Measurement of the Calorimetric Energy Scale in MINOS

1
Measurement of the Calorimetric Energy Scale in
MINOS

• Jeff Hartnell
• Rutherford Appleton Laboratory
• (University of Oxford)
• Thesis Talk
• Week in the Woods 2005

2
Talk Outline

• Motivation
• Track window technique
• Stopping muon selection
• Results
• Bethe-Bloch Measurements
• Sources of systematic error
• Performing the relative calibration in MC
• Impact on MINOS CC Measurements
• Summary

3
Motivation

• Perform relative calibration
• Enable accurate spectral comparisons of beam
• Relative energy scale effects measurement of both
  dm2 and s2t.
• Tune the MC so that muons give correct response
  at all detectors
• MINOS relative calibration target 2

4
What to use?

• Unfortunately no source of, say, exactly 1 GeV
  electrons at all detectors (had them at CalDet!).
• Average dE/dx of through-going cosmic muons
  differs by 50 between 3 detectors.
• Use stopping muons
• Well understood same at all detectors.
• Future cross-checks
• Use neutrino beam stopping muons.
• Use magnetic field to select, say, 20 GeV muons.

5
Track Window Technique

• Sum energy deposition in a window on the
  relativistic rise.
• Robust measurement not reliant on perfect track
  finding.
• Away from sharp change in dE/dx as muon stops.

6
Defining a MEU

• A Muon Energy Unit (MEU) is the same in all 3
  detectors
• As a rule of thumb
• 1 MEU equals the detector response to a
  perpendicular 1 GeV muon traversing 1 plane of
  scintillator
• More technically
• Median of detector response in track window per
  plane
• Note only calibrate scintillator not steel!
• The first 190 planes in FD are 1 thicker than
  the rest -- reconstruction must account for this
• CalDet steel is 1.6 thinner than FD

7
Stopping muon selection

• At CalDet use test-beam muons (1.4-2.0 GeV/c)
• Range cut to remove 98 of pions
• Fiducial volume to ensure containment
• Timing cuts to reject overlapping events
• At FarDet use stopping cosmics (80k data, 40k MC)
• Tight fiducial volume (Rlt3 m)
• 0.5 m away from coil hole
• Track quality checks (views agree, untrkd hits)
• Track projection to detector edge (traceZ)
• Signalbackground is 10001 in MC
• At NearDet (to be started soon)

8
CalDet Results

• Measure response in 3 run periods
• T11 2002
• T7 2002
• T7 2003 (Near/Far)

9
Cross-check with test-beam
Compare calibrated electron response per GeV
between run periods Detector response measured
with muons and electrons is consistent to better
than 2 Proves that the calibration at the CalDet
works!
10
Far Detector Results

• Use same livetime as atmospheric analysis Aug 03
  to Oct 04
• 80000 stopping muons
• Just one number!
• MEU 505 SigMaps

11
Stopping muons as a Standard Candle
Asymmetric (longer clear fibres at top)
Uniform response (almost!)
Symmetric about centre of strips
12
Spatial variations (zoom)
2 stripends x 2 plane views 4
combinations Purple lines show the edge of the
detector read out Clear correlation of
yellow/red patches with stripend read out 15
differences! Looks like problems with both
attenuation and strip-to-strip calibration MC is
perfectly flat!
13
Overall Average Response
MC
Data
Y-dependence of detector response
Uniform response
5 fall in response
14
Temporal fluctuations
4
Clear correlation of detector response with
temperature
No drift points used (not all available)
Drift 1.0 0.1 per degC
At CalDet gain drift 0.8 0.2 (LI)
15
Effect of Spatial and Temporal Variations in
Detector Response

• If only a single neutrino event is considered
  then errors are crudely
• Temporal 2 error
• Spatial 2.5 error
• BUT, any reasonable analysis will use 100s or
  1000s of events errors average out assuming a
  uniform distribution
• Temporal sqrt(1002)/100 0.2 error
• Spatial sqrt(1002.5)/100 0.2 error
• However, stopping muon sample is not uniformly
  distributed (concentrated at top).
• 0.6 correction and assume a 100 error on
  correction

16
Why should problems be fixed if small error?

• We dont understand our detector fully could be
  a deeper problem?
• MC simulation is inaccurate calibration
  constants are used as the true light output of
  each strip
• Potentially susceptible to biases have to check
  that events are uniform
• Worse energy resolution

17
Angular dependence
Only use events with cosThZ gt 0.3
Have a 1 dependence Average is 0.5 different
from horizontal correct Assign a 100 error to
size of correction (0.5)
18
Measuring Bethe-Bloch Curve

• Measure muon energy deposition as a function of
  distance from the end of the track
• Convert
• Distance travelled -gt momentum
• Detector response -gt MeV cm2/g
• Provides valuable cross-check that stopping muon
  reconstruction and calibration is correct

19
FarDet Bethe-Bloch Curve
Good agreement with Bethe-Bloch and MC
Disagreement in data at high momenta
Data and MC slowly start to diverge
Muons all come from above!
Why?
20
FarDet Bethe-Bloch Curve (2)
Make a correction for y-dependence
Now good agreement
21
CalDet Bethe-Bloch Curve
MC agrees well with Bethe-Bloch calculation up to
here
1.8 GeV/c test-beam muons
Data AND MC disagree with Bethe-Bloch calculation
Energy loss ! energy deposited
Delta-rays can punch through more than 1 plane
Data disagrees with BOTH here
Really interesting dependence of BB curve on muon
range at CalDet.
(see next talk)
22
Errors Statistical and Systematic

• Calibration detector
• Statistical lt 0.3
• No atten. correction 0.2
• Strip-to-strip calibration 1.2
• Temporal fluctuations 0.3
• Pion background 0.25
• Off-momentum muons 0.25
• Far detector
• Statistical 0.1
• Temporal drifts 0.2
• Spatial variations 0.6
• Angular dependence 0.5

23
Total Errors

• Error on relative calorimetric energy scale
  measurement
• CalDet total 1.3
• FarDet total 1.1
• So, error on relative calibration of scintillator
  between CalDet and FarDet is
• sqrt(1.32 1.12) 1.6
• This is better than the 2 target

24
Performing the Relative Calibration in MC

• Important cross-check of entire relative
  calibration procedure
• Shows self-consistency of MC calibration/de-calibr
  ation process
• Ensures that the light-level of each detector
  in MC is an accurate simulation of reality

25
Procedure

• PhotonTransport uses CALMIPCALIBRATION table to
  set each detectors light level
• Tune GeVPerMip until MC stopping muons give the
  same response as data at ONE detector only
• Now expect others detectors to give their correct
  response do they?

26
Results in MC

• FD and CD 02 all have the same deviation
  (0.45)
• Very good result
• Stopping muon reconstruction and calibration good
  in both detectors
• MC is self-consistent
• FD CD 02 differ from CD 03 by 1.6
• Due to sparsification of individual ND buckets
  and cross-talk to unconnected pixels (electronics
  pmt differences!)
• Need to figure out a way to compensate for this

27
Impact of Relative Calibration on MINOS CC
Measurements

• Fast MC loglikelihood analysis (by AW)
• Use MC truth smear muons and showers
• Use CC/NC selection efficiencies (by KG)
• Generate ideal spectrum using 32x1020 POT
  sample
• Introduce energy shift to shower in each event
  for ideal spectrum
• 11 points between -15 and 15 energy shift
• Use 500 data samples with only 8x1020 POT
  statistics
• Determine average fractional bias on best fit
  value of dmsq and s2t

28
Fractional bias on dmsq
Bias (fit true) / true Bias changes with the
size of the relative energy shift Size of bias
depends on dmsq
29
Why is effect dependent on dmsq?
If you shift a flat energy spectrum it just
hardly matters!
30
Results of Study

• A shift of 2 in the relative energy scale (for
  SK best fit) means
• 0.6 error on both dmsq and s2t
• For high values of dmsq (0.005) the effect of a
  relative miscalibration is much smaller but at
  the same time we make a 3x more precise
  measurement of dmsq anyway.

31
Summary

• Robust track window technique developed
• Precise measurements of the calorimetric energy
  scale have been made
• Relative calibration (of scintillator) between FD
  and CD performed
• to 1.6 in data
• to better than 2 in MC
• Calibration is below 2 target
• Important cross-checks shown to work
• Bethe-Bloch curve measured
• At CalDet, detector response consistent with
  test-beam E
• MC now tuned to give accurate realistic
  calorimetric response and shown to be
  self-consistent
• Study shows a 2 relative miscalibration gives a
  0.6 error on dmsq and s2t

32
Now to pass my viva Thanks to everyone who
provided advice/software/MC/data/etc.