Systematic Errors of MiniBooNE K. B. M. Mahn, for the MiniBooNE collaboration Physics Department, Mail Code 9307, Columbia University, New York, NY 10027, USA Abstract. Modern neutrino oscillation experiments use a ‘near to far’ ratio to observe oscillation; many systematic errors cancel in a ratio between the near detector’s unoscillated event sample and the far detector’s oscillated one. Similarly, MiniBooNE uses a ν e to ν µ ratio, which reduces any common uncertainty in both samples. Here, we discuss the systematic errors of MiniBooNE and how the ν µ sample constrains the ν e signal sample. PACS: 14.60.Pq INTRODUCTION events at high radius, low energy and in time with the beam with minimal veto activity. The spatial distribution MiniBooNE, a short-baseline neutrino experiment de- and energy spectrum of these events sets their normaliza- signed to test ν µ to ν e oscillations[1], published first re- tion. sults this year. Because MiniBooNE employed a ‘blind’ analysis, the ν e potential signal and backgrounds had to Constraining ν e from µ + decay be understood without direct observation of the signal region. The constraints on some of the ν e backgrounds– misidentified neutral current single pion events (NC π 0 ), The largest single source of background in the ν e sam- out of tank (“dirt”) events and intrinsic electron neutri- ple are events which are really ν e , but are inherent to nos in the beam– are discussed. The implementations of the beam. Charged pions are the main source of neu- trinos in MiniBooNE. A π + decay produces both a ν µ the constraints in the final appearance analysis are also and a µ + , and the µ + can decay into a ν e . However, be- detailed. cause the pion decay is very forward for neutrinos de- tected in MiniBooNE, the ν µ reconstructed energy spec- Constraining the NC π 0 background trum measures the parent π + spectrum very well, and consequently constrains the ν e from µ + background in The largest reducible background in the ν e sample are the signal region. NC π 0 interactions which are misidentified as ν e events. The pion can decay asymmetrically and, if one of the de- cay photons is very low energy, only a single, electron- IMPLEMENTATION OF CONSTRAINTS like ring is observable in the tank. Such events are al- most indistinguishable from a true ν e . To constrain this In this way, the ν µ sample serves as the “near detector” sample, we measure well reconstructed two ring events sample. An expected oscillation would give an unobserv- which is a sample of high purity π 0 events. We compare able 0 . 25% disappearance in the ν µ sample, but, due to the observed rate to the MiniBooNE simulation, and cor- the large size of the potential ν e signal relative to back- rect the simulation’s normalization of these events in π 0 ground, we can observe a noticeable excess. momentum bins. The normalization correction is propa- MiniBooNE employed two independent ν e selection gated to the misidentified π 0 in the signal ν e sample. criterion: a simple, log-likelihood analysis comparing electron to muon to pion like rings, and a boosted deci- sion tree method which takes multiple weaker variables in concert to create a single, powerful classifier. The two Constraining the dirt events ν e analyses also had two different methods to include ν µ information in the final oscillation fit, either by reweight- Events from interactions in the rock surrounding Mini- ing of ν e sample or by a simultaneous fit to both samples. BooNE produce photons which pass the veto and give In the likelihood-based analysis, the ν e reconstructed events in the inner tank, called “dirt” events. Pions which neutrino energy spectrum is reweighted based on the ob- decay near the edge of the tank can lose a photon to the served ν µ spectrum. For example, in the case of flux er- outside of the tank, and also appear as a single electron- rors, a matrix is made to relate the ν µ observed energy like ring. An enhanced sample of dirt events is selects Systematic Errors of MiniBooNE November 9, 2007 1
spectrum to the π + energy spectrum. This is a correction When the fit is done, the bins which contain the error based on data applied to the π + of the ν e from π + . A sec- and correlation between ν µ and ν e bins will reduce the ond correction maps ν µ reconstructed neutrino energy to overall error on the ν e sample. true neutrino energy, and this is applied to the potentially As an example of how the ν µ rate can constrain the oscillated events from ν µ , along with any ν µ induced in- error on the ν e , consider the error matrix for one ν µ bin teraction not already weighted. Then, just the ν e are fit and one ν e bin, for oscillation. The second method, used by the boosted � N e + σ 2 decision tree analysis, is discussed in more detail here. � ρσ e σ µ e In it, both the ν µ and ν e reconstructed neutrino energy M ij = (4) N µ + σ 2 ρσ µ σ e spectra are fit simultaneously; the ν µ spectrum assumes µ no oscillation and constrains the errors on the ν e back- After minimizing the χ 2 with this M ij , the uncertainty grounds, and the total ν e sample provides the oscillation on the signal will be: parameters. ρ 2 � � σ 2 signal = N e + σ 2 1 − (5) e ( N µ / σ µ + 1 ) Oscillation Fit Details If the two bins are highly correlated, ρ → 1 or ρ → − 1, To compare data to a prediction, one can form a simple and if the ν µ has large statistics, N µ χ 2 distribution, σ µ → 0, the error on the fitted signal becomes N e . The error on the signal in the bins fit is therefore limited by the statistical, not systematic χ 2 = ∑ ∆ i M − 1 ij ∆ j (1) error of the ν e sample. In the case of no correlation ( i , j = 1 ρ → 0), then the ν e sample has no extra information with ∆ i = Data i − Prediction i , the difference between on the systematics, and suffers from the full statistical data and prediction in energy bin i. M − 1 is the inverse and systematic error. The high statistics ν µ sample, with ij of the error matrix, which contains all systematic and perfect correlations, fixes the systematic error of the statistical uncertainties. ν e ; any lack of correlation will bring with it associated If M ij were just statistical error, it would contain the unconstrained systematic error. number of data events in each bin along the diagonal, and zero in all other entries (assuming negligible simulation statistical error). Uncorrelated systematic errors, with no Building an error matrix bin to bin correlations across reconstructed energy bins would have the sum of the α sources of error on the To form an error matrix, we sum the error matrices diagonals: from each independent source of error. In the final fit, we consider errors from the production of charged pi- systematics ons and kaons, neutral kaons, our target/beam model, ∑ σ 2 ij ( α ) δ i , j M ij = (2) the neutrino cross section, the NC π 0 rate measurement, α = 1 events from outside the tank, light propagation in the de- Most sources of systematic error can have correlations tector (optical model) and DAQ electronics model. The between different bins in energy. Eq. 3 shows the error next section goes into more detail on the flux and opti- matrix for a single source of systematic error: cal model uncertainties and the construction of those two error matrices. σ 2 ρ 21 σ 2 σ 1 ... ρ N 1 σ N σ 1 1 σ 2 ρ 12 σ Z 1 σ 2 ... ρ N 2 σ N σ 2 M ij = 2 (3) ... ... ... ... Pion production uncertainties σ 2 ρ 1 N σ 1 σ N ρ 2 N σ 2 σ N ... N We compare the existing pion production data from where ρ i , j corresponds to the correlation between the HARP[2] to a Sanford-Wang parameterization function systematic error in those bins, σ i and σ j . of the differential cross section[3]: The final important detail of the fit is that it is a simultaneous to both ν e and ν µ reconstructed neutrino d 2 σ � � energy. The error matrices in the final oscillation fit p c 1 p c 2 dpd Ω = 1 − p beam − c 9 contain not just ν e energy bins, but also include the ν µ � � energy bins as well. So the error matrix contains sections p c 4 − c 6 θ ( p − c 7 p beam cos c 8 θ ) exp − c 3 (6) which have correlations between the ν µ and ν e bins. p c 5 beam Systematic Errors of MiniBooNE November 9, 2007 2
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