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Beam Extrapolation Fit

Beam Extrapolation Fit. Peter Litchfield. An update on the method I described at the September meeting Objective; To fit all data, nc and cc combined, with the minimum of cuts

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Beam Extrapolation Fit

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  1. Beam Extrapolation Fit Peter Litchfield • An update on the method I described at the September meeting • Objective; • To fit all data, nc and cc combined, with the minimum of cuts • To use the beam MC extrapolation parameters event by event to produce a far detector prediction from the near detector data • Not to need beam, cross-section and/or reconstruction error fitting • Status • John Marshall is developing an independent program on the same lines. John (Mark) is reporting his results in the cc session • I have used MDC MC both raw and tweaked to develop and verify my program • I will show that it works, at least on MC data

  2. Reminder of the method Near MC truth event Near MC reco E - Es Weight: near data reco/ near MC reco GNuMI Beam particle Weight: Oscillation Beam extrapolation Gen/Extrapolated ratio Far flattening weight Xsec ratio Far MC truth event weighted Far MC truth event E - y Far MC reco event E - Es Predicted Far reco E - Es distribution Far data reco E - Es distribution  many beam particles compare

  3. Data • All data is MC, I have not looked (for a long time) at any real data • MDC data, R18.2 reconstruction • Pure MC, no tweaking, far data oscillated (original MDC) • Near “data” 385 files : 0.03955 1020 pot • Near MC 382 files : 0.03934 1020 pot • Far “data” 100 files : 102.7 1020 pot • Far MC 177 files : 514.2 1020 pot • Tweaked MC, far data oscillated (MDC3) • Near “data” 396 files : 0.3996 1020 pot • Near MC 379 files : 0.3893 1020 pot • Far “data” 100 files : 103.2 1020 pot • Far MC 177 files : 514.2 1020 pot

  4. Near detector E v Eshw weight Untweaked MC • Plot reconstructed E v Eshw • Only cut is that the reconstructed vertex should be in the fiducial volume • No nc/cc separation • Sign of E is that of the reconstructed  • One bin for events with no  • Bins of 1 GeV 0-10 Gev, 10 GeV 10-60 GeV Tweaked “data” Eshw E

  5. Near detector E v Eshw weight • Weight the beam MC event by the ratio of near data to near mc in the bin of E v Eshw • For untweaked MC should be 1, Could do with more statistics Eshw (GeV) Ratio near data/near mc -ve momentum +ve momentum E (GeV)

  6. Eshw (GeV) Ratio near data/near mc -ve momentum +ve momentum E (GeV) Tweaked Near E v Eshw weight • Tweaked MC, ratio different from 1 • Weights the near MC to allow for beam, cross-section and reconstruction differences

  7. Extrapolation to the far detector • Near-far extrapolation is done with only truth quantities • Each near detector mc event has a truth energy that a neutrino hitting the far detector from the same beam particle decay would have, together with the probabilities that the near and far detectors are hit. • Use far detector mc events with the same truth characteristics as the extrapolated near detector event • Problem: the far detector energy is different from the near therefore cannot use E and Eshw. Instead extrapolate in truth E and y which should at least approximately scale. • Select events with the same truth initial state (nc,cc,qel,dis etc) and in the same bin of E v y • Apply the far detector reconstructed fiducial volume cut and plot the reconstructed E v Eshw distribution with the weights on the next slide • Again the only cut is on the reconstructed fiducial volume

  8. Far detector extrapolation • Each selected far detector MC event has the following weights applied • The ratio of the probability of the neutrino hitting the far detector to the probability of hitting the near detector • The ratio of the far to near fiducial volumes • The ratio of the pot in the far and near detector samples • The ratio of the cross section at the energy of the far detector event to that at the energy of the near detector event • A weight to flatten the far detector events as a function of E and y. Necessary to remove the cross-section dependence in the far MC • A weight to allow for the difference in truth distributions of accepted events in the near and far detectors (see next slides) • The near detector data/MC weight • An oscillation weight, dependent on m2, sin22, fs

  9. Truth E All events Far MC Extrapolated ND -60.0 0.0 E 60.0 Far detector extrapolation • `Problem: the truth MCdistributions in the far detector are not the same as the extrapolated MC near detector spectrum • `Due to split and superimposed events in the near detector • MC truth finder usually associates bigger MC event with the event • Split events, the MC event gets extrapolated twice • Superimposed events, the bigger event gets extrapolated twice, the smaller event is lost

  10. Selected events Far MC Extrapolated ND -60.0 0.0 E 60.0 Far detector extrapolation • `Effect bigger for vertex selected events, • Differences in reconstruction efficiencies? • Non uniform vertex distribution in near detector + vertex resolution? • ? • Weight events with the ratio far/near of events in the E-y bin

  11. Far detector weight • The extrapolation weight for the near to far truth should be close to 1.0 • Could do with more statistics y Far MC/Near MC projected E (Gev)

  12. No oscillations Far data Extrapolated near data nc cc -60.0 0.0 E 60.0 Raw MC fit • Fit tooscillated but untweaked MC, test that the program works. • Use the MDC MC, oscillated with parameters m2=0.0238, sin22=0.93 • Fitted to E v Eshw but difficult to see effects, project onto E • No cc/nc selection but plot E for data divided into nc/cc by Niki’s ann

  13. nc Oscillated cc 0.002 m2 0.0025 0.9 0.95 sin22 1.0 -60.0 0.0 E 60.0 ▲ truth * best fit point Raw MC fit • True oscillated parameters within the 68% confidence contour • MC statistics is lacking, still contributions to likelihood from MC 68 and 90% contours

  14. Eshw (GeV) Ratio near data/near mc -ve momentum +ve momentum E (GeV) Tweaked MC, Near data/MC • MDC3 data. Note ratio now generally > 1.

  15. Tweaked MC , no oscillations • No oscillations Far data Extrapolated near data nc • Prediction from near data includes correction for tweaking • Truth oscillations have different parameters cc -60.0 0.0 E 60.0

  16. nc Oscillated cc 0.0025 m2 0.003 0.75 0.80 sin22 0.85 -60.0 0.0 E 60.0 ▲ truth * best fit point Tweaked MC, best fit

  17. Include sterile oscillations • Fits well with no sterile component, therefore don’t expect much in fit ▲

  18. Summary and Conclusions • The beam event-by-event extrapolation works. • It works (on MC) without beam or cross-section fitting/adjustments • It works (on MC) without any cuts except a fiducial volume cut. • It works (on MC) for a fit to m2, sin22 and fs • It should work for a CPT separated  and fit • Fitting to reconstructed E v Eshw includes the detector resolution in a simple manner • I haven’t thought much about systematics but since it makes very few assumptions and cuts, the systematic errors should be small • It will work as far as there are no effects unique to one detector which are not represented by the MC • Need to compare far and near detector data to check that no such effects are present.

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