1. Preliminary Results for CCQE Scattering with the MINOS Near Detector Mark Dorman, UCL On behalf of the MINOS Collaboration NUINT 09, CC/NC QE Scattering, 19 th May 2009 1

2. 2 Introduction MC / QE Theory Data/MC Comparisons Axial Mass Fits Summary/Outlook Overview Introduction to the NuMI beam and MINOS Near Detector MINOS MC simulation and ν μ -CC QE scattering theory ν μ -CC event selection and sample characteristics ν μ -CC QE event selection and sample characteristics Axial-vector mass fit technique and parameters Fit results and outlook for the analysis NUINT 09, CC/NC QE Scattering, 19 th May 2009

3. 3 The NuMI Beam NUINT 09, CC/NC QE Scattering, 19 th May 2009 The distance between the target and first horn can be changed to give a variable beam energy. In the low energy configuration the beam comprises: Introduction MC / QE Theory Data/MC Comparisons Axial Mass Fits Summary/Outlook

4. 4 The Near Detector (ND) NUINT 09, CC/NC QE Scattering, 19 th May 2009 Steel Plane PMT Dark Box Multi-Anode PMT WLS Fibres Strips on adjacent planes are mounted orthogonal to allow for 3D event reconstruction. Segmentation: 5.94cm longitudinal 4.1cm transverse Scint.: 1cm thick, 4.1cm wide ν beam 1km from target 0.98 kton 282 steel planes B = 1.2 T High rates so ND is instrumented with deadtime-less QIE electronics. Introduction MC / QE Theory Data/MC Comparisons Axial Mass Fits Summary/Outlook

5. 5 Event Generation NUINT 09, CC/NC QE Scattering, 19 th May 2009 σ CC /E E ν (GeV) Total QE Single Pion NEUGEN3 event generator QE: BBA05 vector form factors, dipole F A with M A QE = 0.99 GeV Resonances: Rein-Seghal model DIS: Bodek-Yang modified LO model, tuned to e and n data in resonance/DIS overlap region Coherent production Nuclear model: relativistic Fermi Gas (Pauli-blocking of QE) FSIs: nucleons and pions Hadronization: KNO-scaling -> PYTHIA/JETSET as W increases Introduction MC / QE Theory Data/MC Comparisons Axial Mass Fits Summary/Outlook

6. 6 The Axial-Vector Mass NUINT 09, CC/NC QE Scattering, 19 th May 2009 The uncertainty in the QE cross section is dominated by the uncertainty in the axial-vector form factor. F A is written using a dipole form as: ‘Dipole Form’ Known from neutron beta-decay experiments. The quasi-elastic axial-vector mass. Can measure M A QE by looking at the Q 2 distribution for a QE-like event sample. Both the shape and rate of the distributions are affected by changes to M A QE : 1 GeV neutrinos on free nucleon Introduction MC / QE Theory Data/MC Comparisons Axial Mass Fits Summary/Outlook

7. 7 Selecting ν μ –CC Events NUINT 09, CC/NC QE Scattering, 19 th May 2009 Introduction MC / QE Theory Data/MC Comparisons Axial Mass Fits Summary/Outlook We first remove the majority of NC events by requiring a reconstructed track and then further enrich the sample using a nearest neighbour technique (kNN). The kNN combines variables that differentiate between muon tracks and the pion or proton tracks that can be reconstructed in NC events. ND Good agreement between data and MC. ND CC Selection Efficiency NC Contamination

8. 8 Energy Spectra and Flux Tuning NUINT 09, CC/NC QE Scattering, 19 th May 2009 Introduction MC / QE Theory Data/MC Comparisons Axial Mass Fits Summary/Outlook Different beam configurations sample different regions in parent hadron x f and p T. We fit the data and tune our FLUKA hadron production model. The fits also include nuisance parameters for beam optics effects, NC cross section and ND energy scales. This flux-tuning procedure has been very successful and all of the MC distributions shown in my talk will use the tuned hadron production model.

9. 9 CC Sample Kinematic Coverage NUINT 09, CC/NC QE Scattering, 19 th May 2009 Introduction MC / QE Theory Data/MC Comparisons Axial Mass Fits Summary/Outlook SampleSelection Criteria % of Tuned MC Safe DISQ>1, W>232 Low Q 2 DISQ 212 Transition1.3<W<224 QE / ΔW<1.332 These sub-samples correspond roughly to kinematic regions where the event generator is using a different piece of the interaction model. The MINOS ND sees interactions over a large region of x and Q 2.

10. 10 Safe and Low Q 2 DIS Samples NUINT 09, CC/NC QE Scattering, 19 th May 2009 Introduction MC / QE Theory Data/MC Comparisons Axial Mass Fits Summary/Outlook Default MC with flux tuning (before any other fitting or selection) models the DIS samples reasonably well. Expect systematics from flux, cross section model and intra-nuclear re-scattering to be significant though.

11. 11 Transition and QE/Δ Samples NUINT 09, CC/NC QE Scattering, 19 th May 2009 Introduction MC / QE Theory Data/MC Comparisons Axial Mass Fits Summary/Outlook Again, expect systematics from flux, cross section model and final state interactions to be significant but the flux-tuned default MC shows some large disagreements with the data for QE and resonance interactions.

12. 12 Transition and QE/Δ Samples NUINT 09, CC/NC QE Scattering, 19 th May 2009 Introduction MC / QE Theory Data/MC Comparisons Axial Mass Fits Summary/Outlook Suggests a mis-modeling of nuclear effects for resonance interactions. There is no Pauli-blocking of resonance events in the default MC. Suggests a mis-modeling of both the rate and shape of QE interactions at higher Q 2 as well as at low Q 2.

13. 13 Pauli-Blocking Resonance Interactions NUINT 09, CC/NC QE Scattering, 19 th May 2009 Introduction MC / QE Theory Data/MC Comparisons Axial Mass Fits Summary/Outlook We have not yet included a better nuclear model for resonances but have applied Pauli-blocking (and with increased Fermi momenta) as an effective low Q 2 suppression. This substitute does improve data/MC agreement.

14. 14 Selecting ν μ –CC QE Events NUINT 09, CC/NC QE Scattering, 19 th May 2009 Introduction MC / QE Theory Data/MC Comparisons Axial Mass Fits Summary/Outlook We select a QE-enriched sample using a simple cut on the hadronic shower energy and only consider events with muons that stop in the ND: E had < 250 MeV for QE sampleEfficiency: 53%, Purity: 61%

15. 15 Data/MC Comparison for QE Sample NUINT 09, CC/NC QE Scattering, 19 th May 2009 Introduction MC / QE Theory Data/MC Comparisons Axial Mass Fits Summary/Outlook

16. 16 Data/MC Comparison for QE Sample NUINT 09, CC/NC QE Scattering, 19 th May 2009 Introduction MC / QE Theory Data/MC Comparisons Axial Mass Fits Summary/Outlook Total # of events selected: Data: 344,736 MC: 292,501 Data wants more low Q 2 suppression and a flatter spectrum at higher Q 2.

17. 17 Fitting for an Effective M A QE NUINT 09, CC/NC QE Scattering, 19 th May 2009 Introduction MC / QE Theory Data/MC Comparisons Axial Mass Fits Summary/Outlook Use MINUIT to minimize: # observed events in bin i # expected events in bin i Fit parameters Shift in systematic parameter j from nominal 1σ error for systematic parameter j MC normalization Will show results from 2 shape-only fits to Q 2 QE (>0.3 and >0.0 GeV 2 ). The most important systematic effects are considered directly in the fits whilst other uncertainties are studied via their impact on the fit results. Based on observations of the transition sample we apply Pauli-blocking to the resonance interactions. We also apply a correction for the Coulomb interaction between the nucleus and outgoing lepton.

18. 18 Fit Parameter: M A QE -Scale NUINT 09, CC/NC QE Scattering, 19 th May 2009 Introduction MC / QE Theory Data/MC Comparisons Axial Mass Fits Summary/Outlook Treated as a free parameter in the fits. The effect on the QE sample is asymmetric due to the non-QE background. Note that these figures are absolutely normalized although the fits only consider the Q 2 shape. Nominal = 0.99 GeV

19. 19 Fit Parameter: Muon Energy Scale NUINT 09, CC/NC QE Scattering, 19 th May 2009 Introduction MC / QE Theory Data/MC Comparisons Axial Mass Fits Summary/Outlook We take a 1σ error of 2% for use in the penalty term (this is the published MINOS uncertainty for stopping muons). This parameter changes Q 2 via the muon-only kinematic reconstruction. Nominal = 1.00

20. 20 Fit Parameter: M A RES -Scale NUINT 09, CC/NC QE Scattering, 19 th May 2009 Introduction MC / QE Theory Data/MC Comparisons Axial Mass Fits Summary/Outlook We take a 1σ error of 15% for use in the penalty term (again, this is the published MINOS uncertainty). This parameter can change both the shape and rate of the resonance background in the QE sample. Nominal = 1.12 GeV

21. 21 Fit Parameter: Low Q 2 Suppression NUINT 09, CC/NC QE Scattering, 19 th May 2009 Introduction MC / QE Theory Data/MC Comparisons Axial Mass Fits Summary/Outlook We fit a scaling of the Fermi momentum used to Pauli-block QE events. This is an effective parameter to account for mis-modeled nuclear effects and is only used when we fit for M A QE below Q 2 =0.3 GeV 2. Nominal = 1.00

22. 22 More on Effective Low Q 2 Suppression NUINT 09, CC/NC QE Scattering, 19 th May 2009 Introduction MC / QE Theory Data/MC Comparisons Axial Mass Fits Summary/Outlook Now looking at true Q 2 for true ν μ –CC QE events. We take an assumed 1σ error of 30% on this parameter which corresponds to removing about 50% of the lowest Q 2 events. There are limitations for this parameter…

23. 23 Examples of Nuclear Model Spread NUINT 09, CC/NC QE Scattering, 19 th May 2009 Introduction MC / QE Theory Data/MC Comparisons Axial Mass Fits Summary/Outlook Benhar and Meloni 2009, 0903.2329[hep-ph]Butkevich 2008, Phys.Rev.C 78 (015501) Comparing FG to SF there is a Q 2 shape change persisting out to 0.6 GeV 2. Comparing RFGM to RDWIA there is only a Q 2 shape change out to 0.2 GeV 2.

24. 24 Results for >0.3 GeV 2 Fit NUINT 09, CC/NC QE Scattering, 19 th May 2009 Introduction MC / QE Theory Data/MC Comparisons Axial Mass Fits Summary/Outlook ParameterM A QE (GeV) E μ - Scale M A RES (GeV) Best Fit1.2560.9881.065 Reduced χ 2 : 1.545 -> 0.836 MC Scale Factor: 1.311 -> 1.103 MINOS Preliminary

25. 25 >0.3 GeV 2 Fit Contour and Correlations NUINT 09, CC/NC QE Scattering, 19 th May 2009 Introduction MC / QE Theory Data/MC Comparisons Axial Mass Fits Summary/Outlook Contour drawn from MINUIT and minimized at every point with respect to the other fit parameter; the M A RES -scale. There is a relatively strong anti-correlation between these two fit parameters. Fit Parameter M A QE Scale E μ Scale M A RES Scale M A QE Scale 1.00-0.62-0.55 E μ Scale -0.621.00-0.12 M A RES Scale -0.55-0.121.00 MINOS Preliminary

26. 26 Systematic Errors and >0.3 GeV 2 Result NUINT 09, CC/NC QE Scattering, 19 th May 2009 Introduction MC / QE Theory Data/MC Comparisons Axial Mass Fits Summary/Outlook Systematic SourcePositive Shift (GeV) Negative Shift (GeV) QE Selection Cut0.0180.033 Hadronic Energy Offset0.0450.047 Final State Interactions0.042 DIS Cross Section0.0330.035 Flux Tuning0.025 QE Nuclear Effects0.0000.077 RES Nuclear Effects0.0000.021 Quadrature Sum0.0760.115 Includes effects such as mis-calibration and mis-reconstruction. Changes to intra-nuclear re-scattering parameters such as pion elastic or in-elastic scattering, charge exchange, secondary pion production, the formation time and nucleon absorption. Investigated via changes to the value of the Fermi momentum used to apply Pauli-blocking. Effective M A QE = 1.26 +0.12 -0.10 (fit) +0.08 -0.12 (syst) GeV MINOS Preliminary

27. 27 Results for >0.0 GeV 2 Fit NUINT 09, CC/NC QE Scattering, 19 th May 2009 Introduction MC / QE Theory Data/MC Comparisons Axial Mass Fits Summary/Outlook ParameterM A QE (GeV) E μ - Scale M A RES (GeV) k Fermi - Scale Best Fit1.1920.9881.1121.284 Reduced χ 2 : 216.5 -> 1.023 MC Scale Factor: 1.180 -> 1.140 MINOS Preliminary

28. 28 >0.0 GeV 2 Fit Contours NUINT 09, CC/NC QE Scattering, 19 th May 2009 Introduction MC / QE Theory Data/MC Comparisons Axial Mass Fits Summary/Outlook Contours are drawn from MINUIT and minimized at every point with respect to the other fit parameters; the M A RES -scale and either the QE Fermi momentum scale or stopping muon energy scale.

29. 29 Systematic Errors and >0.0 GeV 2 Result NUINT 09, CC/NC QE Scattering, 19 th May 2009 Introduction MC / QE Theory Data/MC Comparisons Axial Mass Fits Summary/Outlook Systematic SourcePositive Shift (GeV) Negative Shift (GeV) QE Selection Cut0.0270.066 Hadronic Energy Offset0.0650.075 Final State Interactions0.079 DIS Cross Section0.0260.025 Flux Tuning0.044 RES Nuclear Effects0.0230.000 Quadrature Sum0.1200.137 Change in both data and MC -> sanity check. Re-weight the MC for changes to the normalization of low multiplicity channels. Vary flux tuning within errors from beam fits. Effective M A QE = 1.19 +0.09 -0.10 (fit) +0.12 -0.14 (syst) GeV Fit errors are reduced because of the extra statistics from the low Q 2 region. Additional systematic error is increased due to inclusion of low Q 2 region. MINOS Preliminary

30. 30 Summary NUINT 09, CC/NC QE Scattering, 19 th May 2009 Introduction MC / QE Theory Data/MC Comparisons Axial Mass Fits Summary/Outlook From a fit above the region where we might expect serious nuclear effect mis-modeling we find a best fit effective M A QE = 1.26 +0.12 -0.10 +0.08 -0.12 GeV best represents our data. From a fit above Q 2 =0.0 GeV 2 we find that a best fit effective M A QE = 1.19 +0.09 -0.10 +0.12 -0.14 GeV, along with an effective low Q 2 suppression given by taking a Fermi momentum 1.28 times higher than nominal, best represents our data. The MINOS preliminary results, on Iron and at higher energy than K2K and MiniBooNE (2.5 GeV peak with most data from 1-6 GeV), show the same trends as these experiments. Our data wants more low Q 2 suppression, consistent with a ‘beyond the Fermi Gas’ nuclear model. The shape of the Q 2 spectrum requires an increase in the relative number of high Q 2 events, which we accomplish in our model by increasing M A QE.

31. 31 Comments NUINT 09, CC/NC QE Scattering, 19 th May 2009 Introduction MC / QE Theory Data/MC Comparisons Axial Mass Fits Summary/Outlook The extent to which our measured parameters should be considered effective is intrinsically linked to nuclear effect (mis-)modeling. In this analysis, like some other experiments, we have tried to separate the lowest Q 2 behaviour from the middle part of the Q 2 spectrum. Even though our means of applying the low Q 2 suppression is too simple, the way it enters the error on the M A QE shape fit appears to be reasonable and possibly conservative. These results are preliminary because there are areas where we would like to make improvements (for example a more explicit study of Q 2 resolution effects) and because there are some extensions that we would like to make to the results.

32. 32 Analysis Outlook NUINT 09, CC/NC QE Scattering, 19 th May 2009 Introduction MC / QE Theory Data/MC Comparisons Axial Mass Fits Summary/Outlook There are a number of routes for extending and improving this analysis:  use of additional data (we have over 5 times the amount of low energy running as well as data from alternate beam configurations)  potential measurement with anti-neutrino QE events using the 6% contribution of anti-neutrinos to our beam  investigation of absolute rate effects (for example using our kinematic plane sub-samples)  improved QE selection: We are developing an entirely complimentary QE selection procedure that looks for proton tracks. In particular, this sample has a higher Q 2 reach. [See poster by N. Mayer for details.]

33. 1 Backup Slides NUINT 09, CC/NC QE Scattering, 19 th May 2009 Introduction MC / QE Theory Data/MC Comparisons Axial Mass Fits Summary/Outlook

34. 2 NuMI Beam Performance NUINT 09, CC/NC QE Scattering, 19 th May 2009 RUN I - 1.27x10 20 POT RUN IIa 1.23x10 20 POT RUN III 3.0x10 20 POT + Total Protons (e20) 2006 CC Publication Nu08 NC Nu08 CC RUN IIb 0.71x10 20 POT MINOS currently has over 7e20 POT! Other running, HE beam: 0.15x10 20 POT CCQE Analysis Introduction MC / QE Theory Data/MC Comparisons Axial Mass Fits Summary/Outlook

35. 3 QE Scattering: Nucleon Form Factors NUINT 09, CC/NC QE Scattering, 19 th May 2009 Describe hadronic vertex in terms of nucleon form factors which define how much of each type of weak current contributes to a scatter: These form factors are functions of the probe strength, Q 2. In practice, only 3 of the form factors are non-zero: where (V-type and A-type currents) Multiplied by lepton mass in cross section so neglected for our muons. Well measured through electron scattering experiments. Not well measured and only neutrino scattering experiments can extract F A (Q 2 ). Introduction MC / QE Theory Data/MC Comparisons Axial Mass Fits Summary/Outlook

36. 4 MiniBooNE Result NUINT 09, CC/NC QE Scattering, 19 th May 2009 Introduction MC / QE Theory Data/MC Comparisons Axial Mass Fits Summary/Outlook Phys. Rev. Lett 100 (2008) 032301 On Carbon Extra low Q 2 suppression wanted by data. Region below 0.2 is fit with κ ( = extra Pauli-blocking). M A QE = 1.23 ± 0.2

37. 5 K2K Result NUINT 09, CC/NC QE Scattering, 19 th May 2009 Introduction MC / QE Theory Data/MC Comparisons Axial Mass Fits Summary/Outlook Phys. Rev. D 74 (2006) 052002 On Oxygen Extra low Q 2 suppression wanted by data but no attempt to include in model or fit. Region below 0.2 is not fit. M A QE = 1.20 ± 0.12

38. 6 Estimated Q 2 Resolution and Bias NUINT 09, CC/NC QE Scattering, 19 th May 2009 Introduction MC / QE Theory Data/MC Comparisons Axial Mass Fits Summary/Outlook MC estimates of resolution and bias in QE-assumed reconstruction of Q 2 QE. Estimates are made with two methods and in either case the fractional bias is everywhere smaller than the fractional resolution.

39. 7 >0.3 GeV 2 Fit: Absolute Normalisation NUINT 09, CC/NC QE Scattering, 19 th May 2009 Introduction MC / QE Theory Data/MC Comparisons Axial Mass Fits Summary/Outlook MC is now normalized to the POT of the data. The best fit parameters do not fully correct the rate but systematic errors, such as from the flux and intra-nuclear re-scattering, would likely cover the difference.

40. 8 >0.3 GeV 2 Fit: Absolute Normalisation NUINT 09, CC/NC QE Scattering, 19 th May 2009 Introduction MC / QE Theory Data/MC Comparisons Axial Mass Fits Summary/Outlook 2D data over MC ratios. The histograms are only filled when both data and MC contain greater than 7 events.

41. 9 >0.0 GeV 2 Fit: Absolute Normalisation NUINT 09, CC/NC QE Scattering, 19 th May 2009 Introduction MC / QE Theory Data/MC Comparisons Axial Mass Fits Summary/Outlook MC is now normalized to the POT of the data. The best fit parameters do not fully correct the rate but systematic errors, such as from the flux and intra-nuclear re-scattering, would likely cover the difference.

42. 10 >0.0 GeV 2 Fit: Absolute Normalisation NUINT 09, CC/NC QE Scattering, 19 th May 2009 Introduction MC / QE Theory Data/MC Comparisons Axial Mass Fits Summary/Outlook 2D data over MC ratios. The histograms are only filled when both data and MC contain greater than 7 events.

43. 11 >0.0 GeV 2 Fit: Correlation Matrix NUINT 09, CC/NC QE Scattering, 19 th May 2009 Introduction MC / QE Theory Data/MC Comparisons Axial Mass Fits Summary/Outlook Fit Parameter M A QE Scale E μ Scale M A RES Scale k Fermi Scale M A QE Scale 1.00-0.71-0.53-0.85 E μ Scale -0.711.00-0.090.55 M A RES Scale -0.53-0.091.000.26 k Fermi Scale -0.850.550.261.00 MINOS Preliminary

44. 12 Comparison of Fit Results NUINT 09, CC/NC QE Scattering, 19 th May 2009 Introduction MC / QE Theory Data/MC Comparisons Axial Mass Fits Summary/Outlook Left figure shows the two sets of fit results along with the errors returned by the fits and points showing the nominal parameter values and input 1σ errors. Right figure shows an overlay of 1σ contours from the fits.

45. 13 Comparison of Systematic Shifts NUINT 09, CC/NC QE Scattering, 19 th May 2009 Introduction MC / QE Theory Data/MC Comparisons Axial Mass Fits Summary/Outlook Comparison of the shifts in the best fit M A QE for the two fits along with the quadrature sum of the positive and negative shifts in each case.