16 O (pp) 14 C K + K +

16O (pp) 14C K+ K+

LOOKING FOR DOUBLE PROTON DECAY AT SUPER-

KAMIOKANDE…BECAUSE SINGLE PROTON DECAY IS JUST

TOO EASY!

Michael LitosBoston UniversitySuper-Kamiokande Collaboration

March 11, 2010

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First Thing’s First: Single Proton Decay

A Brief History…

• Minimal SU(5) predicts t(p→e+p0) < 1032 years• Minimal SUSY SU(5) predicts t(p→K+n) < 1032 years• In 1980s IMB & Kamiokande built to search for these decay modes.• No proton decay observed; placed lifetime limits on the order of 1032 years.• Super-Kamiokande built in 1990s, > order of magnitude larger than predecessors.• No proton decay observed (so far); placed lifetime limits on the order of 1033 years.

∼1 proton

t 10∼ 32 years

∼1032 protonst 1 year∼

Proton decay methodology: Swap the large numbers

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How to Search for Single Proton Decay

p→e+p0

Experimental Signature3 Cherenkov rings

• 1 from e+

• 2 from p0 (p0→gg)Invariant mass, MINV ≈ Mp

Total momentum, PTOT < PFermi-max

→ Simple 2-D Box: MINV, PTOT

P TOT (

MeV

/c)

MINV (MeV/c2)

p→e+p0 MC

Atm. n MC(500 years)

SK-1 Data(1489 days)

p→K+nExperimental Signature1 Cherenkov ring

• n is invisible• K+ below threshold• 1 ring from m+ (K+→m+n)

Monochromatic momentum, Pm = 236 MeV/c

→ Simple Bump Search: Pm

Pm (MeV/c)Ev

ents


p→K+n MC

empty box no bump

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How to Search for Single Proton Decay

p→e+p0

Experimental Signature3 Cherenkov rings

• 1 from e+

• 2 from p0 (p0→gg)Invariant mass, MINV ≈ Mp

Total momentum, PTOT < pFermi-max

→ Simple 2-D Box: MINV, PTOT

P TOT (

MeV

/c)

MINV (MeV/c2)

p→e+p0 MC

Atm. n MC(500 years)


p→K+nExperimental Signature1 Cherenkov ring

• n is invisible• K+ below threshold• 1 ring from m+ (K+→m+n)

Monochromatic momentum, pm = 236 MeV/c

→ Simple Bump Search: pm

pm (MeV/c)Ev

ents


p→K+n MC

empty box no bump

Too Easy!!

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Basic Concepts of Dinucleon (Double Proton) Decay Search

Dinucleon Decay: Process where two nucleons interact (e.g. exchange a super-heavy non-standard particle) to produce lighter outgoing particles.

16O (pp) 14C K+ K+

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Basic Concepts of Dinucleon Decay Search

Dinucleon Decay: Process where two nucleons interact (e.g. exchange a super-heavy non-standard particle) to produce lighter outgoing particles.

Experimental Search: Two nucleons in the oxygen atom of a water molecule decay into two kaons, which themselves decay into leptons or pions.

16O (pp) 14C K+ K+

leptons

pions

What we see

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• Violates baryon number (DB=2) and strangeness (DS=2) Sakharov conditions require B violation

• Unlike single proton decay, conserves lepton number (DL=0) Single proton has odd spin, requires DL=1 (p→meson+lepton) Two proton system can decay into just mesons

• Very interesting implications in SUSY frameworks: Requires interaction vertex forbidden by R-Parity: l”uds

(not present in other dinucleon decay modes) Can provide best experimental constraint on l”uds

• Only pp→pions and pp→leptons searched for previously (Frejus) pp→kaons never searched for before

• Because we can! Distinct Cherenkov light pattern in Super-K

Motivations for Search

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Terms in Superpotential that threaten lifetime of proton:

violate lepton number violates baryon number

R-Parity & Proton Stability (1)

l’l’’

p

p0

pe+p0

Proton lifetime clearly too short R-Parity to the rescue!

R-Parity removes all terms listed above to prevent this reaction and preserve proton lifetime

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Terms in Superpotential removed by R-Parity:

violate lepton numberassume: mi, lijk, l’ijk = 0

violates baryon numberassume: l’’ijk ≠ 0

R-Parity & Dinucleon Decay Into Kaons

Lagrangian of B and R-Parity violating SUSY term:

u

ud

u

ud

us-

su-

p

p

K+

K+

g~u~

u~

“...proton stability could also be provided by a symmetry that allows only the lepton-number or baryon-number violating terms.” [1] (emphasis mine)

gives rise to dinucleon decay:

ppK+K+[1] Reduced Fine-Tuning in Supersymmetry with R-Parity ViolationL.M.Carpenter, D.E.Kaplan, E.J.RheePhys. Rev. Lett. 99:211801 (2007)

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Super-Kamiokande

• Super-K is a large water Cherenkov detector• 50 kTon of ultra-pure water• 40m diameter, 40m tall cylinder• 22.5 kTon fiducial volume•Inner Detector region has 11,146 PMTs;40% photo-sensitive coverage of inner wall• Outer Detector region has 1,885 PMTs for veto of cosmic rays• 2.7km water equivalent shielding by rock• Event rate: 8.2 fully contained events/day• SK1 dataset: first 1489.2 days of livetime

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Cherenkov Radiation

Super-K PMTQuantum Efficiency

(UV)

Super-KPMT

20”

photon

photo-electron

avalanche

signa

l

Cherenkov radiation cheat-sheet

Cherenkov angle:cos qC = 1/(nwater⋅b)qC max = acos ( 1/(1.33 1.0) ) = 42°⋅

Cherenkov radiation condition:b > 1/nwater = 1/1.33 = .75

Threshold momentum:pthresh = 1.14 × mass →pthresh(m±) = 120 MeV/cpthresh(p±) = 160 MeV/cpthresh(K±) = 560 MeV/cpthresh(p) = 1070 MeV/c

e±, g: produce EM shower (qC ≈ 42°)p0: immediate decay to 2 × g

∼300 photons/cm

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Showering vs. Non-Showering

EM Showering RingFuzzy patternProduced by: e±, g(, p0)

Non-Showering RingCrisp edgeProduced by: m±, p±, K±, p

Super-K Event Display: 1-ring e- Super-K Event Display: 1-ring m-

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K+

m+n (B.R. 64%)

p+p0 (B.R. 21%)

others (B.R. 15%)

K0S (B.R. 50%)

K0L (B.R. 50%)

p+p- (B.R. 69%)

p0p0 (B.R. 31%)

others (B.R. ~0%)K0

Kaon Final State Branching Ratios:

Dinucleon Decay Signal

kaon pair final state B.R.ppK+K+ m+n m+n 40%ppK+K+ m+n p+p0 26%pnK+K0 m+n p+p- 22%

nnK0K0 p+p- p+p- 12%

nnK0K0 p+p- p0p0 11%

pnK+K0 m+n p0p0 10%

pnK+K0 p+p0 p+p- 7%

ppK+K+ p+p0 p+p0 4%pnK+K0 p+p0 p0p0 3%

nnK0K0 p0p0 p0p0 2%

Final State Branching Ratios:

ppK+K+ pnK+K0 nnK0K0Dinucleon Decayinto Kaon Modes:

Studied in this search

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Signal Characteristics

Dinucleon Decay (“DNDK”) Reaction: 16O(pp) → 14C K+ K+ → m+n p+p0

16O

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K+

14C

K+

∼1.3m ∼1.3m

∼800MeV/c

∼800MeV/c

2 K+ rings• shared vertex• back-to-back• p ≈ 800 MeV/c• qC ≈ 30°• non-showering

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K+

14C

K+

gg

p+

(p 0)

∼1.3m ∼1.3m

∼800MeV/c

∼800MeV/c

(207 MeV/c) 2 or 4 g rings• shared vertex• ∼1.3m from event vertex• 20 < p < 227 MeV/c• 207 MeV/c total momentum• qC ≈ 42°• showering


0 p+ rings• barely above threshold• too little light• decay products below threshold

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K+

14C

K+m+

n

gg

p+

(p 0)

∼1.3m ∼1.3m

∼800MeV/c

∼800MeV/c

236 MeV/c



1 or 2 m+ rings• ∼1.3m from event vertex• p = 236 MeV/c• qC = 34°• non-showering


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K+

14C

K+m+

n

gg

p+

(p 0)

∼1.3m ∼1.3m

∼800MeV/c

∼800MeV/c

236 MeV/c





2 Michel electrons• 1 for each m+

• 1 for each p+

• each 1.3m from event vertex∼• ∼2.6m from each other

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K+

14C

K+m+

n

gg

p+

(p 0)

∼1.3m ∼1.3m

∼800MeV/c

∼800MeV/c

236 MeV/c





2 Michel electrons• 1 for each m+

• 1 for each p+

• each 1.3m from event vertex∼• ∼2.6m from each other

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Super-K Event Display

Inner Detector

Outer Detector

kaons

muons

Signal Monte Carlo Eventpp K+K+ m+n m+n

K+14CK+

m+ n

m+

n

Event Geometry

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Event Reconstruction: Vertex

(ti – t

0 ) cH2O

Data in hand• time and charge of each PMT hit• physical location of each PMT

Vertex Reconstruction Algorithm1. Coarse 3-D grid throughout detector volume2. Calculate goodness at each point3. Find point with maximum goodness4. Fine grid in small volume around best point

from coarse grid5. Calculate goodness at each point6. Find point with maximum goodness

(tj – t0 ) cH2O

test vertex

grid points

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Event Reconstruction: Ring Finding

Ring Finding Algorithm1. Calculate relative location of each PMT in

spherical coordinates w.r.t. event vertex2. Redistribute charge of each PMT in (q,f)-space

using Hough Transformation a) Draw ring around each PMT corresponding

to 42° conical projection from vertexb) Redistribute charge uniformly along ring

3. Find peaks in Hough Transform4. Each peak corresponds to a unique ring

Hough Transformation

Hough Transform of2-Ring Event

Ring 1Ring 2

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Multiple Vertex Fitter

Super-K software designed for single vertex events

Had to create new multi-vertex fitter algorithm

Multi-Vertex Fitter AlgorithmFirst, run standard fitting algorithm

• Gives accurate ring directions• Gives accurate C. angles

Next, loop over all ringsFor each ring…

1. Mask light outside of this ring (q > C. angle + 10°)

2. Subtract remaining light from overlapping rings

3. Run 1-ring fitting algorithm (considers track length)

4. Store results for each PID assumption (e±/g, m±, K±)

∼1.3m

∼1.3m

[masked region] [masked region]

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Ring Classification

Rings are classified as either K+, μ+, or g candidates Ring variables used: momentum, Cherenkov angle, showering likelihood Vertex and direction relative to other rings are also used

Classify Two Kaon Candidates• θ > 154°• Invariant mass < 1950 MeV/c2

• Total momentum < 400 MeV/c• Vertex separation < 640cm• Cherenkov angle < 40°• Loose showering likelihood cut

Example DNDK Signal EventFinal State: K+ K+ m+ n p+ p0

K+K+

m+

ng

gp+

q

Grey: True particle vectors Color: Reconstructed vectors

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Event Categorization

final state B.R. B.R. including hadr. effects

m+n m+n 40% 30%m+n p+p0 26% 19%p+p0 p+p0 4% 3%

sum of above 70% 52%

ABC

3 RingsK+K+m+

K+K+gK+m+m+

4 RingsK+K+m+m+

K+K+m+gK+K+ggK+m+gg

5 RingsK+K+m+ggA, B

B, C

A

A

B

B, C

B

B

Accepted Event Categories:

1. Classify rings according to best pp→K+K+ PID hypothesis (K+, m+, g)2. Categorize event based on ring classifications3. Keep events that fall into categories which match chosen pp→K+K+ final states

Calculated using Monte Carlo;includes inefficiencies due to

K+ hadronic interactions

ring classifications

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Atmospheric Neutrino BackgroundOnly source of backgroundOccurs when neutrino interacts with nucleon in waterAtmospheric n event rate in Super-K: 8 per day∼Only multi-ring events are background to nucleon decayMulti-ring event rate in Super-K: ~2.5 per daySources of rings:• Lepton• Pions • (rarely) Recoil Nucleon

Example Atm. n Single pion production

Background events after precuts

CC: Charged CurrentNC: Neutral Current

Mode FractionCC nm 40.7%NC nm 32.1%CC ne 14.5%NC ne 12.7%

n

p

m-

p0ggW+

n

one ring

two rings

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Categorypp→K+K+ MC Atm. n MC SK1 Data

Total Efficiency Evt./1489d Evt./1489dTrue FV 100% 2771.0 --K+K+m+ 6.1% 0.6 0K+m+m+ 5.6% 6.1 5K+m+gg 4.6% 26.1 22

K+K+m+m+ 2.7% 0.0 0K+K+g 1.1% 0.4 0

K+K+m+g 1.1% 0.3 0K+K+gg 0.6% 0.3 0

K+K+μ+gg 0.2% 0.1 0Total 21.9% 33.9 27

Signal, Background, and Data After Precuts

Breakdown of events by category after precuts

Precuts1. 1000< total p.e. <110002. 3 ≤ number of rings ≤ 53. Fully contained (FC) in

inner detector4. Accepted event category5. Event vertex inside

fiducial volume (FV)

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Multivariate Analysis Tool: Boosted Decision TreeBoosted Decision Tree (BDT)• Yields good results with minimal tuning• Simple: 1-D cut at each node• Insensitive to weak variables

large forest of unique trees

tree i

boost weight:ai = 2.75

tree 1 tree 2 tree N…

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test signalevent

tree i



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test signalevent

tree i



37



test signalevent

tree i


output:hi = +1


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testbackground

event

tree i



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testbackground

event

tree i



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testbackground

event

tree i


output:hi = -1


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Boosted Decision Tree Input Variables (1)

Blue: Signal MCRed: Background MC

ROOT-based TMVA software package was used to implement multi-variate analysis

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Boosted Decision Tree Input Variables (2)

ROOT-based TMVA software package was used to implement multi-variate analysis

37 input variables in total

Blue: Signal MCRed: Background MC

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Train Test Analysis

Total MC

Build BDT Use BDTTune BDT

Divide up Signal & Background MC into 3 samples:

Testing of Boosted Decision Tree

Train and Test Compare Test and Analysis Compare

Tuning Criteria• Good separation between Test Sig and Test Bkg• No large-scale jaggedness in Test Sig near signal-like tail of Test Bkg• Not excessively over-trained

Good agreement between Test sample and Analysis sample shows the BDT has consistent performance on statistically similar inputs

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Boosted Decision Tree Output for Monte Carlo

keepreject keepreject

Background Monte Carlo Signal Monte Carlo

Cut Placement SignalEfficiency

Backgroundevt / 1489 days

0.10 14.4% 0.510.11 13.5% 0.380.12 12.6% 0.280.13 11.5% 0.190.14 10.4% 0.16

Final cut placementGoal: maximum signal efficiency for 0 background events

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Final Performance: pp→K+K+ Signal Monte Carlo

Ring Classification PerformanceClassification Number of

Rings PurityK+ 4615 92.6%m+ 3261 81.8%g 984 67.4%

Event Categorization PerformanceNumber of

EventsAll Rings Correct Purity

2596 1701 65.5%

2/3 of all final signal events had every ring correctly classified.

CategoryPrecuts BDT Cut BDT Efficiency:

Total Efficiency Total Efficiency BDT Cut/PrecutsTrue FV 100% 100% --K+K+m+ 6.1% 5.0% 82%K+m+m+ 5.6% 1.8% 32%K+m+gg 4.6% 1.0% 22%

K+K+m+m+ 2.7% 2.5% 93%K+K+g 1.1% 0.8% 73%

K+K+m+g 1.1% 1.0% 91%K+K+gg 0.6% 0.3% 50%

K+K+μ+gg 0.2% 0.2% 100%Total 21.9% 12.6% 58%

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Final Performance: Atm. n Background Monte Carlo

CC: Charged CurrentNC: Neutral Current

Mode FractionCC nm 63.6%NC nm 21.8%CC ne 14.6%NC ne 0.0%

Mode Events Fraction

CC multi p production 0.11 38.9%

CC single p,D resonance 0.10 35.6%

NC single p,D resonance 0.04 14.6%

NC diffractive p production 0.02 7.3%

CC quasi-elastic 0.01 3.6%

Total 0.28 100%

CategoryPrecuts BDT Cut BDT Reduction:

Evt./1489d Evt./1489d 1-BDT Cut/PrecutsTrue FV 2771.0 2771.0 --K+K+m+ 0.6 0.07 88%K+m+m+ 6.1 0.08 99%K+m+gg 26.1 0.08 ∼100%

K+K+m+m+ 0.0 0.00 100%K+K+g 0.4 0.02 95%

K+K+m+g 0.3 0.03 90%K+K+gg 0.3 0.00 100%

K+K+μ+gg 0.1 0.00 100%Total 33.9 0.28 99%

RemainingBackground

After BDT CutK+ Candidate Rings

True PID Amount % of Totalmuon 12 44.44%pion 8 29.63%

proton 5 18.52%gamma 1 3.70%electron 1 3.70%

Total 27 100.00%

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Comparison of SK1 Data to Atm. n MC

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Dinucleon Decay into Kaons Search Results

0 candidate events were found in the data.Expected Background: 0.28 ± 0.13 events

Signal Efficiency: 12.6% ± 3.2%

Boosted Decision Tree Output

keepreject

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Systematic Term Background Events Signal EfficiencyMonte Carlo

K+ Hadronic Int. -- 1.3%Correlated Decay -- 2.5%Fermi Momentum -- 24.1%Kaon Decay B.R. -- <<1%

ν Flux 8% -- ν Cross Section 15% --

π Nuclear Effects 20% --π Propagation 50% --

Detector Knowledge Fiducial Volume 5.4% 2.2%

Energy Scale <<1% <<1%Event Reconstruction Showering Likelihood 14.3% 2.4%

Ring Counting <<1% <<1%Cerenkov Angle 3.6% 1.0%Vertex Position 16.1% 3.9%

Decay-e Counting <<1% <<1%Ring Momentum 5.4% 0.7%

Analysis Technique BDT 30.4% 4.7%Total 46.3% 25.2%

Estimation of Systematic Uncertainties

Signal Efficiency12.6% ± 3.2%

Expected Background0.28 ± 0.13 events

per 1489.2 days

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Lifetime Limit Calculation

A : Exposure = 91.5 kTon yrs for SK1 datasetNd : Number of Oxygen nuclei = 3.3 x 1031 16O kTon-1

e : Efficiency = 12.6%S90: Signal limit at 90% CL = 2.3

B: expected number of Background events = 0.28

NC: Number of candidate events = 0CL: Confidence Level = .90

Simple Poisson Calculation of Partial Lifetime Limit

Use Bayes’ Theorem for limit calculation that includes systematic errors

at 90% C.L.

Comparisons and Conclusions: Lifetime Limit

[2] W-M Yao et al 2006 J. Phys. G: Nucl. Part. Phys. 33 1

Frejus:• 900 ton iron calorimeter• Beneath Alps near French-Italian border• Ran in 1980s• Only experiment to search for dinucleon decay until now

Frejus dinucleon decay limits (PDG) [2]

(x 1030 years)

Super-K Limit

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two orders of magnitude larger than previous dinucleon decay limits

R-Parity Violating Parameter Limit

[3] R.Goity, M.Sher, Bounds on DB=1 couplings in the supersymmetric standard model, Phys.Lett.B 343:1-2, 1995

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Reasonable calculation by Goity & Sher [3]:

Super-K Limit

best experimental limit

generic nucleon decayand Frejus limits

dinucleon decayinto kaons limit

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Thank you for listening!

Comparisons and Conclusions: R-Parity Violation

[3] R.Goity, M.Sher, Bounds on DB=1 couplings in the supersymmetric standard model, Phys.Lett.B 343:1-2, 1995

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Super-K Limit

Reasonable calculationby Goity & Sher [3]:

best experimental limit

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ppK+K+ 1

Nucleon Decay Limits in Context with Theory

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Event Reconstruction: Cherenkov Angle

After determining vertex and ring direction…1. Plot charge as function of opening angle

relative to ring direction2. Take second derivative of this function3. Define edge of ring as first “0” after

minimum peak

16 O (pp) 14 C K + K +

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