MEG DCH Analysis

1. MEG DCH Analysis W. Molzon For the DCH Analysis Working Group MEG Review Meeting 17 February 2010 DCH Analysis

2. Outline • Goals of DC analysis • Overview of calibrations and analysis • Low level performance: show some results, still improving resolutions • Efficiency • Rf resolution • Z resolution • High level resolutions: show some results, still improving resolutions and our measurements of the resolutions • Momentum • Track angle at target • Position at target • Demonstrated performance vs. proposal performance vs. current MC • Prospects for improvement • Hardware • Software DCH Analysis

3. Goals of DCh Analysis • Optimize performance of spectrometer • Best low level resolutions: R-f,Z, efficiency, noise rejection • Best high level resolutions: positron energy, trajectory • Determine hardware limitations and possible improvements • Noise, alignment, stability • Characterize performance for purpose of physics analysis • PDFs for likelihood analysis • Optimize power of physics analysis • Selection criteria vs. efficiency DCH Analysis

4. Positron Spectrometer Impact on MEG Performance • Select on positron energy within interval near 52.8 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 ~ 4 mm sRMS  ~6 mrad both f and q • Track fittingangle uncertainty  4-5 (7) mrad each • 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) • Path-length projection to target has negligible uncertainty • Uncertainty in path-length projection to timing counter dominated by scattering and E loss after spectrometer • Improvements needed to incorporate position at timing counter and material between spectrometer and timing counter into trajectory 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

5. DC Performance 2009 vs. 2008 Hit map 2008 2009 • Significantly improved performance this year Hit in plane near track projection Hit in plane assigned to track DCH Analysis

6. Significant Improvements in Tracking Analysis • Incorporated use of TIC time for track time • Alternative to use of track time deduced from DCH itself • Necessary last year due to inefficient chambers • Track time from DC itself now much improved performance • Much better algorithms for selecting/removing appropriate hits on track • Significantly improves resolution and efficiency • Re-optimize this year for better quality data • Better understanding of merging of multi-turn tracks • Developed technique for measuring resolutions using two-turn tracks • Fit each turn of a two turn track • Project each turn to common point of closest approach to spectrometer axis between two turns – one projected forward, one backward • Measure difference in q, f, R, z, p and infer resolution in these quantities • Improved fit to Michel edge to extract momentum resolution • Better understanding of chamber performance, contributions to resolution • Work done on cross-checks of calibration • Work on cross-check of alignment using cosmic-ray muons • Better understanding of relating measurable resolutions to kinematic resolution DCH Analysis

7. DCH Alignment Optical survey Optical survey after software alignment RMS residual = 18 mm after software alignment RMS residual = 10 mm • Primary alignment of chambers from optical survey • Correct chamber displacements by minimizing mean residuals to fitted tracks using Michel data • Residual chamber rotations after optical survey are negligible: no corrections • Mean residuals reduced from ~100 mm to 10-20 mm • Compare to typical resolutions: • Position resolutions sR ~200 mm; sZ ~1000 mm; • Chamber-to-chamber scattering deviation ~500 mm • CR data recorded with field off for cross-check of alignment • Different drift performance without magnetic field • Possibility of getting higher momentum tracks with less scattering • Remove possibility of correlated DC shifts being missed due to momentum fit Plot of rotation diagnostic DCH Analysis

8. Quality of Baseline Prediction 2009 2008 sped ~1.8 mV sped ~1.3 mV Baseline errors~.586 mV 2009 2008 2009 sz ~1 mm sz ~550 mm • Charge on anodes and pads used for Z measurement • Baseline subtracted by measuring level early in waveform, subtracting average value • Shown to be superior to linear, quadratic extrapolation • Bin to bin pedestal fluctuations larger in 2009 data vs. 2008 data • Precision of prediction of baseline in signal integration affects position resolution • Histogram difference in predicted baseline and average baseline in 50 ns signal region • Measured on pedestal runs simultaneous with recent MEG data • Contribution to Z resolution • Depends on both the precision of the baseline and the size of measured charge • Increased HV in 2009 gives 40-50% increase in mean hit charge wrt 2008 • Error in Z due to baseline fluctuationcalculated for every hit • Contribution of sz ~ 550 mm in 2009 compared to sz ~ 1 mm in 2008 DCH Analysis

9. Drift Performance and Calibration • Alignment of time offsets wire by wire • Fit to leading edge of distribution of thit – ttrackfor each end of each wire • Check procedure by comparing hit time at 2 ends • Typical precision of 1.5 ns • Verification of time to position relationship • HV and B dependent drift using GARFIELD • Incorporate asymmetric response at edge cells • Project track from hits in planes 0,1 to common point – measure residual • Alternative measurement of resolution from residual of hit to fitted track • Measure dependence of residuals on track angles, drift time to verify drift model • Typical single plane resolution 250 mm • Some systematic effects with angle in 2008 data, being studied again in 2009 data Fitted track shape tied to hits dR DCH Analysis

10. Z Coordinate Measurement • Determined first from charge division on anode – calibrated by using know phase and periodicity of cathode pads vs. Z measured by anodes • Primarily used to determine correct cycle of cathode pad • Does not enter directly into precision of Z determination; used when pad signals missing • Precise Z determination from charge induced on pads • Pattern of induced charge studied with image charge method – impact on calibration • Dependence on wire-cathode distance, offsets of wire with respect to center of pattern (in the wire plane), fluctuations of mean Z coordinate of ionization sites • Optimization of technique for measuring charge (integration time, etc.) potentially important • Noise contribution to charge is largest known source of error in Z determination • Standard integration and charge calibration + two alternative methods studied • Preliminary results of alternatives give essentially same performance Show plot of fit to sine wave DCH Analysis

11. Cathode Pad Calibration: Z Determination • Reminder • Z = n*(5 cm) + 5/(2p)*(arctan(Ahood/Acathode)+fh(c) • A = (Qu-Qd)/(Qu+Qd); Qu(d)= a+b*sin(2p*z/5+fu(d)) • a,b depend on pad-anode distance • Precision of dependence of A on z studied with electrostatic calculation – correct to good approximation • Steps in Z calibration • Correctly align time offsets in pads vs. anodes:integrate same part of signal • Adjust time offsets on pad signals to set the mean valueof the difference in the time of the pad and anode to zero • Correct for relative upstream-downstream gains: • Adjust gain to get the mean asymmetry in the cathode and pad for each were equal to zero • Correct for effect of chamber foil bowing • Both the induced charge and the asymmetry depend on the anode-cathode distance • Measure Qcathode/Qanode vs. z for each wire – fit to quadratic dependence on Z • Apply phenomenological correction to each asymmetry depending on mean induced charge for that wire and Z • Bowing correction is ~200 mm in quadrature DCH Analysis

12. Some Details on Chamber Bowing Distance of hood and cathode from anode wire effected by bowing due to gas pressure, foil mass, possibly details of how foils are fixed to frames Electrostatic calculations show effects >10% on induced charge for deflections of order 0.5 mm Measure the ratio of hood to cathode asymmetry amplitude (amplitude of sine wave) by measuring RMS in each 5 cm interval in Z along the wire Measure the ratio of the hood to cathode charge vs. Z Make scatter plot of asymmetry amplitude ratio to charge ratio – agrees with linear correlation predicted by electrostatic calculation Expect biggest effects in center of chamber, where bowing is largest, some different dependence on Z, particularly for first and last cell wire162cell 0 wire 45, cell 0 wire 26cell 8 wire 21cell 3 DCH Analysis

13. Pad Crosstalk from Adjacent Anodes • Effect of charge induced by hits on adjacent wires • Consider hits at same Z in two adjacent wires in same plane, indicated by circles in figure below. • Charge induced on pads due to anode charge in same cell will have asymmetry zero • Charge induced on pads due to anode charge in other cell will have asymmetry different from zero; in the example shown, more charge on DH for top pads, more on UH for bottom pads • Only relevant for in-time hits: short integration time helps • Effect tends to cancel when 2 hits averaged, cancellation not exact, particularly when pulse heights are different • Charge induced on adjacent cell is not trivial (as much as 7-15%) • When Z of two hits is different (for large Z), effect will be different and perhaps larger DCH Analysis

14. Contributions to Z Coordinate Uncertainty DCH Analysis

15. Measuring High Level Resolutions • Need PDFs for likelihood fits or acceptances for a cut and count analysis • For the positron, these have contributions from: • Momentum response function – no fixed momentum calibration line • Positron angles (q and f) at the target – no fixed direction events • Positron intercept at the target – contribution to the photon angle measurement • Response functions not expected to be Gaussian distributions • Resolutions will depend on, for example, track length, pitch angle, etc. • For momentum, can fit to the edge of the Michel spectrum • Sensitive to only the high energy side of the response function, the important one • Lower energy side strongly correlated with momentum dependence of acceptance • For momentum and angles, can exploit tracks that have two full turns in the spectrometer, comparing momenta and angles at a common point near the axis to infer the resolution • For momentum, cannot determine separately the upper and lower edges, must assume it is symmetrical. Complementary to fit to Michel edge • For q, possible systematic differences from dependence on Z • For f, technique excludes contribution from effect of uncertainty in path length in projecting back to target: 1 mm error in path length is about 7 mrad error in f • All resolution functions should be measured after perfecting low level performance and optimizing selection criteria (not yet done) • Results are likely to improve with analysis DCH Analysis

16. Momentum Resolution • Fit to Michel edge • Fit function is sum of offset Gaussians • Fit results depend on acceptance function and dataset: Michel, low intensity, MEG sidebands • Sample fit to 2009 data before DRS correction: RMS for -1.5< dE <1.5 = 0.580 MeV • Alternative measurement from 2 turn comparison • Single Gaussian fit: RMS = 0.490 MeV • Fit to convolution of sum of 2 Gaussians:RMS in region -1.5 < dE < 1.5 = 0.447 MeV • Third possibility to use Mott scattering of mono-energetic electron beam scattered into spectrometer to characterize momentum resolution • De-convolve energy spread in beam, energy loss dispersion in thick scattering target DCH Analysis

17. Angle and Vertex Position Resolutions • Use technique of two-turn tracks to project to common point near spectrometer axis • Theta angle resolution • Reasonably well fit by Gaussian: sRMS of q = 12.7 mrad • Z position resolution • Well fit by Gaussian: sRMS of z = 3.1 mm • Roughly consistent with contribution from scattering • Phi angle resolution • Well fit by Gaussian: sRMS of f = 8.1 mrad • Error is correlated with momentum error • R position resolution • Well fit by Gaussian: sRMS of R= 2.4 mm DCH Analysis

18. Correspondence Between Resolutions at Target and 2-Turn Comparison dq (meas-true) dq (two turns) dZ(meas-true) dq (meas-true) • Can use MC to get correspondence between z position resolution and positron q resolution • For perfect z resolution, q resolution is 7 mrad • Expect ~9 mrad resolution for current Z resolution • Can also use MC to calculate correspondence between resolutions inferred from comparisons of 2 turns to the resolution at the target • Plot s(q1 -q2)/√2vs. s(qmeas-qtrue) parametric in sz • Current resolution in q1 -q2 corresponds to about 10.5 mrad qresolution • Two avenues for improvement • Improve Z resolution • Understand and fix lack of agreement between measured qresolution and that predicted for current Z resolution MC dq vs. dZ MC dq2turnvs. dqtgt DCH Analysis

19. Correlation of Momentum and Quality Measures • Events with p>52.8 MeV/c represent poorly measured tracks; is there a correlation with track properties? • Width of central part of momentum resolution function most important for physics background estimate • Tails in positron momentum resolution function less important; few low momentum positrons satisfy trigger, hence few low momentum positrons can contribute to accidental background. DCH Analysis

20. Can We Estimate Tracking Efficiency from Data? • Use highly pre-scaled timing counter trigger data • ~ 520 C total live protons on target 1.31 x 107m/s/mA (assume livetimesame for MEG, other triggers) Implies ~ 683 x 1010 total muon stops Nm→enn= 1935 muons satisfying selection criteria counted = 6.83x1012muon stops calculated ( few percent uncertainty ) X 10-7 prescale factor known X 0.35 TIC acceptance x efficiency for Michel measured X 0.101 fraction of Michel spectrum > 50 MeV calculated X (0.92-1.0) conditional trigger efficiency for TIC measured* X 0.091 Michel geometric acceptance XeDCH drift chamber reconstruction & cuts unknown eDCH = 1935 x 107 / 0.35 / 0.101 / 0.96 / 0.091 / (6.83x1012)= 0.92 Need to redo TIC efficiency measurement for 2009 DCH Analysis

21. Conclusions • Tracking efficiency in 2009 data is much better due to improved chamber performance. • Intrinsic resolutions are improved wrt last year’s data • Current status is really a lower limit on performance • Central part of Rf resolution is close to expectations, but tails are more than originally anticipated • Z resolution worse than planned and not fully understood from calculated contributions, but now not a dominant contribution to angular resolution • Angle resolutions better understood, still work to be done • Should get better agreement with MC when measured low-level resolutions are used • Incorporate cell dependences in resolutions • Understand contribution to f resolution from momentum error resulting in error in path-length to target DCH Analysis

22. Conclusions • Prospects for improvement • Still early in optimization of even low level performance • Fitting for improved baseline subtraction (noise filtering – some indications of possible improvements) • Drift time-distance model verification • Anode to adjacent pad crosstalk corrections • Re-optimization of integration time with fully calibrated system • Correction of edge effects (near wire ends) in Z determination • Some possible software improvements ( preliminary results show little improvement ) • Alternative alignment • Alternative integration scheme • High level improvements • Incorporating partial turns in fitting • Improved projection to TIC using TIC signal • Incorporating track time as parameter in fitting • Understanding of 1-2 mm offset in magnet vs. spectrometer • Hardware changes • Reduction of noise at hardware level • Additional measurements of resolution with Mott scattering DCH Analysis