Measurement of Muon Neutrino Quasielastic Scattering on Carbon

arXiv:0706.0926v2 [hep-ex] 25 Jan 2008 Measurement of Muon Neutrino Quasi-Elastic Scattering on Carbon A. A. Aguilar-Arevalo5, A. O. Bazarko12, S. J. Brice7 , B. C. Brown7 , L. Bugel5 , J. Cao11 , L. Coney5 , J. M. Conrad5 , D. C. Cox8 , A. Curioni16 , Z. Djurcic5 , D. A. Finley7 , B. T. Fleming16 , R. Ford7 , F. G. Garcia7 , G. T. Garvey9 , C. Green7,9 , J. A. Green8,9 , T. L. Hart4 , E. Hawker15 , R. Imlay10 , R. A. Johnson3 , P. Kasper7 , T. Katori8 , T. Kobilarcik7, I. Kourbanis7 , S. Koutsoliotas2, E. M. Laird12 , J. M. Link14 , Y. Liu11 , Y. Liu1 , W. C. Louis9 , K. B. M. Mahn5 , W. Marsh7 , P. S. Martin7 , G. McGregor9, W. Metcalf10 , P. D. Meyers12 , F. Mills7 , G. B. Mills9 , J. Monroe5 , C. D. Moore7 , R. H. Nelson4 , P. Nienaber13 , S. Ouedraogo10, R. B. Patterson12 , D. Perevalov1, C. C. Polly8 , E. Prebys7 , J. L. Raaf3 , H. Ray9 , B. P. Roe11 , A. D. Russell7 , V. Sandberg9 , R. Schirato9 , D. Schmitz5 , M. H. Shaevitz5 , F. C. Shoemaker12 , D. Smith6 , M. Sorel5 , P. Spentzouris7 , I. Stancu1 , R. J. Stefanski7 , M. Sung10 , H. A. Tanaka12 , R. Tayloe8 , M. Tzanov4 , R. Van de Water9 , M. O. Wascko10 , D. H. White9 , M. J. Wilking4 , H. J. Yang11 , G. P. Zeller5 , E. D. Zimmerman4 (The MiniBooNE Collaboration) 1 University of Alabama; Tuscaloosa, AL 35487 2 Bucknell University; Lewisburg, PA 17837 3 University of Cincinnati; Cincinnati, OH 45221 4 University of Colorado; Boulder, CO 80309 5 Columbia University; New York, NY 10027 6 Embry-Riddle Aeronautical University; Prescott, AZ 86301 7 Fermi National Accelerator Laboratory; Batavia, IL 60510 8 Indiana University; Bloomington, IN 47405 9 Los Alamos National Laboratory; Los Alamos, NM 87545 10 Louisiana State University; Baton Rouge, LA 70803 11 University of Michigan; Ann Arbor, MI 48109 12 Princeton University; Princeton, NJ 08544 13 Saint Mary’s University of Minnesota; Winona, MN 55987 14 Virginia Polytechnic Institute & State University; Blacksburg, VA 24061 15 Western Illinois University; Macomb, IL 61455 16 Yale University; New Haven, CT 06520 (Dated: October 23, 2018) The observation of neutrino oscillations is clear evidence for physics beyond the standard model. To make precise measurements of this phenomenon, neutrino oscillation experiments, including MiniBooNE, require an accurate description of neutrino charged current quasi-elastic (CCQE) cross sections to predict signal samples. Using a high-statistics sample of νµ CCQE events, MiniBooNE finds that a simple Fermi gas model, with appropriate adjustments, accurately characterizes the CCQE events observed in a carbon-based detector. The extracted parameters include an effective eff axial mass, MA = 1.23 ± 0.20 GeV, that describes the four-momentum dependence of the axialvector form factor of the nucleon; and a Pauli-suppression parameter, κ = 1.019 ± 0.011. Such a modified Fermi gas model may also be used by future accelerator-based experiments measuring neutrino oscillations on nuclear targets. The recent observation of neutrino oscillations is strong evidence for massive neutrinos and, therefore, for physics beyond the standard model. Accelerator-based experiments searching for neutrino oscillations, such as MiniBooNE [1] and K2K [2], use charged current quasi-elastic (CCQE) interactions to search for the appearance of electron neutrinos (νe n → e− p) in beams of muon neutrinos. The muon neutrino CCQE interaction (νµ n → µ− p) thus provides a calibration for the neutrino beam and for the interaction cross section. In addition, such events dominate at energies between 200-2000 MeV where the oscillation searches are conducted. To ensure high event yields, these experiments use nuclear media (carbon or water) as the neutrino target; therefore, it is crucial to employ an accurate model of the CCQE interaction on nuclei. In this Letter, we describe the model improvements developed for the recent oscillation search from the MiniBooNE experiment [1]. The modified model describes this reaction remarkably well and should be relevant for future accelerator-based neutrino oscillation searches. To model the scattering from nucleons confined in nuclei, most neutrino oscillation experiments employ an event generator based on the relativistic Fermi gas (RFG) model [3]. Such models assume a flat nucleon momentum distribution up to some Fermi momentum (pF ), assign a single value for the nucleon binding energy (EB ) to account for the initial and final state total energies, and utilize standard nucleon vector and axial-vector on-shell form factors. Many of these model parameters may be inferred from existing data; for example, pF , EB , and the 2 vector form factors can be determined from elastic electron scattering data [4, 5]. Despite providing these constraints, electron data yield limited information on the axial-vector form factor of the nucleon and the CCQE cross section at very low four-momentum transfer (Q2 ). Present knowledge of the axial-vector form factor has been informed largely by past neutrino experiments, but these suffer from low statistics and were performed using predominantly deuterium targets [6]. Since these early measurements, neutrino experiments have encountered difficulties describing their data at low Q2 , where nuclear effects are largest, and have often measured axial-vector form factor parameters above some minimum Q2 value. The MiniBooNE experiment has collected the largest sample of low energy muon neutrino CCQE events to date. We describe here the use of such events in tuning the RFG model to better describe quasi-elastic scattering on nuclear targets. The analysis fits the reconstructed Q2 distribution of the MiniBooNE CCQE data in the region 0 < Q2 < 1 GeV2 to a simple RFG model [3] with two adjustable parameters: the axial mass, MA , appearing in the axial-vector form factor; and κ, a parameter that adjusts the level of Pauli-blocking at low values of Q2 . The best-fit model results in a good description of the data across the full kinematic phase space including the lowQ2 region. This technique is crucial to the MiniBooNE oscillation search [1] as it is used to predict the νe CCQE oscillation events based on the constraints provided by the high-statistics MiniBooNE νµ CCQE sample. The Fermilab Booster neutrino beam, optimized for the MiniBooNE oscillation search, is particularly suited for investigation of low energy neutrino interactions. The Fermilab Booster provides 8.89 GeV/c protons which collide with a 71 cm long beryllium target inside a magnetic horn. The horn focuses positively charged pions and kaons produced in these collisions, which can subsequently decay in a 50 m long decay region, yielding an intense flux of muon neutrinos. A geant4-based [7] beam simulation uses a parametrization [8] of pion production cross sections based on recent measurements from the HARP [9] and E910 [10] experiments, along with a detailed model of the beamline geometry to predict the neutrino flux as a function of neutrino energy and flavor. The resulting flux of neutrinos at the MiniBooNE detector is predicted to be 93.8% (5.7%) νµ (ν̄µ ) with a mean energy of ∼ 700 MeV. Because 99% of the flux lies below 2.5 GeV, the background from high multiplicity neutrino interactions is small. Approximately 40% of the total events at MiniBooNE are predicted to be νµ CCQE, of which 96% result from pion decays in the beam. The MiniBooNE detector is a spherical tank of inner radius 610 cm filled with 800 tons of mineral oil (CH2 ), situated 541 meters downstream of the proton target. An optical barrier divides the detector into two regions, an inner volume with a radius of 575 cm and an outer volume 35 cm thick. The inner region of the tank houses 1280 inward-facing 8 inch photomultiplier tubes (PMTs), providing 10% photocathode coverage. The outer region is lined with 240 pair-mounted PMTs which provide a veto for charged particles entering or leaving the tank. Muons produced in CCQE interactions emit primarily Cherenkov light with a small amount of scintillation light. A large number of muons stop and decay in the main detector volume. The muon kinetic energy resolution is 7% at 300 MeV and the angular resolution is 5◦ . The response of the detector to muons is calibrated using a dedicated muon tagging system that independently measures the muon energy for cosmic ray muons ranging up to 800 MeV. Neutrino interactions within the detector are simulated with the v3 nuance event generator [11]. This program provides the framework for tuning the CCQE cross section parameters (described below) and predicts backgrounds to the sample, including neutrino induced single pion production events (CC 1π). Pion interactions in the nucleus and photon emission from nuclear de-excitation in nuance are tuned to reproduce MiniBooNE and other [12] data. A geant3-based [13] detector model (with gcalor [14] hadronic interactions) simulates the detector response to particles produced in neutrino interactions. The simulation of light production and propagation in mineral oil has been tuned using external small-sample measurements [15], muon decay electrons (also used to calibrate the energy scale), and recoil nucleons from neutrino neutral current (NC) elastic scattering events. The predicted events are additionally overlaid with events measured in a beam-off gate, in order to incorporate backgrounds from natural radioactivity and cosmic rays into the simulated data. Because of the low energy neutrino beam and MiniBooNE detector capabilities, the identification of νµ CCQE interactions relies solely on the detection of the primary muon and associated decay electron in these events: νµ + n → µ− + p, µ− → e− + νµ + ν¯e . This simple selection is highly effective for several reasons. First, the efficiency for detecting the decay of the µ− produced in such events is high, 83%. The losses are due to muon capture on carbon (8% [16]) and insufficient decay time or energy of the decay electron (10%). Second, the CC 1π + contamination is significantly reduced by requiring a single decay electron, since CC 1π + events typically yield two decay electrons, one each from the primary muon and the π + decay chains. The exceptions are cases in which the primary µ− is captured or, more likely, the π + is either absorbed or undergoes a charge-changing interaction in the target nucleus or detector medium. Each of these processes is included in the detector simulation. Finally, by avoiding requirements on the outgoing proton kinematics, the selection is inherently less dependent on nuclear models. Timing information from the PMTs allows the light produced by the initial neutrino interaction (first “subevent”) to be separated from light produced by the decay electron (second sub-event). The time and charge response of the PMTs is used to reconstruct the position, kinetic energy, and direction vector of the primary particle within each sub-event. Once separated into subevents, we require that the first sub-event (the neutrino interaction) must occur in coincidence with a beam pulse, have a reconstructed position < 500 cm from the center of the detector, possess < 6 veto-PMT hits to ensure containment, and have > 200 main-PMT hits to avoid electrons from cosmic ray muon decays. The second subevent (the µ− decay electron) must have < 6 veto-PMT hits and < 200 main-PMT hits. Subsequent cuts specifically select νµ CCQE events and discriminate against CC 1π + backgrounds. First, events must contain exactly two sub-events. Second, the distance between the electron vertex and muon track endpoint must be less than 100 cm, ensuring that the decay electron is associated with the muon track. A total of 193,709 events pass the MiniBooNE νµ CCQE selection criteria from 5.58 × 1020 protons on target collected between August 2002 and December 2005. The cuts are estimated to be 35% efficient at selecting νµ CCQE events in a 500 cm radius, with a CCQE purity of 74%. The 35% efficiency is the product of a 50% probability for containing events within the tank, the aforementioned 83% muon decay detection efficiency, and an 85% efficiency for the electron vertex to muon endpoint requirement. The predicted backgrounds are: 75% CC 1π + , 15% CC 1π 0 , 4% NC 1π ± , 3% CC multi-π, 1% NC elastic, 1% ν̄µ CC 1π − , 1% NC 1π 0 , < 1% η/ρ/K production, and < 1% deep inelastic scattering (DIS) and other events [11]. In the analysis, cross section uncertainties of 25%, 40%, and 25% are assumed on the 1π, multi-π plus η/ρ/K production, and DIS backgrounds, respectively. Because pions can be absorbed via final state interactions in the target nucleus, a large fraction of the background events look like CCQE events in the MiniBooNE detector. “CCQElike” events, all events with a muon and no pions in the final state, are predicted to be 84% of the sample after cuts. The observables in the MiniBooNE νµ CCQE sample are the muon kinetic energy Tµ , and the muon angle with respect to the neutrino beam direction θµ . The high-statistics MiniBooNE data sample allows us to verify the simulation in two dimensions. Figure 1 shows the level of agreement between the shape of the data and simulation in the CCQE kinematic quantities before any CCQE cross section model adjustments. For this comparison, the simulation assumes the RFG model as implemented in nuance [3, 11], with EB = 34 MeV [4], pF = 220 MeV/c [4], updated non-dipole vector form factors [5], and a non-zero pseudoscalar form factor [17]. cos θµ 3 1 (a) (b) (c) (d) (e) (f) 0.8 1.2 1.15 0.6 1.1 (a) Eν=0.4GeV (b) Eν=0.8GeV (c) Eν=1.2GeV 0.4 0.2 -0 2 -0.2 1.05 1 2 (d) Q =0.2GeV 2 (e) Q =0.6GeV2 2 (f) Q =1.0GeV2 -0.4 -0.6 0.95 0.9 0.85 -0.8 -1 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0.8 Tµ (GeV) FIG. 1: Ratio of MiniBooNE νµ CCQE data/simulation as a function of reconstructed muon angle and kinetic energy. The prediction is prior to any CCQE model adjustments and has been normalized to the data. The χ2 /dof = 79.5/53. The ratio forms a 2D surface whose values are represented by the gray scale, shown on the right. If the simulation modeled the data perfectly, the ratio would be unity everywhere. Contours of constant Eν and Q2 are overlaid, and only bins with > 20 events in the data are plotted. The axial-vector form factor is assumed to have a dipole form as a function of Q2 with one adjustable parameter, MA , the so-called “axial mass”, FA (Q2 ) = gA /(1 + Q2 /MA2 )2 . The simulation shown in Fig. 1 specifically assumes gA = 1.2671 [18] and MA = 1.03 GeV [19]. These model parameters are common defaults in most neutrino simulations. The figure shows that the disagreement between data and simulation follows lines of constant Q2 and not Eν . This supports the assumption that the data/model disagreement is not due to a mis-modeling of the incoming neutrino energy spectrum but an inaccuracy in the simulation of the CCQE process itself. We also explicitly assume no νµ disappearance due to oscillations. Guided by indications that the data-model discrepancy is only a function of Q2 , we have modified the existing νµ CCQE model rather than introduce more drastic changes to the cross section calculation. This approach works well and requires adjustment of only two parameters: MA and Elo . The parameter Elo effectively controls the effect of Pauli-blocking. It is the lower bound of integration over initial state nucleon energy and appears within the RFG model together with an upper bound Ehi : q q Ehi = p2F + Mn2 , Elo = p2F + Mp2 − ω + EB , (1) where Mn is the target neutron mass, Mp is the outgoing proton mass, and ω is the energy transfer. In the RFG model, Ehi is the energy of an initial nucleon on the Fermi surface and Elo is the lowest energy of an ini- 4 Q2 = −q 2 = −m2µ + 2Eν (Eµ − pµ cos θµ ) > 0, (2) Eν = 2 2(Mn − EB )Eµ − (EB − 2Mn EB + m2µ + ∆M 2 ) ,(3) 2 [(Mn − EB ) − Eµ + pµ cos θµ ] where ∆M 2 = Mn2 − Mp2 and EB > 0. A small correction is applied to Eν in both data and simulation to account for the biasing effects of Fermi-smearing. This procedure, while yielding a more accurate Eν estimate, has a negligible impact on the Q2 fit to MiniBooNE CCQE data. These expressions, with reconstructed muon kinematics, yield an Eν resolution of 11% and a Q2 resolution of 21% for CCQE events. The model parameters MA and κ are obtained from a least-squares fit to the measured data in 32 bins of reconstructed Q2 from 0 to 1 GeV2 . All other parameters of the model are held fixed to the values listed previously, and a complete set of correlations between systematic uncertainties is considered. The total prediction is normalized to the data for each set of parameter values. Thus, the procedure is sensitive only to the shape of the Q2 distribution, and any changes in the total cross section due to parameter variation do not impact the quality of fit. The Q2 distributions of data and simulation before and after the fitting procedure are shown in Figure 2. The χ2 /dof of the fit is 32.8/30 and the parameters extracted from the MiniBooNE νµ CCQE data are: MAeff = 1.23 ± 0.20 GeV; κ = 1.019 ± 0.011. 12000 (4) (5) While normalization is not explicitly used in the fit, the new model parameters increase the predicted rate of νµ CCQE events at MiniBooNE by 5.6%. The ratio of detected events to predicted, with the best-fit CCQE model parameters, is 1.21 ± 0.24. In general, varying MA allows us to reproduce the high Q2 behavior of the observed data events. A fit for MA 1.5 1.4 1.3 10000 1.2 8000 1.1 6000 1 1.01 1.02 1.03 1.04 1.05 κ 4000 2000 0 0 where mµ is the muon mass, Eµ (pµ ) is the reconstructed muon energy (momentum), and θµ is the reconstructed muon scattering angle. The reconstructed neutrino energy Eν is formed assuming the target nucleon is at rest inside the nucleus: MA (GeV) tial nucleon that leads to a final nucleon just above the Fermi momentum (and thus obeying the exclusion principle in the final state). In practice, a simple scaling of Elo was implemented in the MiniBooNE CCQE data fit q 2 via Elo = κ( pF + Mp2 − ω + EB ). The parameter κ adds a degree of freedom to the RFG model which can describe the smaller cross section observed in the data at low momentum transfer and is likely compensating for the naive treatment of Pauli-blocking in the RFG model. The adjusted RFG model is then fit to the shape of the reconstructed Q2 distribution in the MiniBooNE νµ CCQE data: Events 14000 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 2 0.9 2 1 Q (GeV ) FIG. 2: Reconstructed Q2 for νµ CCQE events including systematic errors. The simulation, before (dashed) and after (solid) the fit, is normalized to data. The dotted (dot-dash) curve shows backgrounds that are not CCQE (not “CCQElike”). The inset shows the 1σ CL contour for the best-fit parameters (star), along with the starting values (circle), and fit results after varying the background shape (triangle). above Q2 > 0.25 GeV2 yields consistent results, MAeff = 1.25±0.12 GeV. However, fits varying only MA across the entire Q2 range leave considerable disagreement at low Q2 (χ2 /dof = 48.8/31). The Pauli-blocking parameter κ is instrumental here, enabling this model to match the behavior of the data down to Q2 = 0 (Figure 2). Figure 3 shows the agreement between data and simulation after incorporation of the MA and κ values from the Q2 fit to MiniBooNE data. Comparing to Figure 1, the improvement is substantial and the data are welldescribed throughout the kinematic phase space. Table I shows the contributions to the systematic uncertainties on MA and κ. The detector model uncertainties dominate the error in MA due to their impact on the energy and angular reconstruction of CCQE events in the MiniBooNE detector. The dominant error on κ is the uncertainty in the Q2 shape of background events. This error (not included in the contour of Figure 2) is evaluated in a separate fit, where MiniBooNE CC 1π + data are used to set the background instead of the event generator prediction, and then added in quadrature. The result reported here, MAeff = 1.23 ± 0.20 GeV, is consistent with a recent K2K measurement on a water target, MA = 1.20 ± 0.12 GeV [20]. Both values are consistent with but higher than the historical value, MA = 1.026 ± 0.021 GeV, set largely by deuterium-based bubble chamber experiments [19]. The MA value reported here should be considered an “effective parameter” in the sense that it may be incorporating nuclear effects not otherwise included in the RFG model. In particular, it may be that a more proper treatment of the cos θµ 5 1 1.2 0.8 1.15 0.6 1.1 0.4 1.05 0.2 1 -0 -0.2 0.95 -0.4 0.9 -0.6 We wish to acknowledge the support of Fermilab, the Department of Energy, and the National Science Foundation in the construction, operation, and data analysis of the MiniBooNE experiment. 0.85 -0.8 -1 0 eter, κ = 1.019 ± 0.011, achieving substantially improved agreement with the observed kinematic distributions in this data set. Incorporation of both fit parameters allows, for the first time, a description of neutrino CCQE scattering on a nuclear target down to Q2 = 0 GeV2 . 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0.8 Tµ (GeV) FIG. 3: Ratio of data/simulation as a function of muon kinetic energy and angle after CCQE model adjustments. The simulation has been normalized to the data. The χ2 /dof = 45.1/53. Compare to Figure 1. eff TABLE I: Uncertainties in MA and κ from the fit to MiniBooNE νµ CCQE data. The total error is not a simple quadrature sum due to correlations between the Q2 bins created by the systematic uncertainties. error source data statistics neutrino flux neutrino cross sections detector model CC π + background shape total error eff δMA 0.03 0.04 0.06 0.10 0.02 0.20 δκ 0.003 0.003 0.004 0.003 0.007 0.011 nucleon momentum distribution in the RFG would yield an MA value in closer agreement to that measured on deuterium. Future efforts will therefore explore how the value of MA extracted from the MiniBooNE data is altered upon replacement of the RFG model with more advanced nuclear models [21]. In summary, modern quasi-elastic scattering data on nuclear targets are revealing the inadequacies of present neutrino cross section simulations. Taking advantage of the high-statistics MiniBooNE νµ CCQE data, we have extracted values of an effective axial mass parameter, MAeff = 1.23 ± 0.20 GeV, and a Pauli-blocking param- [1] A.A. Aguilar-Arevalo et al., Phys. Rev. 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