Expect to improve nuclear tagging efficiency in pK+

90ns8mV1p.e.

2p.e.3p.e.

Pulse Height [mV]

1p.e.2p.e.

3p.e.4p.e.

ped

t

Hits

Hidden by tail

37t

Hits

Better separation

Better t-resolution

38

Test: HPD time resolution with SK4 setup Efficiency curve of tagging

T –T(nsec)

Black: 2.2 nsecRed: 1.1 nsec @1pe

• tagging efficiency close to is increased. K+ decay ~exp(-12ns/t).• Selection efficiency of pK 9.1 % 13.1 % (44% increased)• Background rate: 1.5 1.0 evts/Mt ・ yr (33% decreased) Even though half density of sensor, performance of HK with HPD may be better than SK !

New photo sensor can improve physics sensitivity.

39

Hyper-K open meeting will be held on Jan.29-31, 2015 at IPMU.

Your participations are welcome !http://indico.ipmu.jp/indico/conferenceDisplay.py?confId=52

Backup

40

41

Why efficiencies decreased (45 % 40 %) Because we have updated -interaction in Oxygen.

(1) Charge exchange increased to match experimental data.

(2) Kinematics of scattered changed in P > 500 MeV/c

Final momentum Final angle (degree)

Black: old MCRed: new MC

Increased in large angle

Input: 550 MeV/c

NOTE: Sys.error for -int 15 %

42

Recent improvements on BKG rejection

Fix momentum bias for events with decay-e • Hits in (-50:250nsec) used for momentum.• If decay-e is closer to , P is overestimated generate hit template for VTX fit with larger P VTX is shifted to forward. TOF over-subtracted for backward hits, make mimic signal.• Solution: Time window size is shortened when decay-e is closer

to parent . BKG is reduced by 30 %.

43

Recent improvements on BKG rejection (2)

Proton ID• Dominant BKG is CCQE with high mom. recoiled proton and

invisible , the proton is identified as -ring. VTX is shifted to forward to adjust C-ang. TOF over-subtracted for backward hits, make mimic signal.• Proton and muon ring can be separated using likelihood

function based on opening angle and hit pattern.

Proton

True VTX

Proton

260 <P<400 MeV

Black: DataRed: ATM MC

Agree well.

Fitted VTX

BKG is reduced to ~50 %.

Recent improvement(2): pRecent improvement(2): pKK++,K,K++++00

Charge distribution in angle

Opposite of o dir= + dir

0 dir

0+ zoom

Red: PDK MCBlue: BKG

Conventional method: Use corrected charge sum in <40°EbkNew method: 1. Define Ebk by charge sum in < 35° 2. Make expected charge distribution for signal and BKG, and compare observed charge by likelihood. Compare shape of dist.

44

0 10 20 30 40 50 60

),(Prlog(),(Prlog( exp

40

0exp

40

0

BKGobs

sigobsshape qqobqqobL

45

Input variables: ppInput variables: pp++++

nring2 2.5 3 3.5 4 4.5 5 5.5 6

Even

ts

0

5

10

15

20

25

30

35

signal

background

data

number　of　rings

nmue0 0.5 1 1.5 2 2.5 3 3.5 4

Even

ts

0

2

4

6

8

10

12

14

16

18

20

22

24

number　of　decay　electrons

number　of　pi　candidates2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4

Even

ts

0

10

20

30

40

50

number　of　non-showering　rings

energy　(MeV)0 200 400 600 800 1000 1200 1400 1600

Even

ts

0

2

4

6

8

10

visible　energy

rtot　(corrected　p.e.)0 500 1000 1500 2000 2500 3000

Even

ts

0

1

2

3

4

5

6

7

8

magnitude　of　rtot　vector　sum

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Even

ts

0

2

4

6

8

10

rtot[0]/rtsum

distance　(cm)0 200 400 600 800 1000 1200 1400 1600 1800 2000

Even

ts

0

2

4

6

8

10

12

max　decay-e　distance

angle　(degrees)0 20 40 60 80 100 120 140 160 180

Even

ts

0

2

4

6

8

10

pion　decay-e　opening　angle

angle　(degrees)120 130 140 150 160 170 180

Even

ts

0

1

2

3

4

5

6

7

8

maximum　opening　angle

Number of rings Number of decay-e Number of -like

Visible energy Rtot vector sum Fraction of dominant ring

Max decay-e length -decay-e ang Max opening ang

46

Input variables: pnInput variables: pn++00

momentum　(MeV/c)0 200 400 600 800 1000 1200 1400

Even

ts

0

5

10

15

20

25

30

35 signal

background

data

pi0　momentum

angle　(degrees)120 130 140 150 160 170 180

Even

ts

0

2

4

6

8

10

12

14

16

18

pi0-pi+　opening　angle

momentum　(MeV/c)0 100 200 300 400 500 600 700 800 900 1000

Even

ts

0

5

10

15

20

25

30

35

40

45

pi+　momentum

energy　(MeV)0 200 400 600 800 1000 1200 1400 1600

Even

ts

0

2

4

6

8

10

12

14

visible　energy

charge　ratio0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Even

ts

0

2

4

6

8

10

12

14

16

18

20

22

rtot[0]/rtsum

mass　(MeV/c^2)0 50 100 150 200 250 300 350 400 450 500

Even

ts

0

5

10

15

20

25

30

35

40

45

pi0　mass

nmue0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Even

ts

0

20

40

60

80

100

120

number　of　decay　electrons

0 momentum 0-+ opening ang. + momentum

Visible energy Fraction of dominant ring 0 mass

Number of decay-e

47

Outputs of BDT (SK4 only) Outputs of BDT (SK4 only)

MVA-1 -0.5 0 0.5 1

Even

ts

0

2

4

6

8

10

12

14

16

MVA　output

signalbackgrounddata

MVA-0.6 -0.4 -0.2 0 0.2 0.4 0.6

Even

ts

0

10

20

30

40

50

60

MVA　output

signalbackground

data

pppp++++ pnpn++00