Beam Extrapolation Fit

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 E? - y
Far MC truth event weighted
Far MC reco event E? - Es
Far data reco E? - Es distribution
Predicted Far 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
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
Far detector extrapolation

• Problem the truth MC distributions 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
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
Raw MC fit

• Fit to oscillated but untweaked MC, test that
  the program works.
• Use the MDC MC, oscillated with parameters
  ?m20.0238, 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 Nikis ann

13
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
Tweaked MC, Near data/MC

• MDC3 data. Note ratio now generally gt 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
Tweaked MC, best fit
17
Include sterile oscillations

• Fits well with no sterile component, therefore
  dont 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 havent 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.