Systematic errors of MiniBooNE Kendall Mahn, Columbia University - PowerPoint PPT Presentation

Systematic errors of MiniBooNE Kendall Mahn, Columbia University for the MiniBooNE collaboration NuFact07

Oscillation Analysis ν e selection cuts E ν (QE) Signal E ν (QE) ν µ ( Δ m 2 =1.2eV 2 , sin 2 2 θ =0.003) 0.5% intrinsic ν e Background Do the ν µ oscillate into ν e ? misidentified ν µ (mainly π 0 s)  ν e from µ +  Produce ν µ  + decay ν e from K  from K + + , K , K 0 0 decay decay  Select ν e Δ ⇒ Δ ⇒ Νγ Νγ    Observe an excess or not? Check if the   Out of tank events (‘ Out of tank events ( ‘dirt dirt’ ’) ) excess is consistent with oscillation

Strategy Modern neutrino beam experiments use a ‘near to far’ ratio to observe oscillations  Directly compare initial neutrino beam to final neutrino beam  This causes many systematic errors to cancel between the two samples, such as flux and cross sections MiniBooNE has no near detector, but we can still use measurements to constrain backgrounds Two complementary analysis approaches address constraints  Use a data sample to correct a background  Fit two samples simultaneously to reduce the size of the errors

Constraints with MiniBooNE data Use a data sample to correct a background  We must learn about the signal region without looking at it (blind analysis)  Measure pure or enhanced samples of a given background; rate measurements circumvent flux, cross section errors  Infer the shape and normalization of the background in the signal region  Examples: NC π 0 misIDs, out of tank events, ν e from µ decay

Constraint Example: NC π 0 s M γγ Mass Distribution for Various p π 0 Momentum Bins  Measure π 0 s in MiniBooNE very pure (~90%) sample  Compare the observed π 0 rate to the MC as a function of π 0 momentum, and make a correction factor  Reweight the misidentified π 0 s in the ν e sample based on their momentum by this correction factor  Can also correct radiative events Δ → N + γ

Constraint Example: Out of tank events  Events from interactions in the surrounding rock produce photons which pass the veto and give events Dirt component within the inner tank ( so called “dirt”) Data events  Create a sample of enhanced dirt events in time with beam, minimal veto activity, 1 subevent, not decay electron low energy, high radius  Checks prediction spatial distribution, energy spectrum of these events; sets the normalization visible energy (MeV) for dirt events in the ν e sample

Constraint Example: ν e from µ + Without employing a link between ν e and ν µ , ν e from µ + would have flux, cross section, detector uncertainties However, for each ν e produced from a µ + , there was a corresponding ν µ and we observe that ν µ spectrum This is true here because the pion decay is very forward Therefore, we know that some combination of cross sections, flux, etc errors are excluded by our own data, and so the error is reduced ν µ E ν µ µ + e + π + ν e ν µ E π

Constraints in action Two methods to include ν µ information into the ν e analysis:  Reweight the ν e based on the observed ν µ spectrum, and then fit the ν e s for oscillation (used in likelihood analysis)  Fit simultaneously the ν µ and ν e energy spectrums (used in boosted decision tree analysis) ν µ provide information to constrain errors, ν e provide information for oscillation parameters

Fit Mechanics To fit data d to some prediction p, form a χ 2: bins χ 2 = ∑ Δ i M ij − 1 Δ j i , j = 1 where Δ = (d-p) in each energy bin i or j. 2 parameter mixing scenario included in p ( M ij ) - 1 is the inverse of the error matrix Systematic (and statistical) uncertainties in M ij matrix

If only it were this simple... If M ij were just statistics, it would N 1 0 0 0 0 have values along the diagonals, 0 N 2 0 0 0 and zero elsewhere. This matrix M ij =  0 0 0 0 has no correlations, as each bin 0 0 0 N k 0 contributes to the χ 2 only as the square of itself. 0 0 0 0 N k To construct this matrix for any set of systematics uncertainties α , one would measure ∑ M ij = σ 2 ij ( α ) each α and sum the square of the error in each bin: α = 1 ( σ 21 + σ 2 2 + … + σ 2 α ) 1 0 0 0 0 ( σ 21 + σ 2 2 + … + σ 2 α ) 2 0 0 0 0 M ij =  0 0 0 0 ( σ 21 + σ 2 2 + … + σ 2 α ) k − 1 0 0 0 0 ( σ 21 + σ 2 2 + … + σ 2 α ) k 0 0 0 0

... now to reality Consider a single source of error, but now with correlations: ⎛ ⎞ σ 211 ρ 21 σ 2 σ 1 ρ k 1 σ k σ 1  ⎜ ⎟ ρ 12 σ 1 σ 2 σ 2 22   ⎜ ⎟ M ij = ⎜ ρ kk − 1 σ k σ k − 1 ⎟    ⎜ ⎟ ⎝ ρ 1 k σ 1 σ k ρ k − 1 k σ k − 1 σ k σ 2 kk ⎠  Now, bin i is related to bin j by ρ ij σ i σ j

Fit Mechanics Do a combined oscillation fit to the observed ν µ and ν e energy distribution Note this χ 2 includes ν µ sample and ν e sample bins, and a 2 parameter oscillation scenario. M ij has 4 distinct sections: ν e / ν e bin terms, ν µ / ν µ bin terms, and cross terms which mix ν µ and ν e ν e ν e / ν µ ⎛ ⎞ M ij = ⎜ ⎟ ν µ / ν e ν µ ⎝ ⎠

How this helps: 2x2 case Take just 1 ν µ , ν e bin: ⎛ ⎞ N e + σ 2 e ρσ e σ µ M ij = ⎜ ⎟ ⎝ ρσ µ σ e N µ + σ 2 µ ⎠ Invert, and multiply by ( Δ e Δ µ ) Δ = data-prediction(signal). The χ 2 minimizes for signal of: ⎛ ⎞ ρ Δ µ / σ µ signal = Δ e 1 − ⎜ ⎟ ( ) N µ / σ µ + 1 Δ e / σ e ⎝ ⎠ with an uncertainty of: ⎛ ⎞ ρ 2 σ 2 signal = N e + σ e 2 1 − ⎜ ⎟ ( ) N µ / σ µ + 1 ⎝ ⎠ With ρ approaching 1 (high correlation) and small statistical error for ν µ : signal = Δ e 1 − Δ µ / σ µ ⎛ ⎞ ⎟ ± N e ⎜ ⎝ ⎠ Δ e / σ e or the error on the signal is limited by the statistical error, not systematic error of the ν e sample

Building an error matrix For each error, build a error matrix, and then sum for final error matrix M ij ( π + ) Flux from π + / µ + decay + M ij ( K + ) Flux from K + decay + M ij ( K 0) Flux from K 0 decay + M ij ( tar / beam ) Target/Beam model + M ij ( x sec) ν cross section + M ij ( NC π 0) NC π 0 yield + M ij ( dirt ) Out of tank events + M ij ( OM ) Optical Model + M ij ( DAQ ) DAQ electronics model = M ij ( total )

Building an error matrix: π + production Take existing data ( HARP 8.9 GeV/c pBe π + production data) and fit it to a parameterization (Sanford-Wang) The fit gives the 9 parameters c i and their errors The parameterization provides correlations amongst the c i (covariance matrix) + d 2 σ (p+A-> π + +X) (p , θ ) c5 ) -c 6 θ (p-c 7 p beam cos c8 θ ) ] = c 1 p c2 (c 9 -p/p beam ) exp[-c 3 (p c4 /p beam dp d Ω

Building an error matrix: π + production Throw the c i according to their covariance matrix and within their errors many many times... shape error total error + ... = p1 The error matrix: p3 throws M ij π + prod = 1 ∑ ( N cv − N k ) i ( N cv − N k ) j throws k = 1 p2

Building an error matrix: light propagation in detector For the optical model, use a combination of external and internal measurements to produce the covariance matrix Use measurements of oil, PMTs to decide model’s (39!) parameters and initial errors  Scintillation from p beam (IUCF)  Scintillation from cosmic µ (Cincinnati)  Fluorescence Spectroscopy (FNAL)  Time resolved spectroscopy (JHU, Princeton)  Attenuation (Cincinnati)

Building an error matrix: light propagation in detector Create different ‘universes’ with the parameters varied within errors Compare them to muon decay electron (Michel) sample variables, such as time, charge, hit topology Keep universes which have a p1 first throws good χ 2 as compared to data This restricted space defines the parameters and p3 correlations. Draw from the new space, and build an error matrix: universes M ijOM = 1 ∑ ( N cv − N k ) i ( N cv − N k ) j p2 universes k = 1 second throws

Building an error matrix: light propagation in detector Example: Optical model final error matrix highly correlated highly anticorrelated not correlated ν e ν e / ν µ ⎛ ⎞ M ij = ⎜ ⎟ ν µ / ν e ν µ ⎝ ⎠

Error ‘budget’ source of uncertainty TBL/BDT constrain Reduced by All of our errors are on ν e background relating ν µ to ed by % error highly correlated, but ν e MB data? here are the diagonal Flux from π + / µ + decay 6.2 / 4.3 Y Y errors Flux from K + decay 3.3 /1.0 Y Y Flux from K 0 decay 1.5 / 0.4 Y Y Target/Beam model 2.8 / 1.3 Y Y ν cross section 12.3 / 10.5 Y Y NC π 0 yield 1.8 / 1.5 Y Out of tank events 0.8 / 3.4 Y Optical Model 6.1 / 10.5 Y Y DAQ electronics 7.5 / 10.8 Y model * shows errors before ν e / ν µ constraint is applied

Summary Many oscillation experiments employ a near to far ratio to reduce their systematic errors; MiniBooNE uses a ‘ ν e / ν µ ’ ratio to reduce errors MiniBooNE constrains all backgrounds with data samples The error formalism includes all correlations between ν µ and ν e , which are then exploited in the final fit ν µ small statistical error lowers the ν e effective systematic error