1. Supernova relic neutrinos Kirk Bays December 8, 2011 UC Irvine

2. OUTLINE. 1) Theory and background: supernovae, SN neutrinos, and what has come before 2) Super-K: what is it, how does it work 3) Tools: software used to study neutrinos 4) Event selection: cut out the backgrounds! 5) Remaining backgrounds: understand, model 6) Analysis methodology: fits fits fits 7) Results: getting this is the whole point 8) Discussion: What does it all mean?

3. 1: Theory and background www.smbc-comics.com

4. Supernovae Stars are fueled by nuclear fusion Mostly fuse H into He, as the universe began full of hydrogen When hydrogen is used up, it collapses If the star is massive enough, begins fusing He, becomes layered Stars > ~8 solar masses can fuse elements all the way to iron Iron doesn’t fuse, and without fusion the core collapses on itself This makes the core super-hot and dense; also the collapse rebounds when it becomes dense enough to hit neutron-neutron interactions Rebound shock + emissions from superhot core = supernova

5. Supernova neutrinos Released E: E ~99%, E kinetic ~1%, E light ~0.1% As the core collapses, high temperature and pressure make electron capture favorable: ▫ e + p  n + e (neutronization burst, ~10 44 J, ~10 ms, e ) After the rebound, the core is superheated (~100 billion K), and releases neutrino- antineutrino pairs of all flavors equally. These neutrinos are trapped by the collapsed core, and leak out; they also fuel the explosion (rebound not enough alone) (thermal burst, ~10 46 J,~10 s, all flavors) NC only CC+NC more neutrons Livermore numerical model ApJ 496 (1998) 216

6. SN neutrino bursts SN1987A: first neutrinos definitely seen from farther than the sun Galactic supernova: ~3/century 2140 tons 6800 tons 200 tons scintillator SN 1987A ~10k events Gal. center in SK today: arXiv:hep-ph/0412046v2

7. The DSNB Even though we would not see the burst from far away supernovae, the neutrinos from all supernovae in the history of the universe combined should be a diffuse, detectable signal. This is called the Diffuse Supernova Neutrino Background (DSNB), or Supernova Relic Neutrinos (SRN, `relics’). These terms are interchangeable. This signal has never been seen. Many theorists have constructed models of the DSNB Only a few events/year are expected at SK. This is a rare signal Cosmic Gas Infall – Malaney - R. A. Malaney, Astroparticle Physics 7, 125 (1997) Chemical evolution - D. H. Hartmann and S. E.Woosley, Astroparticle Physics 7, 137 (1997) Heavy Metal Abundance - M. Kaplinghat, G. Steigman, and T. P. Walker, Phys. Rev. D 62, 043001 (2000) Large Mixing Angle - S. Ando, K. Sato, and T. Totani, Astroparticle Physics 18, 307 (2003) (updated NNN05) Failed Supernova - C. Lunardini, Phys. Rev. Lett. 102, 231101 (2009) (assume Failed SN rate = 22%, EoS = Lattimer-Swesty, and survival probability = 68%.) 6/4 MeV FD spectrum - S. Horiuchi, J. F. Beacom, and E. Dwek, Phys. Rev. D 79, 083013 (2009).

8. Anatomy of a DSNB model Main ingredients: star formation history, spectrum Star formation history well measured in recent years As most SN s thermally produced, use Fermi-Dirac spectrum: Leaves 2 free parameters: = luminosity, T = temperature Downside: FD imperfect description  = DSNB flux z = red shift parameter R SN = CC SN rate R SF = star formation rate S. Horiuchi, J. F. Beacom, and E. Dwek, Phys. Rev. D 79, 083013 (2009)

9. Current knowledge In 2003, SK published a paper detailing the first SRN search at SK Final 90% CL flux limit: ▫1.2 cm -2 s -1 19.3<E <83.3 MeV 100x previous limit Most stringent limit ever Methodology: implement cuts to remove most backgrounds Model remaining backgrounds  2 fit (SNR + 2 backgrounds) No indication for SNR events Many theories predict the SRN signal to be on the edge of this limit I have now improved this study significantly L. Strigari, M. Kaplinghat, G. Steigman, T. Walker, The Supernova Relic Neutrino Backgrounds at KamLAND and Super-Kamiokande, JCAP 0403 (2004) 007 ‘Our best estimate for the flux at Super-K is slightly below, but very close to the current SK upper limit. …We estimate that the SRN background should be detected (at 1σ) at Super-K with a total of about 9 years (including the existing 4 years) of data.’ Phys. Rev. Lett. 90, 061101 (2003) decay e’s from `invisible’   ’s e CC 90% CL SRN

10. 2. The Super-Kamiokande detector

11. Super-Kamiokande ‘Inner Detector’, ID ~11,150 inward facing photomultiplier tubes single photon sensitivity ~40% surface coverage 11 39.3 m 41.4 m ‘Outer Detector’, OD Optically separate from ID 1885 outward facing PMTs Water system: filtration, degasification, water flow water entering tank 18.2 MΩ*cm leaving tank 11 MΩ*cm 35-70 tons/hour water flow Radon system: 99.98% effective at reducing radon reduces background, worker health 26 Helmholtz coils reduce Earth’s magnetic field by factor of 9 ID fiducial volume two meters from PMTs; 32.5 ktons -> 22.5 Ktons Kamioka neutrino detection experiment underground 2700 m.w.e. 50 ktons

12. Detector History April 1 1996: begin data taking July 15 2001: stop for maintenance Nov 11 2001: Accident destroys ~60% of PMTs while refilling Oct 8 2002: Masatoshi Koshiba awarded Nobel Prize in physics (25%) Dec 6 2002: Surviving PMTs repositioned, start data taking again Feb 2003: First SRN paper published Late 2005: begin full repair 2006: Kirk joins the team! June 2006: Full repairs complete, start new data taking Aug 2008: Full electronics upgrade Sep 2008: continue data taking Nov 2011: SRN paper submitted to PRD! 12 SK-I (40% coverage, 1497 live days 11,146 PMTs) SK-III (40% coverage, 562 live days) SK-II (19% coverage, 794 live days) SK-IV (40% coverage)

13. Physics in SK High energy particles interact in the water, create light via the well known Cherenkov effect For DSNB events, inverse beta decay is by far the dominant mode arXiv:hep-ph/0412046v2 e - kinetic E (MeV) Event rate (/yr/MeV) Astroparticle Physics 3 (1995) 367-376

14. Triggering, DAQ 14 Dark noise: 3-5 KHz. PMT timing resolution ~3 ns Lower trigger thresholds can detect lower energy events Limited by computing power 2 channels/PMT keep detector mostly dead-time free SK-IV electronics different, not discussed here The Super-Kamiokande Detector The Super-Kamiokande Collaboration, Nucl. Instrum. Meth. A501(2003)418-462.3 p.e. -11 mV Final trigger records data in 1.3 μs range (one ‘event’)

15. Calibration LINAC:  Most important calibration source  Old medical linear accelerator, on site  Shoots mono-energetic electrons ( 5 – 18 MeV) into known positions  Energy known to within 20 KeV  Primary calibration of absolute energy scale (accurate to within 1%)  Also useful for energy resolution, angular resolution, spatial resolution Xe/laser source and scintillator ball:  Helps fine tune high voltage to regulate individual PMT gain N 2 laser and diffuser ball:  Relative PMT timing, ‘tq map’ Deuterium-tritium neutron generator (DT):  double check absolute energy scale, trigger efficiency Decay electrons:  determines water transparency for LE group, stability of energy scale 15 Nucl. Instrum. Meth. A501(2003)418-462

16. Signals in SK 16 Atmospheric neutrinos up to TeV Reactor, solar, relic s (all < 21 MeV) Cosmic ray muons (~2Hz) Spallation (<24 MeV) Stopping muon decay electrons …. solar atmospheric

17. 3. Tools

18. e - /e + reconstruction Vertex fitting: Electrons travel ~10 cm before stopping This is on the order of resolution; can consider a point-like event Reconstructed with BONSAI (by Michael) ▫ uses only the PMT timing information ▫ fits a dark noise component ▫ constructs likelihood, compares to likelihood derived from LINAC data ▫ best resolution of all SK fitters Energy fit: Charge determination for PMTs poor at low levels, assume 1 p.e. per hit Takes into account dark noise, water transparency, geometry, occupancy correction E resolution ~10% @ 18 MeV Direction Fit: Likelihood fit; resolution ~20 degrees Vertex, direction, and energy reconstruction tools are the same as used for the long established SK solar analyses All energies quoted are total electron equivalent energy 18 M.B. Smy, Low Energy Challenges in Super- Kamiokande-III, Nuc. Phy. B, 168, pg 118-121 (2007)

19. Cherenkov angle Reconstructing the Cherenkov angle important for particle ID Reconstruction algorithm takes 3 hit PMTs, forms a cone with an opening angle; looks at all 3-hit combinations, fits to peak of distribution Events with multiple particles, gammas, emit light more isotropically; algorithm biases these to high angles Width of distribution also can be used to discriminate e’s vs  ’s e 

20. Muon fitting Main muon fitter name Muboy Better track resolution than fitter used in 2003 (entry point resolution ~100cm, direction resolution ~6 deg.) Can categorize muons by type: ▫ Single through-going (~82%) ▫ Stopping (~7%) ▫ Multiple muons (2 types) (~7%) ▫ Corner clipper (~4%) ▫ Can’t fit (<1%) We can make a dE/dx distribution of muon track based on Muboy fit Also developed an alternate fitter (Brute Force Fitter, BFF) for when Muboy fails; can refit ~75% of misfit singles dE/dx get dE/dx using timing info assume light travels at v=c/n and muon at v = c; determine where along track light originated quadratic Eqn w/ 2 solutions, keep both Take into account corrections based on water transparency, coverage

21. Multiple Coulomb scattering Electrons can multiple Coulomb scatter in the detector It can be useful to estimate how much an electron scatters Select PMT, construct cone w/ 42 o angle from vertex to PMT; intersection points of cones gives unit vectors Do this for all combination of 2 hit PMTs Vector adding all the direction unit vectors/ # unit vectors gives a value between 0 (completely unaligned) to 1 (all perfectly aligned) This value is used as a `goodness’; estimates multiple Coulomb scattering Best Fit Direction

22. 4. Event selection

23. First reduction SK records immense amount of data Much of this can be removed with some simple cuts Eliminates major backgrounds and makes the rest of the data more manageable Similar to solar first reduction OD triggered events > 2,000 p.e. (1,000 SK-II) > 800 hit tubes (400 SK-II) Calibration events Outside fiducial volume 90 MeV Electronics noise remove: muons reduces data volume by ~2 orders of magnitude

24. Spallation Even at 2700 m.w.e., cosmic ray muons enter detector at ~2Hz The muons can spall on oxygen nuclei, create radioactive products whose decays (mostly beta decays) can mimic SRNs Spallation occurs < 24 MeV; lower the energy, the more spallation Dominant low energy background Want final sample spallation free, as it is hard to model; determines analysis lower energy threshold Spallation eliminated by correlating to preceding muons spallation products expected in SK Spallation cut in 2003: lose 36% signal efficiency uses cut tuned for solar only down to 18 MeV

25. 4 variable likelihood cut The 4 variables: ▫ dl Longitudinal ▫ dt ▫ dl Transverse ▫ Q peak Muboy: better resolution μ fit Tune separate likelihoods for each muon type (single, multiple, stopping) distance along muon track (50 cm bins) p.e.’s Spallation Cut Q Peak = sum of charge in window spallation expected here μ entry point μ track dl Transverse where peak of dE/dx plot occurs dl Longitudinal dE/dx Relic Candidate old likelihood new Correlate events to all muons within previous 30 seconds Muons within 30 seconds after relic candidates make final sample Data sample – random sample = spall sample Make likelihoods (PDFs) for each variable

26. Spallation cut SK-I/III cut combined; SK-II different Additional tracks for multiple muons have own special PDFs If Muboy fails fit, check BFF Examples for SK-I/III singles Q PEAK p.e. (x 10 3 )

27. Spallation cut Improvements allow lowering of energy threshold Requires 2-stage cut Inefficiency calculated for all detector (position dependent) SRN MC vertex distribution used to get overall inefficiency 2003 Old cut 18 < E < 34: 36% signal ineff. New Cut (SK-I/III): 16 < E < 18 MeV: 18% signal ineff. 18 < E < 24 MeV: 9% signal ineff. New Cut (SK-II): 17.5 < E < 20 MeV: 24% signal ineff. 20.0 < E < 26 MeV: 12% signal ineff.

28. Solar 8 B and hep neutrinos are a SRN background (hep at 18 MeV, and both at 16 MeV, because of energy resolution) Cut criteria is optimized using 8 B /hep MC 2003: 1 cut < 34 MeV New cut is now energy dependent, tuned in 1 MeV bins hep 8B8B pep pp e recoil energy (total) (MeV) energy resolution for an event of energy: 16 MeV 18 MeV Solar ν Events 7 Be 1618

29. Solar cut Solar events cut using  sun cos(  sun ) = 1 if reconstructed direction matches sun 2003 cut: remove cos(  sun )>0.87 for all events E < 34 MeV ~15 degree resolution from the physics; multiple scattering of electron makes resolution worse Use multiple Coulomb scattering estimator `MSgood’ to improve efficiency by using a separate cut for each MSgood bin, for each 1 MeV energy bin combined MSgood < 0.4 0.4 < MSgood < 0.5 0.5 < MSgood < 0.6 0.6 < MSgood integrated cos( θ sun )

30. Determine optimal cut points using `significance’ function Significance assumes dominant decay-e background only, represents signal/sqrt(background) Number of solar events modeled using MC spectrum, normalized using data < 16 MeV SK-I/III solar cut same, SK-II different Solar cut cos( θ sun ) significance Significance:  = cut efficiency  = cut effectiveness N solar = # solar ev  = # background ev  * N solar = # solar events after cut applied

31. Incoming event cut Large amounts of background exists near the walls Much is removed by the fiducial volume cut; some survives The d eff variable can help discriminate these events without the inefficiency of removing more volume Incoming events will have smaller d eff ; also incorrectly fit events that are really near the wall tend to have small d eff Retune SK-I to increase efficiency SK-II and SK-III separately tuned; not enough statistics for energy dependent tuning remaining removed (2003) recovered (now)

32. More cuts multiple timing peak multiple rings Pion cut ▫ uses width of 3-hit combination distributions OD correlated ▫ check hit ID tubes for correlations in time and space to OD hit tubs, even if no OD trigger Pre-post activity ▫ remove events +/- 50  s; for SLE events require 5 m correlation

33. Efficiency Efficiency greatly increased from 2003 With lower energy threshold, efficiency is 87% greater in SK-I Including new SK-II and SK-III data, efficiency is increased by 227% Sensitivity improvement: ▫ sqrt(3.3)  80% better sensitivity Systematic errors calculated on efficiency; mostly from studying LINAC data vs LINAC MC final efficiency (sys error) SK-I

34. 5. Remaining backgrounds www.smbc-comics.com

35. Cut backgrounds single muons dt (s) final sample data random sample After cuts, want final sample `free’ of these backgrounds (spallation, solar, pions, decay electrons, etc) Check many distributions to try and determine if this is true Due to low statistics, very difficult to be sure backgrounds completely gone; can only so no statistically significant amount remaining Estimated remaining in SK-I/II/III Spall: < 4 Solar: < 2 d eff cut: < 2 Any remaining background likely to make limit more conservative

36. Remaining Backgrounds Final sample still mostly backgrounds, from atmospheric interactions; modeled w/ MC 1)  CC events – muons from atmospheric  ’s can be sub-Cherenkov; their decay electrons mimic SRNs – modeled with decay electrons 2) e CC events – indistinguishable from SRNs 3) NC elastic – low energy mostly 4 )  /  events – combination of muons and pions remaining after cuts all SRN cuts applied # events estimated in SK-I Backgrounds 1) and 2) were considered in the 2003 study. Backgrounds 3) and 4) are new! SK-I backgrounds

37. SRN events expected (98% SK-I) in the central, signal region (38-50 o ) ‘Sidebands’ previously ignored Now that we consider new background channels, sidebands useful ▫ NC elastic events occur at high C. angles ▫  /  events occur at low C. angles Sidebands help normalize new backgrounds in signal region not used e e+e+ p n (invisible) Signal region 42 o μ, π Low angle events 25-45 o NC region N reconstructed angle near 90 o

38. 6. Analysis methodology

39. Maximum likelihood fit 2003 study used binned  2 to fit final sample Found that changing the binning could change answer (up to 20%) Instead use unbinned maximum likelihood fit Fit all 4 backgrounds in all three Cherenkov regions, (for SK-I/II/III each), make PDFs Also make PDFs for all relic models Loops over all combinations of events, maximize likelihood F is the PDF for a particular channel; E is the event energy; c is the magnitude of each channel; i represents a particular event, and j represents a channel (SRN + 4 backgrounds)

40. Systematic errors Many systematics considered, were not considered in 2003 All the systematics operate by distorting the likelihood 1) Energy resolution/ E scale ▫ Error on MC ▫ considered independent ▫ distortions added in quadrature 2) Energy independent efficiency ▫ Systematic from cut reduction ▫ Also cross section, FV errors Spectral shape systematics ▫ Apply very conservative errors to NC elastic, e CC channels. ▫ decay electron background from data, no error; neglect  /  L(r)  L’(r,  ) Make likelihood function of amount of distortion Then sum all combinations of distorted likelihoods, weighed by Gaussian envelope example: E res/scale L =c 1 PDF 1 (E) + c 2 p 2 (E) …. SRN decay-e apply E res/scale distortion to PDF1: L(  ) =c 1 PDF 1 (E,  ) + c 2 p 2 (E) …. sum with weights for new likelihood

41. 7. Results

42. Fit results Ando et al.’s LMA model; SRN best fit 0

43. Fit results SK-II and SK-III give a positive fit for SRN signal This positive indication is not significant

44. New Results: flux limits ( cm -2 s -1, 90% cl) E e+ > 16 MeVSK-ISK-IISK-IIICombinedPredicted LMA (03) <2.5<7.7<8.0<2.91.7 Cosmic gas Infall (97) <2.1<7.5<7.8<2.80.3 Heavy Metal (00) <2.2<7.4<7.8<2.80.4 - 1.8 Failed Supernova (09) <2.4<8.0<8.4<3.00.7 Chemical Evolution (97) <2.2<7.2<7.8<2.80.6 6 MeV (09)<2.7<7.4<8.7<3.11.5

45. LMA = Ando et al (LMA model) HMA = Kaplinghat, Steigman, Walker (heavy metal abundance) CGI = Malaney (cosmic gas infall) FS = Lunardini (failed SN model) CE = Hartmann/Woosley (chemical evolution) 4/6 MeV = Horiuchi et al n temp Kamiokande 1987A allowed IMB 1987A allowed

46. 8. Discussion

47. /cm 2 /s >18 MeV Published limit (SK-I only)1.2 cross section update to Strumia-Vissani1.2  1.4 Gaussian statistics  Poissonian statistics in fit1.4  1.9 New SK-I Analysis: E THRESH 18  16 MeV (2.5  1.7) ε = 52%  78 % (LMA) (small statistical correlation in samples) improved fitting method takes into account NC 1.7 New SK-I/II/III combined fit1.7  2.0 (2.9 > 16 MeV) COMPARISON TO PUBLISHED LIMIT 2003 now

48. What’s next for SRNs? Analysis already includes 176 ton-years of data Now highly optimized Further improvements will be slow There is some hope for background reduction in SK-IV with new electronics (neutron tagging) Still, it is unlikely that a discovery can be made at SK in the near future Gd doping could be a solution ▫ neutron tagging allows background reductions ▫ removes most spallation, lower energy threshold Otherwise wait for next generation detectors

49. 49 END.

50. Backups:

51. Energy reconstruction Start with N hit = number hit PMTs (within 50 ns window) Assume 1 p.e. per PMT Convert to `Effective’ # hits = # p.e.  dark = dark noise,  tail = MCS tail N all /N norm = bad channel correction R cover = cathode coverage S = angular coverage correction = water transparency r = distance from vertex to PMT G = gain factor X = occupancy Occupancy: ▫ search surrounding PMTs to guess true # p.e.’s in PMT Take PMT as center of 3x3 patch Use Poissonian probability: ▫ P(k; )= k e - /k! Assume all hit PMTs see same #p.e. N = total # p.e.’s seen; =N/9 x i = fraction hit in 3x3 patch P(>=1)=1-P(0)=1-e - =x i  log(1/(1-x i ))=#p.e./9PMTs Not all PMTs hit; want #p.e./hit PMT #p.e./hit PMT = /x i =log(1/(1-x i ))/x i

52. LINAC DT generator: 2 H+ 3 H  4 H+n (n = 14.2 MeV) n + 16 O  16 N + p 16 N decay (7.13 s halflife) 1)(66%) 6.13 MeV  +  2)(28%)  10.4 MeV total Q (isotropic)

53. Solar Cut 16-17 MeV 26.2%/0.11 17-18 MeV 17.9%/0.12 18-19 MeV 12.2%/0.04 19-20 MeV 3.5%/0.08 TOTAL 15%/.35 20 MeV ~ 0.05 events in total no cut necessary SK-I/III ineff/#remain 1617181920 cut 1 cut 2 cut 3 cut 4 SK-I/III SK-II + ~1MeV E (MeV) SK-I SK-II

54. Near Invisible Muon Sample E (MeV) from decay electrons that can be correlated to low energy muons with no OD trigger (from atm. neutrinos) `near invisible’ and most like real background

55. SK-II - Spallation Sample Invert SK-I/III spallation cut to get a ‘spallation sample’ of spallation events Fit spectrum to exponential Have SK-I, SK-II energy resolution functions from SK-II solar paper Solve for S actual Get Compare spectrums 55

56. 56 16 18 17(MeV) 17.4 MeV  round to 17.5 MeV SK-I SK-II

57. SK-I SK-II SK-III

58. Systematics: Inefficiency Define: ▫ r = # relic events we see in data ▫ R = # relic events actually occurring in detector ▫ ε = efficiency (SK-I/II/III dependent) ▫ assume ε follows a probability distribution P(ε) ▫ assume P(ε) is shaped like Gaussian w/ width σ ineff ▫ then we alter likelihood: then the 90% c.l. limit R 90 is such that σ ineff SK-I: 3.5% SK-II: 4.7% SK-III: 3.4%

59. Systematics: energy scale, resolution Method : ▫ Use MC, parameterize effects ▫ ie for e-res, parameterize : f e-resolution (E) = (E true +(E recon - E true )*error) δ(E) = (f e-scale (E) 2 + f e-resolution (E) 2 ) 1/2 59 e-scale e-res SK-I: 1% 2.5% SK-II: 1.5% 2.5% SK-III: 1% 2.5%

60. Systematics: NC elastic Keep spectra the same Change normalization in signal region by 100% ▫ +1  = double (14.8% SK-I) ▫ -1  = 0% Because of physical bound, apply error asymmetrically (-1  to +3  ) Instead of standard Gaussian weighing function (appropriate for symmetric case), use a weighted Gaussian function Maintain necessary properties: ▫ expectation value = 0 ▫ variance =  2 SK-I NC elastic normalization 20-38 º 38-50 º 78-90 º 5.6%7.4%87% #  affect Weighing function applied (weighted Gaussian)

61. Systematics: e CC For n e CC case, keep normalization, distort spectrum Use large error of 50% at 90 MeV (0 distortion at 16 MeV, linear between) Use same range (-1 to 3 s) and weighing function as NC case -2 s would bring spectrum to 0 at 90 MeV, which is unphysical No distortion -1  +1  SK-I e CC PDF same weight fxn as NC case

62. dE/dx BFF good

63. other cuts: pre/post activity, pion, OD correlated, electronics noise

64. decaye

65. NC study Lots of 15.1 MeV  and pion absorption events in MC 15.1 MeV  ’s from mistake in NEUT code (improper branching ratio). Was 1.3% should be 0.007% Pion absorption also incorrect the  -rays from 14 N are >99% < 7.6 MeV. Ignore both incorrect event types all NC 15.1 MeV  pion abs 15 (MeV) 10 5 0 14 N p+ 13 C 1 + (g.s.) 0 + (2.31) 1 + (3.95) 2 + (7.03) 3 + (11.05) S p =7.55Me V  S p =7.550MeV  S n =10.55MeV

66. NC background all NC (after fixes) single p NC elastic multi-pi all NC (SK-I): neglect  -,  + > 200  + < 200  0  on O Most important basically Michel can be modeled linear comb. other backgrounds ignore

67. atm flux http://arxiv.org/abs/1102.2688v1