Transcript oscfit

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
Far MC
truth
event
E - y
Weight: Oscillation
Beam extrapolation
Gen/Extrapolated ratio
Far flattening weight
Xsec ratio
 many
beam
particles
Predicted
Far reco
E - Es
distribution
Weight:
near data reco/
near MC reco
compare
Far MC
truth
event
weighted
Far data
reco
E - Es
distribution
Far MC
reco
event
E - Es
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
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”
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
Ratio near data/near mc
Eshw
(GeV)
-ve momentum
E (GeV)
+ve momentum
Tweaked Near E v Eshw weight
Tweaked MC, ratio different from 1
Ratio near data/near mc
 Weights the near MC to allow for beam, cross-section and
reconstruction differences
Eshw
(GeV)
-ve momentum
E (GeV)
+ve momentum
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
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
Far detector extrapolation
 `Problem: the truth MC distributions in the far detector are not the
same as the extrapolated MC near detector spectrum
Truth E
Far MC
All events
-60.0
Extrapolated ND
0.0
E
60.0
`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 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
Selected
events
-60.0
Far MC
Extrapolated ND
0.0
E
60.0
Far detector weight
 The extrapolation weight for the near to far truth should be close to
1.0
Far MC/Near MC projected
Could do with more statistics
y
E (Gev)
Raw MC fit
 No oscillations
 Fit to oscillated but
untweaked MC, test that
the program works.
Far data
Extrapolated
near data
nc
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
cc
-60.0
0.0
E
60.0
Raw MC fit
True oscillated parameters within the 68% confidence contour
MC statistics is lacking, still contributions to likelihood from MC
nc
m2 0.0025
Oscillated
0.002
cc
-60.0
0.0
E
60.0
68 and 90% contours
0.9
0.95
▲ truth
sin22 1.0
* best fit point
Tweaked MC, Near data/MC
Note ratio now generally > 1.
Ratio near data/near mc
 MDC3 data.
Eshw
(GeV)
-ve momentum
E (GeV)
+ve momentum
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
Tweaked MC, best fit
nc
cc
-60.0
0.0
E
60.0
0.0025
m2 0.003
Oscillated
0.75
▲ truth
0.80
sin22
0.85
* best fit point
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.