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

edy

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.