Download - 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
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
Reminder of the method
GNuMI Beam particle
Near MC truth event
Near MC reco E - Es
Weight: near data reco/ near MC reco
Far MC truth event E - y
Weight: Oscillation Beam extrapolation Gen/Extrapolated ratio Far flattening weight Xsec ratio
Far MC truth event weighted
Far MC reco event E - Es
Far data reco E - Es
distribution
compare many beam particles
Predicted Far reco E - Es
distribution
DataAll 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
Near detector E v Eshw weight
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
E
Eshw
Tweaked “data”
Untweaked MC
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
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mcEshw
(GeV)
E (GeV) +ve momentum-ve momentum
Tweaked Near E v Eshw weightTweaked MC, ratio different from 1
Weights the near MC to allow for beam, cross-section and reconstruction differences
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mc
Eshw (GeV)
E (GeV) +ve momentum-ve momentum
Extrapolation to the far detectorNear-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
Far detector extrapolationEach 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
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
Far MC
Extrapolated ND
Truth E
All events
-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
Far MC
Extrapolated ND
Selected events
-60.0 0.0 E 60.0
Far detector weight
The extrapolation weight for the near to far truth should be close to 1.0
Could do with more statistics
E (Gev)
Fa
r M
C/N
ear
MC
pro
ject
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Raw MC fit
Fit to oscillated 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
nc
cc
Far data
Extrapolated near data
No oscillations
-60.0 0.0 E 60.0
Raw MC fitTrue oscillated parameters within the 68% confidence contour
MC statistics is lacking, still contributions to likelihood from MC
68 and 90% contours
▲ truth * best fit point
0.9 0.95 sin22 1.0 0.00
2
m
2
0.00
25
Oscillatednc
cc
-60.0 0.0 E 60.0
Tweaked MC, Near data/MC
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mc
Eshw (GeV)
E (GeV) +ve momentum-ve momentum
MDC3 data. Note ratio now generally > 1.
Tweaked MC , no oscillations
nc
cc
Far data
Extrapolated near data
No oscillations
-60.0 0.0 E 60.0
Prediction from near data includes correction for tweaking
Truth oscillations have different parameters
Tweaked MC, best fit
▲ truth * best fit point
0.75 0.80 sin22 0.850.00
25
m2
0.
003
Oscillatednc
cc
-60.0 0.0 E 60.0
Include sterile oscillations
Fits well with no sterile component, therefore don’t expect much in fit
▲
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.