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## MEG DCH Analysis

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**MEG DCH Analysis**W. Molzon For the DCH Analysis Working Group MEG Review Meeting 18 February 2009 DCH Analysis**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 DCH Analysis**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 sRMS=180 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 fittingangle 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 DCH Analysis**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 DCH Analysis**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 DCH Analysis**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 ( < 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 DCH Analysis**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 DCH Analysis**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 > 1 hit are found, assign unmatched hits as “single hit clusters” Single hit clusters Correct wrong pad cycle 3,4 hit clusters DCH Analysis**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 R>Rmin 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 DCH Analysis**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 DCH Analysis**Intrinsic Drift Chamber Performance from Tracking**sRMS=1.61 (z1 – z2)/ √(σ2z1+ σ2z2) • 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 DCH Analysis**Definition of Selection Criteria for Tracking Efficiency,**Resolution Tight Cuts have additional requirements Nhits > 9, dE < 0.0006 DCH Analysis**Momentum Resolution from Monte Carlo**sRMS=420 keV sRMS=420 keV • 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? DCH Analysis**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 DCH Analysis**Check of Angular Resolution**Monte Carlo Calculated uncertainty in q, data 6 mrad Calculated uncertainty in f, data12 mrad Data f~0 Data f>0 Data f<0 • 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 • Beam spot has different shape • Hole on falling distribution • Work in progress • First try requires increasing resolution in dZ, dY by 50% • Position of hole good to at least 1 mm – neglibible contribution to qeg uncertainty DCH Analysis**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 • Fully corrected photon-positron timing difference currently at level of 150 ps in RD signal with photon energy above 40 MeV DCH Analysis**Use DCH Data and Analysis to Study Timing Counter**Loose matching criteria Tighter position match, timing criteria • Use DCH trigger data • Require 4 hits in 5 contiguous chambers • Run standard analysis, positron selection criteria • Measure probability of having a TIC hit DCH Analysis**Tracking Efficiency From Monte Carlo**• Put actual typical patterns of inefficient chambers into Monte Carlo • Generate signal events over extended region |f| < 1, cos(q) < 0.45 • Define efficiency as (# positrons accepted in fiducial region) (# positrons generated in fiducial region) • Efficiency loss due to track-finding and fitting requirements: • <2 missing chambers in seed • at least one chamber with 2 planes in seed • <2 missing chamber in track extension each direction • at least 8 hits on fitted track • difficulty with getting track time and resolving L/R ambiguity with many single plane chambers DCH Analysis**Reconstructed Tracks per Trigger**arrows correspond to typical configurations • 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 DCH Analysis**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 107m/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 107prescale factor known X 0.30 TIC acceptance x efficiency for Michel measured X 0.182 fraction of Michel spectrum > 48 MeV calculated X (0.92-1.0) conditional trigger efficiency for TIC measured* X 0.091 Michel geometric acceptance assumed XeDCH drift chamber reconstruction & cuts unknown eDCH = 11895 x 107 / 0.3 / 0.182 / 0.92 / 0.091 / 8.4 / 1013 = 0.28-0.31**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 DCH Analysis**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 DCH Analysis