1. Details of the MiniBooNE Oscillation Result Chris Polly, Indiana University

2. 2Chris Polly, Urbana Seminar, 27 Apr 2007 University of AlabamaLos Alamos National Laboratory Bucknell UniversityLouisiana State University University of Cincinnati University of Michigan University of ColoradoPrinceton University Columbia UniversitySaint Mary’s University of Minnesota Embry Riddle University Virginia Polytechnic Institute Fermilab Western Illinois University Indiana UniversityYale University The MiniBooNE Collaboration

3. 3Chris Polly, Urbana Seminar, 27 Apr 2007 Neutrino Oscillations  oscillations first postulated by Pontecorvo in 1957, based on analogy to kaons. A non-zero n mass allows for lepton flavor changes. mass eigenstates ≠ flavor eigenstates: Flavor composition changes as n propagates: For simple 2-neutrino mixing: Many experiments have hunted for n oscillations, some have found them!

4. 4Chris Polly, Urbana Seminar, 27 Apr 2007 Evidence for n oscillations First evidence came in 1968 from Davis' solar n e experiment found 1/3 of the expected e from sun disappearance e → x Δ m 12 2 ̴ 810 -5 eV 2, sin 2 (2  ) ~ 0.8 Confirmed by SNO, Super-K, Kamland New mixing found by Super-K through atmospheric  oscillations found 1/2 as the upward  as downward disappearance  → x Δ m 23 2 ̴ 210 -3 eV 2, sin 2 (2  ) ~ 1.0 Confirmed by IMB, Soudan, K2K, and most recently MINOS Only one unconfirmed observation!

5. 5Chris Polly, Urbana Seminar, 27 Apr 2007 — — MiniBooNE's motivation...LSND LSND found an excess of e in  beam Signature: Cerenkov light from e + with delayed n-capture (2.2 MeV) Excess: 87.9 ± 22.4 ± 6.0 (3.8  ) Other experiments, i.e. Karmen and Bugey, have ruled out portions of the LSND signal MiniBooNE was designed to cover the entire LSND allowed region

6. 6Chris Polly, Urbana Seminar, 27 Apr 2007 Interpreting the LSND signal e        m 2 atm ~2.4x10 –3 eV 2  m 2 sol ~8x10 –5 eV 2 The other two measured mixings fit conveniently into a 3-neutrino model With  m 13 2 =  m 12 2 +  m 23 2, the LSND  m 2 ~ 1 eV 2 does not fit 'Simplest' explanation...a 4 th neutrino Width of the Z implies 2.994 + 0.012 light neutrino flavors Requires 4 th neutrino to be 'sterile' or an even more exotic solution Sterile neutrinos hep-ph/0305255 Neutrino decay hep-ph/0602083 Lorentz/CPT violation hep-ex/0506067 Extra dimensions hep-ph/0504096

7. 7Chris Polly, Urbana Seminar, 27 Apr 2007 The MiniBooNE design strategy Start with 8 GeV proton beam from FNAL Booster Add a 174 kA pulsed horn to gain a needed x6 Requires running (not anti- ) to get flux Pions decay to with E in the 0.8 GeV range Place detector to preserve LSND L/E: MiniBooNE: (0.5 km) / (0.8 GeV) LSND:(0.03 km) / (0.05 GeV) Detect interations in 800T pure mineral oil detector 1280 8” PMTs provide 10% coverage of fiducial volume 240 8” PMTs provide active veto in outer radial shell dirt (~500 m) target and horn proton s (8 GeV) + - K+K+ K0K0 ✶ ✶ + ✶ decay region (50 m) detecto r (not to scale) oscillations ?

8. 8Chris Polly, Urbana Seminar, 27 Apr 2007 1.6  s Simple cuts eliminate random backgrounds Left: trigger window with no cuts applied Right: Simple cuts applied PMT hits in veto 200 show clean beam window Removes cosmic m and their decay electrons Subevent structure also used for particle identification (PID) Time structure on right expected for most common n interaction in MB: n m charged-current quasi- elastic n m CCQE

9. 9Chris Polly, Urbana Seminar, 27 Apr 2007 Calibration sources span various energies

10. 10Chris Polly, Urbana Seminar, 27 Apr 2007 Key points about the signal LSND measured an oscillation probability of 0.3% After cuts, MiniBooNE has to be able to find ~300 n e CCQE interactions in a sea of ~150,000 n m CCQE Intrinsic e background Actual n e produced in the beamline from muons and kaons Irreducible at the event level E spectrum differs from signal Mis-identified events n m CCQE easy to identify, lots of them Neutral-current (NC) p 0 and radiative D are rarer, but harder to separate Can be reduced with better PID MiniBooNE is a ratio measurement with the n m constraining flux X cross-section

11. 11Chris Polly, Urbana Seminar, 27 Apr 2007 MiniBooNE analysis structure ✔ Start with a Geant 4 flux prediction for the n spectrum from p and K produced at the target ✔ Predict n interactions using Nuance ✔ Pass final state particles to Geant 3 to model particle and light propagation in the tank ✔ Starting with event reconstruction, independent analyses form: Boosted Decision Tree (BDT) and Track Based Likelihood (TBL) ✔ Develop particle ID/cuts to separate signal from background ✔ Fit reconstructed En spectrum for oscillations

12. 12Chris Polly, Urbana Seminar, 27 Apr 2007 Blind analysis in MiniBoone The MiniBooNE signal is small but relatively easy to isolate As data comes in it is classified into 'boxes' For boxes to be opened to analysis they must be shown to have a signal < 1 s In the end, 99% of the data were available Other Signa l Box

13. 13Chris Polly, Urbana Seminar, 27 Apr 2007 Flux Prediction

14. 14Chris Polly, Urbana Seminar, 27 Apr 2007  HARP (CERN)  5% Beryllium target  8.9 GeV proton beam momentum HARP collaboration, hep-ex/0702024 Data are fit to a Sanford-Wang parameterization. Modeling pion production

15. 15Chris Polly, Urbana Seminar, 27 Apr 2007 K + Data from 10 - 24 GeV. uses a Feynman scaling parameterization. data -- points dash --total error (fit  parameterization) K 0 data are also parameterized. Modeling kaon production

16. 16Chris Polly, Urbana Seminar, 27 Apr 2007 “Intrinsic” e + e sources:    e +   e (52%)  K +    e + e (29%)  K 0   e e (14%)  Other ( 5%)   e   e K   e e K       Antineutrino content: 6% e /  = 0.5% Final neutrino flux estimation - -

17. 17Chris Polly, Urbana Seminar, 27 Apr 2007 X-Section Model

18. 18Chris Polly, Urbana Seminar, 27 Apr 2007 NUANCE Monte Carlo D. Casper, NPS, 112 (2002) 161 Neutrino interactions before cuts Input neutrino spectrum

19. 19Chris Polly, Urbana Seminar, 27 Apr 2007 ν +C/H cross sections comprehensive XS simulation used elsewhere in community tuned on external, internal data Nuance charged-current cross section

20. 20Chris Polly, Urbana Seminar, 27 Apr 2007 Model describes CCQE  data well Kinetic Energy of muon data/MC~1 across all angle vs.energy after fit Example of tuning Nuance From Q 2 fits to MB  CCQE data: M A eff -- effective axial mass E lo SF -- Pauli Blocking parameter From electron scattering data: E b -- binding energy p f -- Fermi momentum

21. 21Chris Polly, Urbana Seminar, 27 Apr 2007 Optical Model

22. 22Chris Polly, Urbana Seminar, 27 Apr 2007 Light propagation in the detector Optical model is very complex Cerenkov, scintillation, fluorescence PMT Q/t response Scattering, reflection, prepulses Overall, about 40 parameters Michel electron t distribution

23. 23Chris Polly, Urbana Seminar, 27 Apr 2007 Tuning the optical model Initial optical model defined through many benchtop measurements Subsequently tuned with in situ sources, examples Left: Michel e populate entire tank, useful for tuning extinction Right: NC elastic n interactions below Cerenkov threshold useful for distinguishing scintillation from fluorescence Using Michel electrons... Using NC elastic n interactions...

24. 24Chris Polly, Urbana Seminar, 27 Apr 2007 Track-Based Likelihood (TBL) Reconstruction and Particle ID

25. 25Chris Polly, Urbana Seminar, 27 Apr 2007 data MC Pre-cuts in the TBL analysis Oscillation analysis pre-cuts Only 1 subevent Veto hits < 6 Tank hits > 200 Radius < 500 cm  CCQE events (2 subevent)

26. 26Chris Polly, Urbana Seminar, 27 Apr 2007 Maximum likelihood reconstruction Event ⇔ collection of 1280 PMT signals (Q/T) Fit event under different hypotheses: (1) single e track (2) single μ track, E t,x,y, z ligh t ➢ 7 parameters needed ➢ form Q & T p.d.f.'s on-the-fly using knowledge of track and detector properties ➢ maximize likelihood w.r.t. track parameters scintillation production along 300 MeV μ track The fitter knows about: ➢ Cer./scint. production profiles ➢ -dependent light propagation, detection ➢ scattering, fluorescence, reflections ➢ PMT efficiencies, solid angles

27. 27Chris Polly, Urbana Seminar, 27 Apr 2007 Separating e from m positive (negative) log(L e /L μ ) favors the e ( μ ) hypothesis easier to distinguish at higher energies >90% efficient for signal check simulation with tagged μ sample signal cut Monte Carlo

28. 28Chris Polly, Urbana Seminar, 27 Apr 2007 Separating e from p 0 1,11,1 E1E1 t,x,y, z ligh t s1s1 s2s2 2,22,2 E2E2 (3) two tracks (4) two tracks with mass=M π ⁰ Two more event hypotheses: blin d

29. 29Chris Polly, Urbana Seminar, 27 Apr 2007 Expected event totals showe r dir t escape s showe r dirt 17 Δ→ N γ 20 ν e K 94 ν e μ 132 π ⁰ 62 475 MeV – 1250 MeV other 33 total 358 LSND best-fit ν μ →ν e 126

30. 30Chris Polly, Urbana Seminar, 27 Apr 2007 Boosted Decision Tree (BDT) Reconstruction and Particle ID

31. 31Chris Polly, Urbana Seminar, 27 Apr 2007 BDT Reconstruction Same oscillation pre-cuts as TBL (taking R from different recon) Simpler fit Treats particles more like points sources instead of accounting carefully for dE/dx. Not as tenacious about find its way out of local minima, particularly with pion fit Cons: Not as successful at reconstructing pions Resolution not as good TBL Resolution: vertex: 22 cm direction: 2.8º energy 11% BDT Resolution: vertex: 24 cm direction: 3.8º energy 14% Pro: Ten times faster...we used ~1M CPU hours in the TBL error analysis To make up for the simple fit, the BDT analysis relies on a form of machine learning, the boosted decsion tree.

32. 32Chris Polly, Urbana Seminar, 27 Apr 2007  CCQE U Z = cos  z E visibl e First step: Define variables Input variable defined from event topology and reconstructed quantities A total of 172 variables were used in the BDT analysis, 3 of which are shown here All 172 variables were checked for agreement in 5 important boxes before being incorporated

33. 33Chris Polly, Urbana Seminar, 27 Apr 2007 “A procedure that combines many weak classifiers to form a powerful committee” Boosted Decision Trees hit level (charge, time, position) analysis variables One single PID “score” Byron P. Roe, et al., NIM A543 (2005) 577. Step two: Reduce varibles to one PID score

34. 34Chris Polly, Urbana Seminar, 27 Apr 2007 (sequential series of cuts based on MC study) ( N signal /N bkgd ) 30,245/16,305 9755/23695 20455/3417 9790/12888 1906/11828 7849/11867 sig-like bkgd-like sig-lik e bkgd-like etc. This tree is one of many possibilities... Variable 1 Variable 2 Variable 3 Decision tree example

35. 35Chris Polly, Urbana Seminar, 27 Apr 2007 A set of decision trees can be developed, each re-weighting the events to enhance identification of backgrounds misidentified by earlier trees (“boosting”) For each tree, the data event is assigned +1 if it is identified as signal, -1 if it is identified as background. The total for all trees is combined into a “score” negativepositive Background-like signal-like

36. 36Chris Polly, Urbana Seminar, 27 Apr 2007 BDT cuts on PID score as a function of energy We can define a “sideband” just outside of the signal region Third step: Define cuts on PID score

37. 37Chris Polly, Urbana Seminar, 27 Apr 2007 Event composition in the sideband

38. 38Chris Polly, Urbana Seminar, 27 Apr 2007 signa l backgroun d Efficiency after precuts BDT efficiency and background in signal region

39. 39Chris Polly, Urbana Seminar, 27 Apr 2007 Systematic Error Analysis

40. 40Chris Polly, Urbana Seminar, 27 Apr 2007 For a given source of uncertainty, Errors on a wide range of parameters in the underlying model For a given source of uncertainty, Errors in bins of E QE and information on the correlations between bins What we begin with...... what we need Handling uncertainties in the analysis

41. 41Chris Polly, Urbana Seminar, 27 Apr 2007 TBL: Reweight MC prediction to match measured  result (accounting for systematic error correlations) Two Approaches Systematic (and statistical) errors are included in (M ij ) - 1, where i, j are bins of E QE BDT: include the correlations of  to e in the error matrix: Incorporating the n m constraint into the errors

42. 42Chris Polly, Urbana Seminar, 27 Apr 2007 M A QE, e lo sf 6%, 2% (stat + bkg only) QE  norm 10% QE  shape function of E  e /  QE  function of E NC  0 rate function of  0 mom M A coh, coh  ±25%   N  rate function of  mom + 7% BF E B, p F 9 MeV, 30 MeV  s 10% M A 1  25% M A N  40% DIS  25% determined from MiniBooNE  QE data determined from MiniBooNE  NC  0 data determined from other experiment s (Many are common to  and e and cancel in the fit) Example: Underlying X-section parameter errors

43. 43Chris Polly, Urbana Seminar, 27 Apr 2007 external measurements essential finish with μ decay events (low-energy electrons) (~unlimited supply and fast to simulate) ➔ use a Monte Carlo method to reduce uncertainty: ➔ compare data/MC events in relevant distributions for many allowed models ➔ de-weight disallowed regions of model space ➔ NC elastic events help out with scintillation starting uncertainties in three of the distributions (near) ending uncertainties Extracting the OM systematic error

44. 44Chris Polly, Urbana Seminar, 27 Apr 2007 number of multisims Number of events passing cuts in bin 500<E QE <600 MeV 1000 multisims for K + production 70 multisims Optical Model red line: standard MC “Multisim” approach to assessing systematics A multisim is defined as a random draw from the underlying parameter that is considered allowed Allowed means the draw does not violate internal or external constraints Draws are taken from covariance matrices that dictate how parameters are allowed to change in combination, imagine Cerenkov and scintillation as independent sources of light but requiring the Michel energy to be conserved For flux and X-section multisims can be done via reweighting, optical model requires running hit level simulation e 

45. 45Chris Polly, Urbana Seminar, 27 Apr 2007 Correlations between E QE bins from the optical model: N is number of events passing cuts MC is standard monte carlo  represents a given multisim M is the total number of multisims i,j are E QE bins Total error matrix is calculated from the sum of 9 independent sources TB: e -only total error matrix BDT:  - e total error matrix MC BDT Optical model error matrix = S

46. 46Chris Polly, Urbana Seminar, 27 Apr 2007 Flux from  + /  + decay 6.2 / 4.3 √ √ Flux from K + decay3.3 / 1.0 √ √ Flux from K 0 decay 1.5 / 0.4 √ √ Target and beam models2.8 / 1.3 √ -cross section 12.3 / 10.5 √ √ NC  0 yield1.8 / 1.5 √ External interactions (“Dirt”) 0.8 / 3.4 √ Optical model6.1 / 10.5 √ √ DAQ electronics model7. 5 / 10.8 √ Source of uncertainty on e background Checked or constrained by MB data Further reduced by tying e to  TBL/BDT error in % Final error budget (diagonals only)

47. 47Chris Polly, Urbana Seminar, 27 Apr 2007 Sensitivity and Final Results

48. 48Chris Polly, Urbana Seminar, 27 Apr 2007 BDT/TBL sensitivity comparison Sensitivity is determined from simulation only Decided before unblinding that the analysis with higher sensitivity would be the final analysis TBL is better at high D m 2 90% CL defined by: Dc 2 = 1.64

49. 49Chris Polly, Urbana Seminar, 27 Apr 2007 In the words of Bill Louis, “It will be a cold, snowy day in Naperville before...”

50. 50Chris Polly, Urbana Seminar, 27 Apr 2007 Finally we see the data in the signal region... BDT has a good fit and no sign of an excess, in fact the data is low relative to the prediction Also sees an excess at low E, but larger normalization error complicates TBL show no sign of an excess in the analysis region (where the LSND signal is expected for the sterile neutrino interpretation) Visible excess at low E

51. 51Chris Polly, Urbana Seminar, 27 Apr 2007 Both analyses show no evidence for   e appearance-only oscillations. Fit results mapped into sin 2 (2 q ) D m 2 plane Energy-fit analysis: solid: TBL dashed: BDT Independent analyses in good agreement Note that this looks like the sensitivity because of the lack of a signal Had there been a signal, these curves would have curled around and closed into contours

52. 52Chris Polly, Urbana Seminar, 27 Apr 2007 For each  m 2, determine the MB and LSND measurement: z MB   z MB, z LSND   z LSND where z = sin 2 (2  ) and  z is the 1  error For each  m 2, form  2 between MB and LSND measurement Find z 0 that minimizes  2 and this gives  2 min Find probability of  2 min for 1 dof this is the joint probability for this  m 2 A MiniBooNE-LSND compatibility test Maximum Joint Probability  m 2 (eV 2 ) MiniBooNE and LSND MiniBooNE is incompatible with a   e appearance only interpretation of LSND at 98% CL

53. 53Chris Polly, Urbana Seminar, 27 Apr 2007 Future work for MiniBooNE Papers in support of this analysis NC p 0 background measurement n m CCQE analysis Joint MiniBooNE +LSND+Karmen Continued improvements of the n oscillation analysis Combined BDT and TBL More work on reducing systematics Re-examine low E backgrounds and significance of low E excess More exotic oscillation analyses n m disappearance Oscillation in CC pi+ channel Anti- n oscillation Limits on Lorentz Violation and 3+2 mixing Lots of work on cross-sections MiniBooNE has more n m interactions than any prior experiment and they are in an energy range relevant to future n experiments. Event count before cuts: Currently running in anti- n mode for anti- n cross sections

54. 54Chris Polly, Urbana Seminar, 27 Apr 2007 Backup Slides

55. 55Chris Polly, Urbana Seminar, 27 Apr 2007 Stability of running: Observed and expected events per minute Full Run

56. Chris Polly, Urbana Seminar, 27 Apr 2007 Stepwise Box Opening: Blind 2 Test: Perform signal extraction fit Propagate best-fit signal into interesting distributions Report 2 only Most quantities: good agreement Visible energy: Poor 2 Re-examine backgrounds/errors ➔ Allows us to test best-fit without knowing signal

57. Chris Polly, Urbana Seminar, 27 Apr 2007 Suspect low energy: Look at unsigned deviation of data relative to best fit (blind to excess/deficit) MC indicates backgrounds pile up in this region. Increase E ν cut to 475 MeV, Re-optimize cuts

58. Chris Polly, Urbana Seminar, 27 Apr 2007 No loss in sensitivity with increased threshold sidebands suggest low energy issues also Re-check data/MC agreement with new cuts (okay)

59. 59Chris Polly, Urbana Seminar, 27 Apr 2007 CCQE (Charged Current Quasi-Elastic) 39% of total Events are “clean” (few particles) Energy of the neutrino can be reconstructed   or e  or e  n p Reconstructed from: Scattering angle Visible energy (E visible ) An oscillation signal is an excess of e events as a function of E QE

60. 60Chris Polly, Urbana Seminar, 27 Apr 2007 N  00 N NC  0 The  0 decays to 2 photons, which can look “electron-like” mimicking the signal... <1% of  0 contribute to background. N   N  25% 8%8% CC  + Easy to tag due to 3 subevents. Not a substantial background to the oscillation analysis. Events producing pions (also decays to a single photon with 0.56% probability)

61. Chris Polly, Urbana Seminar, 27 Apr 2007

62. 62Chris Polly, Urbana Seminar, 27 Apr 2007  2 Prob for mass<50 MeV (“most signal-like”): 69% mass<200 (low mass) log(L e /L  )>0 (e-like) log(L e /L  )<0 (  -like) BLIND Monte Carlo π 0 only Next: look here.... 1 subevent log(L e /L  )>0 (e-like) log(L e /L  )<0 (  -like) mass<200 (low mass)

63. 63Chris Polly, Urbana Seminar, 27 Apr 2007 We have two categories of backgrounds: (TB analysis)  mis-id intrinsic e Predictions of the backgrounds are among the nine sources of significant error in the analysis

64. 64Chris Polly, Urbana Seminar, 27 Apr 2007 Tying the e background and signal prediction to the  flux constrains this analysis to a strict   e appearance-only search Data/MC Boosted Decision Tree: 1.22 ± 0.29 Track Based: 1.32 ± 0.26 BDT Predict Normalization & energy dependence of both background and signal From the  CCQE events

65. 65Chris Polly, Urbana Seminar, 27 Apr 2007   e   e    Measure the  flux Kinematics allows connection to the  flux E (GeV) E  (GeV) E = 0.43 E  Once the  flux is known, the  flux is determined   constraint on intrinsic e from  + decay chains

66. 66Chris Polly, Urbana Seminar, 27 Apr 2007 K + and K 0 decay backgrounds At high energies, above “signal range”  and “ e -like” events are largely due to kaon decay Signal examples:  m 2 =0.4 eV 2  m 2 =0.7 eV 2  m 2 =1.0 eV 2 Predicted range of significant oscillation signal: 300<E QE <1500 MeV 0 1 2 3 Neutrino Energy (GeV) Arbitrary Units signal range

67. 67Chris Polly, Urbana Seminar, 27 Apr 2007 TBTB In Boosted Decision Tree analysis: Low energy bin (200<E QE <300 MeV) constrains  mis-ids:  0,  N , dirt... signal range signal up to 3000 MeV BDT In both analyses, high energy bins constrain e background Use of low-signal/high-background energy bins

68. 68Chris Polly, Urbana Seminar, 27 Apr 2007 We constrain  0 production using data from our detector Because this constrains the  resonance rate, it also constrains the rate of  N  Reweighting improves agreement in other variables, e.g.  This reduces the error on predicted mis-identified  0 s

69. 69Chris Polly, Urbana Seminar, 27 Apr 2007 Other Single Photon Sources From Efrosinin, hep-ph/0609169, calculation checked by Goldman, LANL Neutral Current: + N  + N +  Charged Current + N   + N’ +  negligible where the presence of the  leads to mis-identification Use events where the  is tagged by the michel e -, study misidentification using BDT algorithm. < 6 events @ 95% CL

70. 70Chris Polly, Urbana Seminar, 27 Apr 2007 “Dirt” Events Event Type of Dirt after PID cuts Enhanced Background Cuts interactions outside of the detector N data /N MC = 0.99 ± 0.15 Cosmic Rays: Measured from out-of-beam data: 2.1 ± 0.5 events External Sources of Background

71. 71Chris Polly, Urbana Seminar, 27 Apr 2007 Summary of predicted backgrounds for the final MiniBooNE result (Track Based Analysis): (example signal)

72. 72Chris Polly, Urbana Seminar, 27 Apr 2007 Counting Experiment: 475<E QE <1250 MeV data: 380 events expectation: 358  19 (stat)  35 (sys) events significance: 0.55  The Track-based   e Appearance-only Result:

73. 73Chris Polly, Urbana Seminar, 27 Apr 2007 96 ± 17 ± 20 events above background, for 300<E QE <475MeV Deviation: 3.7  As planned before opening the box.... Report the full range: 300<E QE <3000 MeV to E>475 MeV Background-subtracted:

74. 74Chris Polly, Urbana Seminar, 27 Apr 2007 Best Fit (dashed): (sin 2 2 ,  m 2 ) = (1.0, 0.03 eV 2 )  2 Probability: 18% Fit to the > 300 MeV range: } Examples in LSND allowed range

75. 75Chris Polly, Urbana Seminar, 27 Apr 2007 This will be addressed by MiniBooNE and SciBooNE This is interesting, but requires further investigation  A two-neutrino appearance-only model systematically disagrees with the shape as a function of energy.  We need to investigate non-oscillation explanations, including unexpected behavior of low energy cross sections. This will be relevant to future   e searches

76. 76Chris Polly, Urbana Seminar, 27 Apr 2007 Boosted Decision Tree E QE data/MC comparison: error bars are stat and sys (diagonals of matrix) data -predicted (no osc) error (sidebands used for constraint not shown)