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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]
Andy Blake, Cambridge University Fiducial Volume Study, slide 3
Fiducial Volume Study
Andy Blake, Cambridge University Fiducial Volume Study, slide 4
• 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
Andy Blake, Cambridge University Fiducial Volume Study, slide 5
• 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
Andy Blake, Cambridge University Fiducial Volume Study, slide 6
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
Andy Blake, Cambridge University Fiducial Volume Study, slide 7
Bias in reconstructed muon momentum for tracks exiting through end of detector
Shower Extent : Transverse
Andy Blake, Cambridge University Fiducial Volume Study, slide 8
Transverse extent of showers:
Shower Extent: Longitudinal
Andy Blake, Cambridge University Fiducial Volume Study, slide 9
BACK FORWARD
Longitudinal extent of showers:
Shower Energy Bias
Andy Blake, Cambridge University Fiducial Volume Study, slide 10
• 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
Andy Blake, Cambridge University Fiducial Volume Study, slide 11
Shower Energy Loss
Andy Blake, Cambridge University Fiducial Volume Study, slide 12
• 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
Andy Blake, Cambridge University Fiducial Volume Study, slide 13
Distance to detector edge
Shower Energy Loss
Andy Blake, Cambridge University Fiducial Volume Study, slide 14
Distance to forward face of detectorDistance to back face of detector
Oscillation Sensitivity
Andy Blake, Cambridge University Fiducial Volume Study, slide 15
• 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
Andy Blake, Cambridge University Fiducial Volume Study, slide 16
• 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
Andy Blake, Cambridge University Fiducial Volume Study, slide 17
m2 sensitivity (99% confidence) sin22 sensitivity (99% confidence)
Oscillation Sensitivity: Coil Cut
Andy Blake, Cambridge University Fiducial Volume Study, slide 18
m2 sensitivity (99% confidence) sin22 sensitivity (99% confidence)
Oscillation Sensitivity: Back Edge
Andy Blake, Cambridge University Fiducial Volume Study, slide 19
m2 sensitivity (99% confidence) sin22 sensitivity (99% confidence)
Oscillation Sensitivity: Forward Edge
Andy Blake, Cambridge University Fiducial Volume Study, slide 20
m2 sensitivity (99% confidence) sin22 sensitivity (99% confidence)
What are the optimal fiducial cuts ?
Andy Blake, Cambridge University Fiducial Volume Study, slide 21
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
Andy Blake, Cambridge University Fiducial Volume Study, slide 22
reco shower energy
could relax fiducial cuts for lowest energy showers
Energy-Dependent Fiducial Cuts
Andy Blake, Cambridge University Fiducial Volume Study, slide 23
• 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
Andy Blake, Cambridge University Fiducial Volume Study, slide 24
>10 cm (2 strips) >15 cm (2 planes)
Distance to forward face of detectorDistance to radial edge of detector
Shower Edge Cut
Andy Blake, Cambridge University Fiducial Volume Study, slide 25
Distance to forward face of detectorDistance to radial edge of detector
After edge cut
All showersAfter edge cut
All showers
Oscillation Sensitivity Plots
Andy Blake, Cambridge University Fiducial Volume Study, slide 26
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
Andy Blake, Cambridge University Fiducial Volume Study, slide 27
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
Andy Blake, Cambridge University Fiducial Volume Study, slide 28
• 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.