Far Detector Fiducial Volume Study Andy Blake Cambridge University Thursday December 7 th 2006.

Far Detector Fiducial Volume Study

Andy BlakeCambridge University

Thursday December 7th 2006

Overview

Andy Blake, Cambridge University Fiducial Volume Study, slide 2

Fiducial volume optimization encompasses the following:

All Showers

Showers <2 GeV

• Previous study by Andy Culling (see, for example, doc-db #1136).

– Studied bias in reconstructed shower energy close to detector edges.

– Studied sensitivity to oscillation parameters as function of fiducial cuts.

Previous Study [A. Culling]


Fiducial Volume Study


• Study following four fiducial containment parameters:

– radial edge of detector. – front/back plane of detector – coil hole.

COIL HOLE

radial cut

coil cut

back Z cut forward Z cut

COIL HOLE

SM1 SM2

forward Z cut back Z cut

N.B: For purposes of this study, same fiducial cuts applied to both super-modules.

Fiducial Volume Study


• Use “Cedar” beam MC ntuples for this study.

– contained interactions (approx. 800 x 1020 PoTs).

– rock interactions (approx. 100 x 1020 PoTs).

• Optimize fiducial cuts by studying the following:

Track containment – compare tracks from contained and rock CC interactions.

– study bias in reconstructed muon energy close to detector edges.

Shower containment – study bias in reconstructed shower energy close to detector edges. – measure visible energy escaping through detector edges.

Oscillation sensitivity – vary each of the fiducial parameters in turn. – calculate sensitivity in m2 and sin22.

Track Containment: Front Edge


rock CC events

contained CC events.

• Rock muons can sneak into the detector:

– up to ~10 cm through the detector edge. – up to ~4 planes through the front plane.

Track Containment: Back Edge


Bias in reconstructed muon momentum for tracks exiting through end of detector

Shower Extent : Transverse


Transverse extent of showers:

Shower Extent: Longitudinal


BACK FORWARD

Longitudinal extent of showers:

Shower Energy Bias


• Calculate mean energy bias as function of radial vertex position.

– Only use events where vertex is >20 planes from front and back planes.

Distance to detector edge Distance to centre of coil hole

• Calculate mean energy bias as function of vertex Z position.

– Only use events where vertex is >50cm from edge and >40 cm from centre.

Distance to back face of detector Distance to forward face of detector

Shower Energy Bias


Shower Energy Loss


• Create a fake detector edge to study shower containment.

– Calculate the proportion of visible energy contained inside the fake detector volume as a function of the position of the visible shower edge.

Shower Energy Loss


Distance to detector edge

Shower Energy Loss


Distance to forward face of detectorDistance to back face of detector

Oscillation Sensitivity


• Calculate sensitivity as function of fiducial cuts.

– Vary each cut in turn, holding the others constant.

• Initial Event Selection.

– Reconstructed muon track (must pass track fitter).

– Use standard PID with cut placed at PID>0.0.

• Mechanics of Oscillation Fit.

– Purely statistical (ignore all systematic errors).

– Fit to overall reconstructed neutrino energy spectrum. E (GeV) = [ 0, 30 ] (60 bins) + 1 bin overflow.

– Perform oscillation fit on 120 x 120 grid. m2 (10-3 eV2) = [ 1.5, 4.5 ] , Sin22 = [ 0.7, 1.0 ].

– True Oscillation Parameters: m2 = 3 x 10-3 eV2, Sin22 = 1.0.

– True Normalization: 2.5 x 1020 PoTs.

– Simulate 20 experiments at each grid point.

Oscillation Sensitivity


• Input Data. – Use BOTH rock interactions AND contained events.

• Sensitivity Calculation. – Determine best fit m2 along line of sin22=1.0.

Calculate 99% confidence interval in m2.

– Determine best fit sin22 along line of best fit m2.

Calculate 99% confidence interval in sin22.

• Fiducial cut parameters.

Fiducial Cut Default Range

Radial Edge 0.3 m 0.0 - 1.0 m

Coil Hole 0.4 m 0.0 - 1.0 m

Back Face 0.5 m 0.1 - 1.5 m

Forward Face 1.5 m 0.5 - 5.0 m

Oscillation Sensitivity: Radial Cut


m2 sensitivity (99% confidence) sin22 sensitivity (99% confidence)

Oscillation Sensitivity: Coil Cut



Oscillation Sensitivity: Back Edge



Oscillation Sensitivity: Forward Edge



What are the optimal fiducial cuts ?


Radial Edge Coil Hole Back Plane Forward Plane

Track

containment>10 cm > 25 cm > 100 cm

Shower

energy bias> 20 cm > 40 cm > 60 cm

Shower

energy loss> 20 cm > 10 cm > 80 cm

Oscillation sensitivity < 30 cm < 180 cm

• require minimal contamination from rock muons.• mean track momentum bias must be less than 500 MeV.• mean shower energy bias must be less than 100 MeV. • visible energy loss must be less than 10%.• require optimal sensitivity for oscillation parameters.

Criteria

Optimal? > 20 cm > 40 cm > 25 cm > 100 cm

i.e. must not be more than double the bias observed for highly contained events.

Energy-Dependent Fiducial Cuts


reco shower energy

could relax fiducial cuts for lowest energy showers

Energy-Dependent Fiducial Cuts


• Various schemes for energy-dependent fiducial cuts.

– Shower Edge Cuts Cut on position of shower edge relative to detector edge. Need to define position of shower edge, plus size of cut.

– Fiducial Activity Cuts Cut on amount of shower activity close to detector edge. Need to optimize size of edge region, plus allowed charge.

– Apply in addition to, or instead of, fixed fiducial cuts? Apply energy-dependent cuts to all events? Just use these cuts to recover events around detector edge?

• Example: shower edge cut.

– Find closest distance of shower to detector edges.

– apply cut at r > 10 cm and z > 15 cm.

Shower Edge Cut


>10 cm (2 strips) >15 cm (2 planes)

Distance to forward face of detectorDistance to radial edge of detector

Shower Edge Cut


Distance to forward face of detectorDistance to radial edge of detector

After edge cut

All showersAfter edge cut

All showers

Oscillation Sensitivity Plots


Radial

Edge

Coil

Hole

Back

Face

Forward

Face

(1) Fixed Fiducial Cuts

det.edge - evt.vtx > 20 cm > 40 cm > 25 cm det.edge - evt.vtx > 100 cm

(2) Shower Edge Cuts

det.edge - evt.vtx > 10 cm

OR

det.edge - shw.edge > 10 cm

> 40 cm > 25 cm det.edge - shw.edge > 15 cm

(2a) = (1) || (2) (1) || (2)

(3) Fiducial Activity Cuts

det.edge - evt.vtx > 10 cm

OR

<10% shw.ph 10cm from edge

> 40 cm > 25 cm <10% shw.ph 15cm from edge

(3a) = (1) || (3) (1) || (3)

Oscillation Sensitivity Plots


99% confidence limits

(1) Fixed fiducial cuts

(2) Shower edge cuts

(2a) = (1) || (2)

(3) Fiducial activity cuts

(3a) = (1) || (3)

• Confidence limits are Similar in all cases.

• Fixed fiducial cuts give best sensitivity contour. – but energy-dependent cuts aren’t optimized.

• Rescuing events around edge of detector makes sensitivity worse. – needs careful optimization to make sensitivity better.

• Energy-dependent cuts push contour down.

true oscillations

Summary


• Homing in on optimal fiducial cuts. – studies of biases in reconstructed muon and shower energy.

– optimization of sensitivity to oscillation parameters.

• Current results in good agreement with previous study.

• Future work: – re-do oscillation fits with finer binning and higher statistics.

– study optimization of fiducial cuts at supermodule boundary.

– study optimization of energy-dependent fiducial cuts.

Far Detector Fiducial Volume Study Andy Blake Cambridge University Thursday December 7 th 2006.

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