MEG DCH Analysis

1
MEG DCH Analysis
W. Molzon For the DCH Analysis Working Group
MEG Review Meeting 18 February 2009
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Outline

• Impact on MEG performance
• Analysis algorithms
• DCH Calibration
• DCH position resolutions Rf and q
• Positron reconstruction
• Momentum
• Position and angle at target
• Projection to timing counters
• DCH efficiency
• Required improvements in analysis
• Drift model
• Reducing noise and its impact on resolution
• Improved tracking efficiency with lower than
  expected DCH efficiency
• Fitting

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Positron Spectrometer Impact on MEG Performance

• Select on positron energy within interval
  near52.8 MeV
• For fixed m?eg acceptance, BG/S proportional to
  dp (MEG prediction sRMS180 keV/c)
• Select on qeg near p
• For fixed acceptance, BG/S proportional to df x
  dq (MEG prediction sRMS 8x8 mrad2)
• photon position resolution 6 mm sRMS ? 9
  mrad both f and q
• Track fitting angle uncertainty
  ? 12 mrad f, 6 mrad q
• Position of stopping target uncertainty 0.5 mm
  ? 6 mrad f
• Project to target and timing counter and correct
  te for propagation delay
• For fixed acceptance, BG/S proportional to dt
  (MEG prediction sRMS 64 ps, 2 cm)
• Projection to target has negligible uncertainty
• Uncertainty in timing counter projection
  dominated by scattering and E loss after
  spectrometer
• Improvements needed from incorporating position
  at timing counter and material between
  spectrometer and timing counter into fit.
• For all effects, tails in resolution function ?
  loss of acceptance proportional to integral in
  tail, small increase in background because source
  of background is uniform

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Tracking Analysis

• Outline of algorithms
• Extract hits from waveform on each cell two
  anode ends, four pads
• Extract hit position in Rf from hit time and in Z
  from anode and pad charges
• Form clusters of hits on a particular chamber
  coming from single particle
• Form track candidates from groups of hits
  consistent with Michel positron
• Fit the hits from track candidates to form tracks

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Waveform Analysis

• Based on waveforms on 2 anode ends and 4 pads
  associated with each cell
• waveform noise limits resolution
• DRS voltage calibrated with on-board constant
  voltage presented to input of DRS
• DRS time calibrated with off-board sine-wave of
  known frequency presented to each board.
  Bin-by-bin time calibration done for each DRS
  channel (2x105 points)
• Readout rate dependent baseline offset for some
  DRS bins not corrected, trigger waveform
  crosstalk onto DRS not corrected hardware
  improvements anticipated
• Improvement in noise level would significantly
  improve resolution

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DCH Calibrations and Corrections

• Alignment of chambers radial offsets, z
  offsets, chamber tilts
• All from fits to Michel data
• Typical systematic residuals after alignment
  small ( lt 100 mm)
• Calibration of preamp gains, effective wire
  length
• Use known periodicity of cathode pads to
  calibrate anode preamp gains, input impedance,
  wire resistivity that affects anode z position
• Calibrate relative gains of cathode pads by ratio
  of signal on two ends of pads to sine function
  with variable relative gain
• Correct drift times for signal propagation on
  wire reduce dispersion on time difference
  between two ends by 20
• Identify and correct for incorrect pad cycle
  assignment due to errors in anode Z position
  exceeding 2.5 cm
• Measure effect of noise on pad charge
  measurements on Z resolution optimize
  integration time to minimize effect of noise

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Hit Finding

• Smooth waveforms to reduce high frequency noise
• Determine constant baseline offset event-by-event
  for each waveform
• Only time before hit used small slope from
  earlier hits not corrected
• Find max peak in anode waveform iterate after
  removing signal in peak
• Integrate around peak in limited time interval to
  get 2 anode, 6 pad charges optimized to minimize
  impact of noise on charge integration typically
  50 ns.
• Get hit time from simple threshold discriminator
  on unsmoothed waveform correct for propagation
  along wire using Z coordinate
• Get Z first from anode charge division, then from
  interpolation with pads

Time difference two ends
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Cluster Finding

• Find group of hits consistent with coming from
  single charge particle
• Start with groups of hits in contiguous wires on
  chamber
• Split clusters that have hits at inconsistent Z
  locations
• Identify and fix clusters that have hits
  separated in Z by one pad cycle (5 cm) due to
  incorrect anode Z position
• Reassess assignment of hits to clusters during
  track-finding, when track angle at the cluster is
  known
• After all clusters with gt 1 hit are found, assign
  unmatched hits as single hit clusters

Single hit clusters
Correct wrong pad cycle
3,4 hit clusters
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Track Candidate Finding

• Find group of clusters consistent with coming
  from single charge particle with fixed momentum
  going through spectrometer
• Self-contained code, independent of TIC (i.e. for
  track time)
• Start with seed with 3 clusters in 4 adjacent
  chambers at RgtRmin
• Given a seed, propagate in both directions,
  adding hits within range in dR and dZ consistent
  with Michel momentum
• At each stage, determine track candidate time
  from drift times
• Consistent radial coordinate, consistent Z
  coordinate
• Track time that minimizes residual of hit
  positions to local helix fit
• L/R resolution by minimizing deviations from
  local helix fit
• Hits can be removed from clusters at tracking
  stage

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Track Fitting

• Kalman filter using hits found by trackfinder
• Uses fully aligned chamber coordinates from
  optical alignment software alignment
• Use hit-by-hit uncertainty in Rf and Z
  coordinates parameterized as function of hit
  charge, magnitude of drift distance (determined
  from data)
• Phenomenological corrections to drift time vs.
  drift distance based on parameterization of data
• Removes hits that are inconsistent with positron
  trajectory
• Group of clusters consistent with coming from
  single charge particle with fixed momentum going
  through spectrometer
• Optimization of fitting algorithm for sparse hits
  to be done
• Incorporation of TIC position into filter to
  improve trajectory after spectrometer to be done

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Intrinsic Drift Chamber Performance from Tracking

• Rf position resolution
• Look at difference in hits in 2 planes in chamber
  projected to central plane using trajectory
  information insensitive to multiple scattering
• Typical spatial resolution of 260 microns
• Systematic effects with drift distance and angle
  ad-hoc corrections applied
• dr for opposite side more sensitive to errors
  in track time
• 
  
  sRMS of central region 260 mm
• non-Gaussian tails, larger for
  opposite side hits
• Z position resolution
• Similar technique to that for Rf resolution

Inferred sz 0.15 cm
Za-Zb
normalized Za-Zb
Za-Zb vs charge
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Definition of Selection Criteria for Tracking
Efficiency, Resolution

• Tight Cuts have additional requirements Nhits gt
  9, dE lt 0.0006

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Momentum Resolution from Monte Carlo

• No source of fixed momentum particles fit to
  edge of Michel spectrum, first MC
• Generate Michel spectrum, including radiative
  decays in this study without inefficiencies
• Fit convolution of generated MC spectrum with
  single Gaussian to reconstructed MC spectrum
• Fit range (51.5-54.0) MeV/c
• Done for tight cuts
• Resolution worse than original MEG predictions
  DRS noise ?
• Tails from large angle scattering, pattern
  recognition?, others?

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Momentum Resolution from Data

• No source of fixed momentum particles to measure
  response function
• Fit to edge of Michel spectrum to demonstrate
  resolution
• Generate Michel spectrum with radiative
  corrections
• Impose momentum dependence of TIC acceptance x
  efficiency measured using DCH triggered data
• Fit measured energy distribution to convolution
  of acceptance-corrected Michel spectrum and
  hypothetical resolution function
• Edge of spectrum most sensitive to Gaussian part
  of resolution function fit of high energy tail
  very dependent on model for tail in resolution
  function
• Currently worse than MC by a factor of 2, but
  inefficiencies not yet in MC resolution fits

early datasRMS 830 keV
tight cuts, early datasRMS 772 keV
late datasRMS 1002 keV
tight cuts, late datasRMS 795 keV
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Check of Angular Resolution

• No source of positrons of known direction
• Fitting provides event-by-event estimate of dq,
  df
• Target designed with holes to test of resolution
  in projection to the target ? infer dq, df
• Take slice in target projection around hole, try
  to match depth of dip data to MC
• Position of hole vs. angle of track with respect
  to target normal sensitive to target position
• Difficult to quantitatively match distributions

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Project to TIC, Require Space and Time Match,
Calculate Propagation Time

• Need to correct for track propagation delay to
  precision of 50 ps ? track length to 1.5 cm
• Trajectory known from target plane through
  spectrometer to very good precision
• Projection to TIC complicated by material after
  spectrometer causing scattering, energy loss
• Currently, project to fixed f of timing counter
  with signal using propagation of Kalman state
  vector
• No correction for mismatch with reconstructed
  position in timing counter
• Typical propagation distance is of order 1 m
• Systematic uncertainties in dR, dZ seen, of order
  1 cm
• First attempts at simple corrections to
  path-length based on dR, dZ not successful

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Use DCH Data and Analysis to Study Timing Counter

• Use DCH trigger data
• Require 4 hits in 5 contiguous chambers
• Run standard analysis, positron selection
  criteria
• Measure probability of having a TIC hit

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Tracking Efficiency From Monte Carlo

• Put actual typical patterns of inefficient
  chambers into Monte Carlo
• Generate signal events over extended region f lt
  1, cos(q) lt 0.45
• Define efficiency as ( positrons accepted
  in fiducial region)
• (
  positrons generated in fiducial region)

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Reconstructed Tracks per Trigger

• Look at fraction of events with at least one
  reconstructed track at high momentum measure of
  relative (not absolute) tracking efficiency
• Absolute scale depends on trigger purity, other
  factors not relevant to DCH performance

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Can We Estimate Tracking Efficiency from Data

• Use highly pre-scaled timing counter trigger
  data
• 6000 C total live protons on target 2.8 x 107
  m/s/2mA (assume livetimesame for MEG, other
  triggers Implies 8400
  x 1010 total muon stops
• Nm?enn 11895 satisfying selection cuts
  counted
• 8.4x1013 Number of muon
  stops calculated
• X 107 prescale factor known
• X 0.30 TIC acceptance x efficiency for
  Michel measured
• X 0.182 fraction of Michel spectrum gt 48
  MeV calculated
• X (0.92-1.0) conditional trigger efficiency
  for TIC measured
• X 0.091 Michel geometric
  acceptance assumed
• X eDCH drift chamber reconstruction
  cuts unknown
• eDCH 11895 x 107 / 0.3 / 0.182 / 0.92 / 0.091 /
  8.4 / 1013 0.28-0.31

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Conclusions

• Tracking efficiency in current run is poor,
  mostly due to chamber performance
• Intrinsic resolutions are not as good as expected
• Rf resolution close to expectations, but tails
  are more than originally anticipated
• time-distance relationship
• operation at less than optimal voltages
• noise
• perhaps other causes
• Z resolution significantly worse than planned,
  almost all due to noise
• Momentum resolution not as good as expected with
  measured Gaussian uncertainties as input to
  fitter
• reflection of tails in Rf and Z resolution
• reduced number of hits and shorter tracks
• full inefficiencies not yet represented in MC

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Conclusions

• DCH analysis currently adequate for data with MEG
  sensitivity of order few x 10-12
• Find radiative decay signal requiring track
  projecting to timing counter hit, timing
  correction for track propagation
• Trigger on and reconstruct with good precision
  Michel positrons to help with calibration and
  understanding of TIC performance
• Reduced background rejection due to reduced
  momentum resolution adequate at current MEG
  sensitivity to m?eg
• Significant improvement in MEG sensitivity per
  day of running can be achieved
• Improvements in central part of resolution
  function
• improved chamber efficiency (hardware)
• some (non-trivial) tuning
• ? reduction of background by 1/2
• Improved noise performance (hardware)
• ? additional background reduction by 1/2
• Higher chamber efficiency will increase
  reconstruction efficiency
• ? increase in sensitivity per day by 3
• Strong effort is needed to achieve MEG
  sensitivity goal