16 O (pp)  14 C K + K +

Looking for Double Proton Decay at Super-Kamiokande …because single proton decay is just too easy! 16O (pp) 14C K+ K+ Michael Litos Boston University Super-Kamiokande Collaboration March 11, 2010

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. Proton decay methodology: Swap the large numbers t ∼1032 years ∼1 proton t ∼1 year ∼1032 protons

How to Search for Single Proton Decay p→e+p0 p→K+n p→e+p0 MC • Experimental Signature • 3 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 • Experimental Signature • 1 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 p→K+n MC Atm. n MC (500 years) PTOT (MeV/c) SK-1 Data (1489 days) SK-1 Data (1489 days) Events empty box no bump Pm (MeV/c) MINV (MeV/c2)

How to Search for Single Proton Decay p→e+p0 p→K+n p→e+p0 MC • Experimental Signature • 3 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 • Experimental Signature • 1 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 p→K+n MC Atm. n MC (500 years) PTOT (MeV/c) SK-1 Data (1489 days) SK-1 Data (1489 days) Too Easy!! Events empty box no bump pm (MeV/c) MINV (MeV/c2)

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+

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 What we see pions

Motivations for Search • 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

R-Parity & Proton Stability (1) Terms in Superpotential that threaten lifetime of proton: violate lepton number violates baryon number l’’ l’ 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 p p0 pe+p0

R-Parity & Dinucleon Decay Into Kaons Terms in Superpotential removed by R-Parity: violate lepton number assume: mi, lijk, l’ijk = 0 violates baryon number assume: l’’ijk ≠ 0 Lagrangian of B and R-Parity violating SUSY term: gives rise to dinucleon decay: “...proton stability could also be provided by a symmetry that allows only the lepton-number orbaryon-number violating terms.” [1](emphasis mine) - u s u u K+ K+ - s u p p d d u u ~ ~ ~ g u u [1] Reduced Fine-Tuning in Supersymmetry with R-Parity Violation L.M.Carpenter, D.E.Kaplan, E.J.Rhee Phys. Rev. Lett. 99:211801 (2007) ppK+K+

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

Cherenkov Radiation • Cherenkov radiation cheat-sheet • Cherenkov angle: • cosqC = 1/(nwater⋅b) • qC max = acos ( 1/(1.33⋅1.0) ) = 42° • Cherenkov radiation condition: • > 1/nwater = 1/1.33 = .75 • Threshold momentum: • pthresh = 1.14 × mass → • pthresh(m±) = 120 MeV/c • pthresh(p±) = 160 MeV/c • pthresh(K±) = 560 MeV/c • pthresh(p) = 1070 MeV/c • e±, g: produce EM shower (qC≈ 42°) • p0: immediate decay to 2 × g photon Super-K PMT signal photo- electron 20” avalanche Super-K PMT Quantum Efficiency (UV) ∼300 photons/cm

Showering vs. Non-Showering Super-K Event Display: 1-ring e- Super-K Event Display: 1-ring m- EM Showering Ring Fuzzy pattern Produced by: e±, g(, p0) Non-Showering Ring Crisp edge Produced by: m±, p±, K±, p

Dinucleon Decay Signal Dinucleon Decay into Kaon Modes: pnK+K0 nnK0K0 ppK+K+ Kaon Final State Branching Ratios: Final State Branching Ratios: Studied in this search m+n (B.R. 64%) p+p- (B.R. 69%) K+ p+p0 (B.R. 21%) K0S (B.R. 50%) p0p0 (B.R. 31%) K0 others (B.R. 15%) K0L (B.R. 50%) others (B.R. ~0%)

Signal Characteristics Dinucleon Decay (“DNDK”) Reaction: 16O(pp) → 14C K+ K+ → m+np+p0 16O

Signal Characteristics Dinucleon Decay (“DNDK”) Reaction: 16O(pp) → 14C K+ K+ → m+np+p0 • 2 K+ rings • shared vertex • back-to-back • p ≈ 800 MeV/c • qC ≈ 30° • non-showering K+ K+ ∼800MeV/c ∼800MeV/c 14C ∼1.3m ∼1.3m

Signal Characteristics Dinucleon Decay (“DNDK”) Reaction: 16O(pp) → 14C K+ K+ → m+np+p0 • 2 K+ rings • shared vertex • back-to-back • p ≈ 800 MeV/c • qC ≈ 30° • non-showering • 0 p+ rings • barely above threshold • too little light • decay products below threshold K+ K+ ∼800MeV/c ∼800MeV/c p+ 14C g g (p0) (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 ∼1.3m ∼1.3m

Signal Characteristics Dinucleon Decay (“DNDK”) Reaction: 16O(pp) → 14C K+ K+ → m+np+p0 • 2 K+ rings • shared vertex • back-to-back • p ≈ 800 MeV/c • qC ≈ 30° • non-showering • 0 p+ rings • barely above threshold • too little light • decay products below threshold • 1 or 2 m+ rings • ∼1.3m from event vertex • p = 236 MeV/c • qC = 34° • non-showering 236 MeV/c ∼800MeV/c ∼800MeV/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 K+ K+ m+ (207 MeV/c) p+ 14C g g (p0) n ∼1.3m ∼1.3m

Signal Characteristics Dinucleon Decay (“DNDK”) Reaction: 16O(pp) → 14C K+ K+ → m+np+p0 • 2 K+ rings • shared vertex • back-to-back • p ≈ 800 MeV/c • qC ≈ 30° • non-showering • 0 p+ rings • barely above threshold • too little light • decay products below threshold • 1 or 2 m+ rings • ∼1.3m from event vertex • p = 236 MeV/c • qC = 34° • non-showering 236 MeV/c ∼800MeV/c ∼800MeV/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 K+ K+ m+ (207 MeV/c) p+ 14C g • 2 Michel electrons • 1 for each m+ • 1 for each p+ • each ∼1.3m from event vertex • ∼2.6m from each other g (p0) n ∼1.3m ∼1.3m

Super-K Event Display Signal Monte Carlo Event pp  K+K+m+nm+n Outer Detector Inner Detector kaons muons Event Geometry 14C K+ K+ m+ m+ n n

Event Reconstruction: Vertex • Data in hand • time and charge of each PMT hit • physical location of each PMT • Vertex Reconstruction Algorithm • Coarse 3-D grid throughout detector volume • Calculate goodness at each point • Find point with maximum goodness • Fine grid in small volume around best point from coarse grid • Calculate goodness at each point • Find point with maximum goodness (tj – t0) cH2O (ti – t0) cH2O test vertex grid points

Event Reconstruction: Ring Finding • Ring Finding Algorithm • Calculate relative location of each PMT in spherical coordinates w.r.t. event vertex • Redistribute charge of each PMT in (q,f)-space using Hough Transformation  • Draw ring around each PMT corresponding to 42° conical projection from vertex • Redistribute charge uniformly along ring • Find peaks in Hough Transform • Each peak corresponds to a unique ring Hough Transformation Ring 2 Ring 1 Hough Transform of 2-Ring Event

Multiple Vertex Fitter Super-K software designed for single vertex events  Had to create new multi-vertex fitter algorithm • Multi-Vertex Fitter Algorithm • First, run standard fitting algorithm • Gives accurate ring directions • Gives accurate C. angles • Next, loop over all rings • For each ring… • Mask light outside of this ring (q > C. angle + 10°) • Subtract remaining light from overlapping rings • Run 1-ring fitting algorithm (considers track length) • Store results for each PID assumption (e±/g, m±, K±) [masked region] [masked region] ∼1.3m ∼1.3m

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 Example DNDK Signal Event Final State: K+ K+m+np+p0 • 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 q p+ m+ g K+ K+ n g Grey: True particle vectors Color: Reconstructed vectors

Event Categorization Classify rings according to best pp→K+K+ PID hypothesis (K+, m+, g) Categorize event based on ring classifications Keep events that fall into categories which match chosen pp→K+K+ final states ring classifications Accepted Event Categories: A B 3 Rings K+K+μ+ K+K+γ K+μ+μ+ 4 Rings K+K+μ+μ+ K+K+μ+γ K+K+γγ K+μ+γγ 5 Rings K+K+μ+γγ C A B A, B B B, C Calculated using Monte Carlo; includes inefficiencies due to K+hadronic interactions B, C A B

Atmospheric Neutrino Background • Only source of background • Occurs when neutrino interacts with nucleon in water • Atmospheric n event rate in Super-K: ∼8 per day • Only multi-ring events are background to nucleon decay • Multi-ring event rate in Super-K: ~2.5 per day • Sources of rings: • Lepton • Pions • (rarely) Recoil Nucleon n m- one ring W+ Example Atm. n Single pion production p0gg Background events after precuts n p two rings CC: Charged Current NC: Neutral Current

Signal, Background, and Data After Precuts Precuts 1000< total p.e. <11000 3 ≤ number of rings ≤ 5 Fully contained (FC) in inner detector Accepted event category Event vertex inside fiducial volume (FV) Breakdown of events by category after precuts

Multivariate Analysis Tool: Boosted Decision Tree • Boosted 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 1 tree 2 tree N tree i boost weight: ai = 2.75

Multivariate Analysis Tool: Boosted Decision Tree • Boosted 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 1 tree 2 tree N tree i test signal event boost weight: ai = 2.75

Multivariate Analysis Tool: Boosted Decision Tree • Boosted 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 1 tree 2 tree N tree i test signal event boost weight: ai = 2.75 output: hi = +1

Multivariate Analysis Tool: Boosted Decision Tree • Boosted 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 1 tree 2 tree N tree i test background event boost weight: ai = 2.75

Multivariate Analysis Tool: Boosted Decision Tree • Boosted 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 1 tree 2 tree N tree i test background event output: hi = -1 boost weight: ai = 2.75

Boosted Decision Tree Input Variables (1) Blue: Signal MC Red: Background MC ROOT-based TMVA software package was used to implement multi-variate analysis

Boosted Decision Tree Input Variables (2) Blue: Signal MC Red: Background MC ROOT-based TMVA software package was used to implement multi-variate analysis 37 input variables in total

Testing of Boosted Decision Tree Total MC Divide up Signal & Background MC into 3 samples: Test Analysis Train Tune BDT Use BDT Build BDT Test and Analysis Compare Train and Test Compare Good agreement between Test sample and Analysis sample shows the BDT has consistent performance on statistically similar inputs • 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

Boosted Decision Tree Output for Monte Carlo Background Monte Carlo Signal Monte Carlo reject reject keep keep Final cut placement Goal: maximum signal efficiency for 0 background events

Final Performance: pp→K+K+ Signal Monte Carlo 2/3 of all final signal events had every ring correctly classified.

Final Performance: Atm. n Background Monte Carlo Remaining Background After BDT Cut CC: Charged Current NC: Neutral Current

Comparison of SK1 Data to Atm. n MC

Dinucleon Decay into Kaons Search Results Boosted Decision Tree Output reject keep 0 candidate events were found in the data. Expected Background: 0.28 ± 0.13 events Signal Efficiency: 12.6% ± 3.2%

Estimation of Systematic Uncertainties Expected Background 0.28 ± 0.13 eventsper 1489.2 days Signal Efficiency 12.6% ± 3.2%

Lifetime Limit Calculation Simple Poisson Calculation of Partial Lifetime Limit A : Exposure = 91.5 kTon yrs for SK1 dataset Nd: Number of Oxygen nuclei = 3.3 x 103116O 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 = 0 CL: Confidence Level = .90 Use Bayes’ Theorem for limit calculation that includes systematic errors at 90% C.L.

16 O (pp)  14 C K + K +

16 O (pp)  14 C K + K +

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