1. 2015/6/23 1 How to Extrapolate a Neutrino Spectrum to a Far Detector Alfons Weber (Oxford/RAL) NF International Scoping Study, RAL 27 th April 2006

2. 2015/6/23 2 Overview Introduction – How to measure neutrino oscillation parameters The Problem – Cross Section – Neutrino Flux – Reconstruction Different Solutions – Dead Reckoning – Near Detector fits – Near over Far ratios – Matrix

3. 2015/6/23 3 Disclaimer What will be presented in this talk are NOT MINOS RESULTS or METHODS! I present my private views on how different methods can be used to estimate a far detector energy spectrum given a near detector measurement. However, these methods have been investigated, discussed and used within the MINOS experiment. I present my best understanding of them and their differences. None of this is my work!

4. 2015/6/23 4 Look for a deficit of ν μ events at Far Detector Unoscillated Oscillated ν μ spectrum Monte Carlo Spectrum ratio MINOS Methodology The Million $ Question: How to predict the Far Detector spectrum?

5. 2015/6/23 5 Producing the Neutrino Beam 9 μ s spill of 120GeV protons every 2s 0.2 MW average beam power 20  10 12 protons per pulse (ppp)

6. 2015/6/23 6 The Neutrino Beam Spectrum LE pME pHE How well do we know it this spectra? –neutrino flux depends on hadron production –neutrino cross section

7. 2015/6/23 7 Problem 1: Hadron Production Uncertainties Atherton 400 GeV Be Barton 100 GeV C Spy 450 GeV Be Hadron production not well known! –120 GeV proton beam – thick – thick graphite target

8. 2015/6/23 8 Problem 2: Cross Sections World knowledge on cross sections is limited –few measurements –theoretical uncertainties Needs good beam prediction to make measurement

9. 2015/6/23 9 LE-10pMEpHE LE-10pMEpHE Error envelopes shown on the plots reflect uncertainties due to cross- section modeling, beam modeling and calibration uncertainties Reconstructed Energy (GeV) Ratios of Data/MC Dead Reckoning

10. 2015/6/23 10 How to use this data Dead reckoning not good enough We want to understand differences Two Steps 1.Measure ND spectrum 2.Extrapolate to Far Detector the ultimate goal Different methods can do this –NDFit –2DGrid –N/F Ratio –Matrix

11. 2015/6/23 11 Extrapolate to Far Detector Near and Far Detector energy spectra are not identical –Both detectors cover different solid angles –Near Detector sees extended line source Just kinematics ff to Far Detector Decay Pipe   (soft) (stiff) nn target ND

12. 2015/6/23 12 NDFit Method Use un-tuned MC Determine weights as a function of –x f and p T of parent hadron, which generated the neutrino –neutrino energy Result –modified Near Detector MC Apply weight to Far Detector MC event  Far Detector energy spectrum Contains –improved hadron production model –Can treat cross section uncertainties the same way different beam setting help to untangle effects

13. 2015/6/23 13 Re-weighting Function Parameterize hadrons distribution coming out of target with change cross section parameters –ma, mares, dis,... –uses generator

14. 2015/6/23 14 Agreement between data and Fluka05 Beam MC is pretty good, but by tuning the MC by fitting to hadronic x F and p T, improved agreement can be obtained. LE-10/185kA pME/200kA pHE/200kA Weights applied as a function of hadronic x F and p T. LE-10/ Horns off LE-10 events Not used in the fit Result of Fit

15. 2015/6/23 15 NDFit Method (II) Improved description of Near Detector energy spectrum Advantage –Very flexible, can be used to improve hadron production distributions(++) cross sections(++) horn currents distribution(++)... Disadvantage –Only works, if changes can be parameterised.

16. 2015/6/23 16 2D Grid Method Bin data in reconstructed –E ν & y Fit weight as a function of true –E ν & y Corrects for un-modelled effects –cross section (+++) –Hadron production(++) – Reconstruction (+) Apply weight to Far Detector MC events Result –Far Detector Energy spectrum

17. 2015/6/23 17 N/F Ratio Look at differences between data and MC in Near Detector as a function of reconstructed Energy Apply correction factor to each bin of re- constructed energy to Far Detector MC –c = n data / n MC

18. 2015/6/23 18 N/F Ratio (II) Predicts the right spectrum in the FD almost independently, whether the distortion was generated by –beam flux diff. –cross section diff –reconstruction diff.

19. 2015/6/23 19 The Beam Matrix Method This method does not re-weight MC events It uses the measure Near Detector distribution and extrapolates it using a BEAM Matrix to the Far Detector. Can be used on original or wrong/bad MC

20. 2015/6/23 20 Beam transport matrix step A) step B) step C) The Beam Matrix Method NC background subtraction correct for selection efficiency and purity correct for detector response measured E (ND) true E (ND) Maps true E from ND to FD using pion decay kinematics beamline geometry true E (FD) predicted visible E (FD) add detector response efficiency background oscillations

21. 2015/6/23 21 1 2 Correction for purity Step A, Beam Matrix Method Reconstructed =>True and Correction for efficiency

22. 2015/6/23 22 Beam Matrix encapsulates the knowledge of pion 2-body decay kinematics & geometry. Beam Matrix provides a very good representation of how the Far Detector spectrum relates to the near one. Beam Matrix Method : Near to Far extrapolation

23. 2015/6/23 23 Predicted true FD spectrum higher than nominal FD MC in high energy tail expected, given that the ND visible energy spectrum is also higher than the nominal MC in this region Predicted spectrum Nominal MC 0.93  10 20 POT Predicted FD true spectrum from the Matrix Method

24. 2015/6/23 24 The Beam Matrix Method (II) Robust method to predict the FD spectrum Uses Near Detector data and hadron decay kinematics to predict FD spectrum Advantages –robust Disadvantages –implicitly assumes that all differences are due to neutrino flux

25. 2015/6/23 25 4 methods predict identical FD energy spectrum –NDfit –2D Grid –F/N ratio –matrix Systematic error propagate differently Predicted FD unoscillated spectra Comparison of the Methods

26. 2015/6/23 26 Summary NDFit method –Treats hadron prod. (+++) cross section(+++) beam focus(++) –Caveat needs parameterisation of effect(--) 2D Grid –Treats cross section (+++) reconstruction (++) beam/hadron production (+) N/F Ration –Treats Reconstruction (+++) cross section (++) beam/hadron production (+) Matrix –Treats beam/hadron production (+++) cross section (++) Reconstruction (+)

27. 2015/6/23 27 Conclusions Near Detector is essential for oscillation analysis –hadron production / neutrino spectrum –cross section –reconstruction –only inclusive measurements can be done Conceptually different methods give same results –but all need a Near Detector Difficult to get a two detector experiment wrong