# Presentation: 948459

## First Anti-neutrino results!

- H. Ray , University of Florida

## The Notorious LSND Result

- E =20-52.8 MeV
- L  =25-35 meters
- 3.8 excess
- Different from other oscillation signals
- Higher m2
-  Smaller mixing angle
- Much smaller probability (very small signal) ~0.3%

**P****osc**** =****sin****2****2******** sin****2**** 1.27 ********m****2**** ****L**
**	****	****        ****E**

- H. Ray , University of Florida

## Testing LSND

- Want same L/E
- Different detection method
- Different sources of systematic errors
- Test for oscillations using neutrinos, anti-neutrinos

- H. Ray , University of Florida

**Notes:**
Me < 2.2 ev, mmu < 170 keV, mtau < 1.5 MeV

## MiniBooNE Neutrino Beam

- Mesons decay into the anti-neutrino beam seen by the detector
- K- / -  - + 
- -  e- +  +  e
- MiniBooNE L/E = 0.5 km   / 0.8 GeV   (.625)
-          LSND L/E = 0.03 km / 0.05 GeV (.6)
- Anti-nu analysis uses 3.386E20 protons on target

- H. Ray , University of Florida

## MiniBooNE Detector

- 12.2 meter diameter sphere
**Pure**** **mineral oil
- 2 regions
**Inner light-tight region, 1280 PMTs (10% coverage)**
**Optically isolated outer veto-region, 240 PMTs**

- H. Ray , University of Florida

**Notes:**
1st expt to use non-doped oil!
MB = 800 tons, index of refraction = 1.47
1 PE = 0.2 MeV
Charge resolution = 1.4, 0.5 PE
Time resolution = 1.7 ns, 1.1 ns
Laser calibration system

## Event Signature

**charged-current quasi-elastic events****   *****ν******e****** p ******→ ******e******+****** n***

- H. Ray , University of Florida

## MiniBooNE Analysis

- MiniBooNE is looking for  e  oscillations
- MiniBooNE is looking for an excess of e  (appearance)
- MiniBooNE performing a blind analysis
- Some of the info in all of the data
- Charge per PMT as a function of time
- All of the info in some of the data
- ~oscillation free sample to be open for analysis
- Low-E NC elastic events,  CCQE,  CC+
- e candidate events locked away until the analysis 100% complete
- Same strategy as neutrino mode

- H. Ray , University of Florida

## Neutrino Mode Result

- Used 2 complementary analyses
- ruled out interpretation of LSND as νμ→νe oscillations
- two-nu oscillations
- standard L/E depend.
- no CP, CPT violation
- Unexplained excess of events in low-energy region
- Excess incompat. With 2-nu lsnd-style oscillations**	****	**

**Phys. Rev. Lett. 98, 231801 (2007)**

- H. Ray , University of Florida

## Anti-neutrino Analysis

- Similarities with neutrino mode
- Using two complementary analyses
- Using same algorithms
- Same event selection cuts
- Changes made wrt neutrino mode
- Added an event selection cut that removes most of the dirt (out of tank) background at low energy
- Added k- production systematic error
- New NC π0 measurement
- New dirt fraction extracted

- H. Ray , University of Florida

## Analysis Chain

**Beam Flux ****Prediction**

**Cross Section ****Model**

**Optical Model**

**Event ****Reconstruction**

**Particle ****Identification**

**Simultaneous ****Fit to anti-**********
** ****and anti- ********e**** ****events**

**Start with a Geant 4 flux prediction for the nu spectrum from ******** and K produced at the target**

**Use track-based event reco**

**Predict nu interactions using the Nuance event generator**

**Pass final state particles to Geant 3 to model particle, light propagation in the tank**

**Fit reco. energy spectrum for oscillations**

**Use hit topology and timing to identify electron-like or muon-like charged current neutrino interactions**

- Track Based Analysis

- H. Ray , University of Florida

## Analysis Chain

**Beam Flux ****Prediction**

**Cross Section ****Model**

**Optical Model**

**Event ****Reconstruction**

**Particle ****Identification**

**Simultaneous ****Fit to anti-**********
** ****and anti- ********e**** ****events**

**Start with a Geant 4 flux prediction for the nu spectrum from ******** and K produced at the target**

**Use point-source event reco**

**Predict nu interactions using the Nuance event generator**

**Pass final state particles to Geant 3 to model particle, light propagation in the tank**

**Fit reco. energy spectrum for oscillations**

**Use boosted decision tree to identify electron-like or muon-like charged current neutrino interactions**

- Boosted Decision tree

- H. Ray , University of Florida

## Expected Backgrounds

- Boosting Analysis

- Track Based Analysis

- 500 MeV < Reconstructed Neutrino Energy < 1.25 GeV

- Intrinsic e backgrounds

-  mis-id backgrounds

- 3.386e20 POT

- H. Ray , University of Florida

**Notes:**
Predictions of these bgds = majority of errors
Dirt + ccqe + other numu = 578 + 492 + 126 vs + 17 + 24 + 15
Pi0 = 1096 vs 84
Delta = 135 vs 19
Kp = 334 vs 121
K0 = 86 vs 28
Mup  = 413 vs 160
Pip = other nue = 12 vs 5

## Expected Sensitivity

- As in neutrino mode, TBA is the more sensitive (default) analysis.
- BDT is the cross-check analysis

- H. Ray , University of Florida

## Expected Background Events

- Background composition for TBA analysis (3.386e20 POT)

- LSND best-fit
- (Δm2, sin22θ)=(1.2,0.003)

**[note: statistical-only errors shown]**

| e from ±, ± | 8.44 | 17.14 |
| --- | --- | --- |
| e from k±,0 | 8.20 | 24.88 |
| Other e | 1.11 | 1.21 |
| CCQE | 2.86 | 1.24 |
| NC 0 | 24.60 | 7.17 |
| Delta Rad | 6.58 | 2.02 |
| Dirt | 4.69 | 1.92 |
| Other  | 3.82 | 2.20 |
| Total Bgd | 60.29 | 57.78 |
| LSND Best Fit | 4.33 | 12.63 |

- Intrinsic e

-  mis-id

**200-475 **
**   ****MeV**

**475-1250 **
**    ****MeV**

- H. Ray , University of Florida

## Systematic Uncertainties

| Source

           EνQE range (MeV) | 

200-475 | 

475-1100 | 

200-475 | 

475-1100 |
| --- | --- | --- | --- | --- |
| Flux from π+/μ+ decay  | 0.4 | 0.7 | 1.8 | 2.2 |
| Flux from π-/μ- decay  | 3.3 | 2.2 | 0.1 | 0.2 |
| Flux from K+ decay | 2.3 | 4.9 | 1.4 | 5.7 |
| Flux from K- decay | 0.5 | 1.1 | - | - |
| Flux from K0 decay | 1.5 | 5.7 | 0.5 | 1.5 |
| Target and beam models | 1.9 | 3.0 | 1.3 | 2.5 |
| ν-cross section  | 6.4 | 12.9 | 5.9 | 11.9 |
| NC π0 yield | 1.7 | 1.6 | 1.4 | 1.9 |
| Hadronic interactions | 0.5 | 0.6 | 0.8 | 0.3 |
| External interactions (dirt) | 2.4 | 1.2 | 0.8 | 0.4 |
| Optical model | 9.8 | 2.8 | 8.9 | 2.3 |
| Electronics & DAQ model | 9.7 | 3.0 | 5.0 | 1.7 |
| Total (unconstrained) | 16.3 | 16.2 | 12.3 | 14.2 |

**From fits to world’s data (HARP, Kaon production)**

- Track Based Analysis

- Antinu Mode          Nu Mode

- H. Ray , University of Florida

## Systematic Uncertainties

| Source

           EνQE range (MeV) | 

200-475 | 

475-1100 | 

200-475 | 

475-1100 |
| --- | --- | --- | --- | --- |
| Flux from π+/μ+ decay  | 0.4 | 0.7 | 1.8 | 2.2 |
| Flux from π-/μ- decay  | 3.3 | 2.2 | 0.1 | 0.2 |
| Flux from K+ decay | 2.3 | 4.9 | 1.4 | 5.7 |
| Flux from K- decay | 0.5 | 1.1 | - | - |
| Flux from K0 decay | 1.5 | 5.7 | 0.5 | 1.5 |
| Target and beam models | 1.9 | 3.0 | 1.3 | 2.5 |
| ν-cross section  | 6.4 | 12.9 | 5.9 | 11.9 |
| NC π0 yield | 1.7 | 1.6 | 1.4 | 1.9 |
| Hadronic interactions | 0.5 | 0.6 | 0.8 | 0.3 |
| External interactions (dirt) | 2.4 | 1.2 | 0.8 | 0.4 |
| Optical model | 9.8 | 2.8 | 8.9 | 2.3 |
| Electronics & DAQ model | 9.7 | 3.0 | 5.0 | 1.7 |
| Total (unconstrained) | 16.3 | 16.2 | 12.3 | 14.2 |

- Track Based Analysis

**Internal MB measurements**

- Antinu Mode          Nu Mode

- H. Ray , University of Florida

## Systematic Uncertainties

| Source

           EνQE range (MeV) | 

200-475 | 

475-1100 | 

200-475 | 

475-1100 |
| --- | --- | --- | --- | --- |
| Flux from π+/μ+ decay  | 0.4 | 0.7 | 1.8 | 2.2 |
| Flux from π-/μ- decay  | 3.3 | 2.2 | 0.1 | 0.2 |
| Flux from K+ decay | 2.3 | 4.9 | 1.4 | 5.7 |
| Flux from K- decay | 0.5 | 1.1 | - | - |
| Flux from K0 decay | 1.5 | 5.7 | 0.5 | 1.5 |
| Target and beam models | 1.9 | 3.0 | 1.3 | 2.5 |
| ν-cross section  | 6.4 | 12.9 | 5.9 | 11.9 |
| NC π0 yield | 1.7 | 1.6 | 1.4 | 1.9 |
| Hadronic interactions | 0.5 | 0.6 | 0.8 | 0.3 |
| External interactions (dirt) | 2.4 | 1.2 | 0.8 | 0.4 |
| Optical model | 9.8 | 2.8 | 8.9 | 2.3 |
| Electronics & DAQ model | 9.7 | 3.0 | 5.0 | 1.7 |
| Total (unconstrained) | 16.3 | 16.2 | 12.3 | 14.2 |

- Track Based Analysis

- Antinu Mode          Nu Mode

**Determined by special runs of the beam MC.  All beam uncertainties not coming from meson production by 8 GeV protons are varied one at a time. variations are treated as 1****σ**** ****excursions, prop into a final error matrix.**

**Uncert. in a number of hadronic processes, mainly photonuclear interaction final state**

**uncertainties in light creation, propagation, and detection in the Tank. Use  set of 130 MC “multisims” that have been run where all these parameters are varied according to their input uncertainties.**

- H. Ray , University of Florida

## Systematic Uncertainties

| Source

           EνQE range (MeV) | 

200-475 | 

475-1100 | 

200-475 | 

475-1100 |
| --- | --- | --- | --- | --- |
| Flux from π+/μ+ decay  | 0.4 | 0.7 | 1.8 | 2.2 |
| Flux from π-/μ- decay  | 3.3 | 2.2 | 0.1 | 0.2 |
| Flux from K+ decay | 2.3 | 4.9 | 1.4 | 5.7 |
| Flux from K- decay | 0.5 | 1.1 | - | - |
| Flux from K0 decay | 1.5 | 5.7 | 0.5 | 1.5 |
| Target and beam models | 1.9 | 3.0 | 1.3 | 2.5 |
| ν-cross section  | 6.4 | 12.9 | 5.9 | 11.9 |
| NC π0 yield | 1.7 | 1.6 | 1.4 | 1.9 |
| Hadronic interactions | 0.5 | 0.6 | 0.8 | 0.3 |
| External interactions (dirt) | 2.4 | 1.2 | 0.8 | 0.4 |
| Optical model | 9.8 | 2.8 | 8.9 | 2.3 |
| Electronics & DAQ model | 9.7 | 3.0 | 5.0 | 1.7 |
| Total (unconstrained) | 16.3 | 16.2 | 12.3 | 14.2 |

- Track Based Analysis

**Fit to the anti-****ν****μ**** CCQE and anti-****ν****e**** candidate ****spectra simultaneously.  takes advantage of strong correlations between anti-****ν****e**** ****signal, background, and the anti-****ν****μ**** CCQE sample, reduces systematic uncertainties and constrains intrinsic  anti-****ν****e**** from muon decay**

- Antinu Mode          Nu Mode

- Antineutrino appearance search is statistics limited!

- H. Ray , University of Florida

## Observed Event Distribution

- Counting Expt :
- 475 MeV < EQE< 1.250 GeV
- 61 observed evts
- 57.8 ± 10.0 expected events
**Excess over background : ****0.3******

- Counting Expt :
- 200 MeV < EQE< 475 MeV
- 61 observed evts
- 61.5 ± 11.7 expected events
**Excess over background : ****-0.04******

- H. Ray , University of Florida

## Excess Distribution

- (Δm2, sin22θ) = (4.4 eV2, 0.004)

- χ2best-fit(dof) = 18.18 (17)
- χ2-probability = 37.8%

- H. Ray , University of Florida

## Event Summary

***E******ν******QE****** range (MeV)******	******     ******	******	******	******anti-******ν ******mode ******	******	******ν****** mode ******	******	******	******	******	******	******	******(3.386e20 POT)******	******(6.486e20 POT)***
***200-300***
***300-475***
***200-475***
***475-1250***
***	***

**Excess**
**Deficit**

***Data******	******	******	******24******	******	******232***
***MC ******±****** sys+stat (constr.)******	******	******27.2 ******± 7.4******	******	******186.8 ******± 26.0***
***Excess (******σ******)******	******	******	******-3.2 ******± 7.4 ******(-0.4******σ******)******	******45.2 ******± 26.0 ******(1.7******σ******)***

***Data******	******	******	******37******	******	******312***
***MC ******±****** sys+stat (constr.)******	******	******34.3 ± 7.3******	******	******228.3 ± 24.5***
***Excess (******σ******)******	******	******	******2.7 ******± 7.3 ******(0.4******σ******)******	******83.7 ******± 24.5 ******(3.4******σ******)***

***Data******	******	******	******61******	******	******544***
***MC ******±****** sys+stat (constr.)******	******	******61.5 ± 11.7******	******	******415.2 ± 43.4***
***Excess (******σ******)******	******	******	******-0.5 ******± 11.7 ******(-0.04******σ******)******	******128.8****** ± 43.4 ******(3.0******σ******)***

***Data******	******	******	******61******	******	******408***
***MC ******±****** sys+stat (constr.)******	******	******57.8 ± 10.0******	******	******385.9 ± 35.7***
***Excess (******σ******)******	******	******	******3.2 ******± 10.0 ******(0.3******σ******)******	******22.1****** ± 35.7 ******(0.6******σ******)***

***arXiv:0812.2243***

- H. Ray , University of Florida

## Implications for Low-E Excess

**Same  ****ν**** and ****ν**** ****NC cross-section (HHH axial anomaly)****, ****POT scaled, Low-E Kaon scaled: ****strongly disfavored**** as an explanation of the MiniBooNE low energy excess!**
**most preferred**** modeL: low-energy excess comes from neutrinos in the beam (no contribution from anti-neutrinos)**

**Currently in process of more careful consideration of **_**correlation**_** of systematics in neutrino and antineutrino mode... results coming soon!**

**	****	****Stat Only****	****Correlated Syst****	****Uncorrelated Syst**
**Same ****ν****,****ν ****NC  ****	****0.1%****	****	****0.1%****	****	****6.7%****NC ****π****0**** scaled****	****3.6%****	****	****6.4%****	****	****21.5%****POT scaled****	****0.0%****	****	****0.0%****	****	****1.8%****Bkgd scaled****	****2.7%****	****	****4.7%****	****	****19.2%****CC scaled****	****2.9%****	****	****5.2%****	****	****19.9%****Low-E Kaons****	****0.1%****	****	****0.1%****	****	****5.9%****ν**** scaled****	****	****38.4%****	****	****51.4%****	****	****58.0%**

**Maximum ****χ****2**** probability from fits to ****ν**** and ****ν**** ****excesses in 200-475 MeV range**

- Preliminary
- (upper and lower bounds)

- _

- _

- H. Ray , University of Florida

## Final Limits

- No strong evidence for oscillations in anti-nu mode
- Analysis limited by stat
- No evidence of excess at low energy in anti-nu mode
- Combine nu, anti-nu for low-E analysis
- Data collection continuing through June, 09
- NuMI analysis in 2009!

**3.386e20 POT**

- H. Ray , University of Florida

**Notes:**
Add BDT limit

## Backup Slides

## The Notorious LSND

- 800 MeV proton beam + H20 target, Copper beam stop
- 167 ton tank, liquid scintillator, 25% PMT coverage
- E =20-52.8 MeV
- L  =25-35 meters
-  e + p  e+ + n
- n + p  d  +  (2.2 MeV)

-  e

- H. Ray , University of Florida

## Neutrino Event Composition

**Boosting Analysis**** **

**Likelihood Analysis**

- intrinsic e
-  mis-id

- H. Ray , University of Florida

**Notes:**
Predictions of these bgds = majority of errors
Dirt + ccqe + other numu = 578 + 492 + 126 vs + 17 + 24 + 15
Pi0 = 1096 vs 84
Delta = 135 vs 19
Kp = 334 vs 121
K0 = 86 vs 28
Mup  = 413 vs 160
Pip = other nue = 12 vs 5

## Flux Prediction

- Much larger wrong sign component in anti-neutrino analysis

- nu mode

- Anti-nu mode

- Intrinsic background to oscillation analysis

- Intrinsic background to oscillation analysis

- Wrong sign contamination

- Wrong sign contamination

- H. Ray , University of Florida

## Systematic Errors

- Use Multisims to calculate systematic errors
- In each MC event vary all parameters at once, according to a full covariance matrix
- Ex : Feynman scaling of K+ varies 8 params simultaneously
- Vary full set of parameters many times per event
- OM = 70 multisims.  All other errors = 1000
- Use this information to form an error matrix

**Central Value MC**

- #evts in 1 E bin

- # multisims

- K+ error

- H. Ray , University of Florida

## Systematic Errors

| Error | Track vs Boosting (%) | Checked or Constrained by data |
| --- | --- | --- |
| DAQ | 7.5 / 10.8 |  |
| Target/Horn | 2.8 / 1.3 |  |
| + Flux | 6.2 / 4.3	 |  |
| K+ Flux | 3.3 / 1.0 |  |
| K0 Flux | 1.5 / 0.4 |  |
| Dirt | 0.8 / 3.4  |  |
| NC 0 yield | 1.8 / 1.5 	 |  |
| Neutrino Xsec | 12.3 / 10.5 |  |
| OM | 6.1 / 10.5 |  |

- H. Ray , University of Florida

**Notes:**
Daq/target/horn : skin depth, horn currenet, nucl inelastic xsec,
Nuc qe xsec, nuc tot xsec, pion inel & qe & tot xsec

## Slide 30

- H. Ray , University of Florida

## Expected Event Composition

- W+

- p

- 

****

- n

- μ+ can...
- ...capture on C
- ...decay too quickly
- ...have too low energy

**N****events****	****      **** 200-475 MeV****	****475-1250 MeV**
**intrinsic ****ν****e         ****17.74****	****43.23****from ****π****±****/****μ****±          ****8.44****	****	****17.14****from K****±****, K****0        ****8.20****	****	****24.88****other ****ν****e****	****        1.11****	****	****1.21**
**mis-id ****ν****μ****	****            ****42.54**** ****	****14.55****CCQE****	****        2.86****	****	****1.24****NC**** π****0****	****   **** ****       ****24.60****	****7.17****Δ**** radiative      6.58****	****	****2.02****Dirt****	****        4.69****	****	****1.92****other ****ν****μ****	****        3.82****	****	****2.20**
**Total bkgd      60.29****	****57.78****	**
**LSND best fit  4.33****	****	****12.63**

- H. Ray , University of Florida

## Expected Event Composition

- Z

- A

- 

- 

- 

**N****events****	****      **** 200-475 MeV****	****475-1250 MeV**
**intrinsic ****ν****e         ****17.74****	****43.23****from ****π****±****/****μ****±          ****8.44****	****	****17.14****from K****±****, K****0        ****8.20****	****	****24.88****other ****ν****e****	****        1.11****	****	****1.21**
**mis-id ****ν****μ****	****            ****42.54**** ****	****14.55****CCQE****	****        2.86****	****	****1.24****NC**** π****0****	****   **** ****       ****24.60****	****7.17****Δ**** radiative      6.58****	****	****2.02****Dirt****	****        4.69****	****	****1.92****other ****ν****μ****	****        3.82****	****	****2.20**
**Total bkgd      60.29****	****57.78****	**
**LSND best fit  4.33****	****	****12.63**

- Coherent π0 production

- A

**γ**

**γ**

- H. Ray , University of Florida

## Expected Event Composition

- Z

- p

- 

- 

- 

**N****events****	****      **** 200-475 MeV****	****475-1250 MeV**
**intrinsic ****ν****e         ****17.74****	****43.23****from ****π****±****/****μ****±          ****8.44****	****	****17.14****from K****±****, K****0        ****8.20****	****	****24.88****other ****ν****e****	****        1.11****	****	****1.21**
**mis-id ****ν****μ****	****            ****42.54**** ****	****14.55****CCQE****	****        2.86****	****	****1.24****NC**** π****0****	****   **** ****       ****24.60****	****7.17****Δ**** radiative      6.58****	****	****2.02****Dirt****	****        4.69****	****	****1.92****other ****ν****μ****	****        3.82****	****	****2.20**
**Total bkgd      60.29****	****57.78****	**
**LSND best fit  4.33****	****	****12.63**

- Resonant π0 production

- 

- p

**γ**

**γ**

- H. Ray , University of Florida

## Expected Event Composition

- Z

- p

****

- 

- 

**N****events****	****      **** 200-475 MeV****	****475-1250 MeV**
**intrinsic ****ν****e         ****17.74****	****43.23****from ****π****±****/****μ****±          ****8.44****	****	****17.14****from K****±****, K****0        ****8.20****	****	****24.88****other ****ν****e****	****        1.11****	****	****1.21**
**mis-id ****ν****μ****	****            ****42.54**** ****	****14.55****CCQE****	****        2.86****	****	****1.24****NC**** π****0****	****   **** ****       ****24.60****	****7.17****Δ**** radiative      6.58****	****	****2.02****Dirt****	****        4.69****	****	****1.92****other ****ν****μ****	****        3.82****	****	****2.20**
**Total bkgd      60.29****	****57.78****	**
**LSND best fit  4.33****	****	****12.63**

- ...and some times...
-   Δ radiative decay

- 

- p

- H. Ray , University of Florida

## Expected Event Composition

**N****events****	****      **** 200-475 MeV****	****475-1250 MeV**
**intrinsic ****ν****e         ****17.74****	****43.23****from ****π****±****/****μ****±          ****8.44****	****	****17.14****from K****±****, K****0        ****8.20****	****	****24.88****other ****ν****e****	****        1.11****	****	****1.21**
**mis-id ****ν****μ****	****            ****42.54**** ****	****14.55****CCQE****	****        2.86****	****	****1.24****NC**** π****0****	****   **** ****       ****24.60****	****7.17****Δ**** radiative      6.58****	****	****2.02****Dirt****	****        4.69****	****	****1.92****other ****ν****μ****	****        3.82****	****	****2.20**
**Total bkgd      60.29****	****57.78****	**
**LSND best fit  4.33****	****	****12.63**

- MiniBooNE detector

- H. Ray , University of Florida

**How consistent are excesses in neutrino and antineutrino mode under different ****underlying hypotheses**** as the source of the low energy excess in neutrino mode?**

***Data******	******	******	******61******	******	******544***
***MC ******±****** sys+stat (constr.)******	******	******61.5 ± 11.7******	******	******415.2 ± 43.4***
***Excess (******σ******)******	******	******	******-0.5 ******± 11.7****** ******(-0.04******σ******)******	******128.8****** ± 43.4 ******(3.0******σ******)***

***200-475 MeV***

- ν

- ν

- _

**Scales with POT **
**Same NC cross section for neutrinos and antineutrinos**** **
**Scales as ****π****0**** ****background **
**Scales with neutrinos (not antineutrinos)**
**Scales with background **
**Scales as the rate of Charged-Current interactions**
**Scales with Kaon rate at low energy**

- H. Ray , University of Florida

**Notes:**
Give a more detailed example of the simplest case, where the excess is assumed to scale with POT, and then brefly discuss the assumptions behing some of the other hhypotheses

***Data******	******	******	******61******	******	******544***
***MC ******±****** sys+stat (constr.)******	******	******61.5 ± 11.7******	******	******415.2 ± 43.4***
***Excess (******σ******)******	******	******	******-0.5 ******± 11.7****** ******(-0.04******σ******)******	******128.8****** ± 43.4 ******(3.0******σ******)***

***200-475 MeV***

**Performed 2-bin ****χ****2**** test for each assumption**
**Calculated ****χ****2**** ****probability assuming 1 dof**
**	****The underlying signal for each hypothesis was allowed to vary ****(thus accounting for the possibility that the observed signal in neutrino mode was a fluctuation up, and the observed signal in antineutrino mode was a fluctuation down),**** and an absolute ****χ****2**** minimum was found.****	**
**Three extreme fit scenarios were considered:**
**Statistical-only**** uncertainties**
**Statistical + fully-correlated systematics **
**Statistical + fully-uncorrelated systematics**

- ν

- ν

- _

- H. Ray , University of Florida

**Notes:**
Throwing out everything we know on how much systematic errors and fluctuations are allowed, we consider three fit scenarios in extracting a chi2 probability...
In reality the true chi2 probability will fall somewhere between the second and third fit, 

**Eg.: ****scales with POT *****(e.g. “paraphotons”,...)***
**Antineutrino POT: 3.386e20****	****	****Antineutrino POT****	**
**Neutrino POT: 6.486e20****	****	****     Neutrino POT**
**One would expect a ****ν**** ****excess of ~(128.8 events)*0.52 = ~67 events**

***Data******	******	******	******61******	******	******544***
***MC ******±****** sys+stat (constr.)******	******	******61.5 ± 11.7******	******	******415.2 ± 43.4***
***Excess (******σ******)******	******	******	******-0.5 ******± 11.7****** ******(-0.04******σ******)******	******128.8****** ± 43.4 ******(3.0******σ******)***

***200-475 MeV***

- Obviously this should be highly disfavored by the data, but one could imagine a scenario where the neutrino mode observed excess is a fluctuation up from true underlying signal and the antineutrino mode excess is a fluctuation down, yielding a lower χ2...

**= 0.52**

- ν

- ν

- _

- H. Ray , University of Florida

**Notes:**
Or any other process stemming from production of neutral particles at target

**Eg.: ****Same NC cross section for neutrinos and antineutrinos *****(e.g., HHH axial anomaly)***
**Expected rates obtained by ****integrating flux across all energies ****for neutrino mode, and antineutrino ****mode**

***Data******	******	******	******61******	******	******544***
***MC ******±****** sys+stat (constr.)******	******	******61.5 ± 11.7******	******	******415.2 ± 43.4***
***Excess (******σ******)******	******	******	******-0.5 ******± 11.7****** ******(-0.04******σ******)******	******128.8****** ± 43.4 ******(3.0******σ******)***

***200-475 MeV***

- ν

- ν

- _

**[Harvey, Hill, and Hill, hep-ph0708.1281]**

- H. Ray , University of Florida

**Eg.: ****Scales as ****π****0**** background (same NC ****ν**** ****and ****ν**** ****cross-section ratio)**
**Expected rates obtained by integrating flux across all energies for neutrino mode, and antineutrino mode**
**Mis-estimation of ****π****0**** background? **
**Or other Neutral-Current process? **
**	****For ****π****0**** background to fully account for MB ****ν**** mode excess, it would have to be mis-estimated by a factor of two...**
**	****...****but we have measured MB ****π****0**** ****event rate**** ****to a few percent!**** ****	**

***Data******	******	******	******61******	******	******544***
***MC ******±****** sys+stat (constr.)******	******	******61.5 ± 11.7******	******	******415.2 ± 43.4***
***Excess (******σ******)******	******	******	******-0.5 ******± 11.7****** ******(-0.04******σ******)******	******128.8****** ± 43.4 ******(3.0******σ******)***

***200-475 MeV***

- ν

- ν

- _

**[Phys. Lett. B664, 41 (2008)]**

- _

- H. Ray , University of Florida

**Eg.: ****Scales with neutrinos (in both running modes)**
**In ****neutrino mode, 94%**** of flux consists of ****neutrinos**
**In ****antineutrino mode,**** 82% of flux consists of antineutrinos, ****18%**** of flux consists of ****neutrinos**
**Predictions are allowed to scale according to ****neutrino**** content of the beam**

***Data******	******	******	******61******	******	******544***
***MC ******±****** sys+stat (constr.)******	******	******61.5 ± 11.7******	******	******415.2 ± 43.4***
***Excess (******σ******)******	******	******	******-0.5 ******± 11.7****** ******(-0.04******σ******)******	******128.8****** ± 43.4 ******(3.0******σ******)***

***200-475 MeV***

- ν

- ν

- _

- H. Ray , University of Florida

## χ2null(dof)1            	χ2best-fit(dof)1	χ2LSND best-fit(dof)

**χ****2****null****(dof)****1****            ****	****χ****2****best-fit****(dof)****1****	****χ****2****LSND best-fit****(dof)**
**χ****2****-prob****	****	****χ****2****-prob****	****	****χ****2****-prob**
**20.18(19)****	****18.18(17)****	****20.14(19)**
**38.4%****	****	****37.8%****	****	****38.6%**
**17.88(16)****	****15.91(14)****	****17.63(16)**
**33.1%****	****	****31.9%****	****	****34.6%**

**E****ν****QE****  fit**
**> ****200 ****MeV**
**> 475 MeV**

**E****ν****QE**** > 200 MeV and E****ν****QE**** > 475 MeV fits are consistent with each other.**
**No strong evidence for oscillations in antineutrino mode.****(3.386e20 POT)**

**(****1****Covariance matrix approximated to be the same everywhere by its value at best fit point)**

- H. Ray , University of Florida

**Notes:**
Once a 2 parameter fit is performed, the following chi2’s are obtained.
Note that the chi2’s calculated at the null (no oscillations), chi2 best fit, and lsnd best fit yield similar oscillation probabilities. 
Delta chi2 null vs best fit is less than 4.91, the 2d deltachi2 cut for 90% CL, and therefore with current data at hand we place a limit to oscillations

## 2D global fit 

- H. Ray , University of Florida