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Tomi Ylinen & Jan Conrad

Direction and Position Reconstruction in the Calorimeter. Tomi Ylinen & Jan Conrad. GLAST INFN-Pisa Workshop – 28-30 June, 2006. Contents. Introduction Direction reconstruction Position reconstruction Conclusions Discussion/questions. GLAST INFN-Pisa Workshop – 28-30 June, 2006.

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Tomi Ylinen & Jan Conrad

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  1. Direction and PositionReconstruction in theCalorimeter Tomi Ylinen&Jan Conrad GLAST INFN-Pisa Workshop – 28-30 June, 2006

  2. Contents • Introduction • Direction reconstruction • Position reconstruction • Conclusions • Discussion/questions GLAST INFN-Pisa Workshop – 28-30 June, 2006

  3. I n t r o d u c t i o n KTH plans • Check calorimeter reconstruction of shower direction and position against beam test data • - Identify important variables (for example Ψ68%) • - Estimate the statistics needed for the required precision (?) • Calibration studies of the individual crystals in the calorimeter • - Three studies proposed by David Smith (Bordeaux) GLAST INFN-Pisa Workshop – 28-30 June, 2006

  4. Monte Carlo CAL z y Mc Ψ x Cal D i r e c t i o n R e c o n s t r u c t i o n Background • Study the difference between the generated particle direction and the recorded particle direction in the calorimeter • Mc[X/Y/Z]Dir – generated particle direction cosines • Cal[X/Y/Z]Dir – recorded particle direction cosines in the calorimeter • Space angle is given by GLAST INFN-Pisa Workshop – 28-30 June, 2006

  5. D i r e c t i o n R e c o n s t r u c t i o n Background • The 68% integral is done with GetQuantiles(quantile) in ROOT, which calculates a given fractional (quantile) integral starting from the left and gives the space angle corresponding to that fraction • Error in counts is assumed to have binomial distribution • New integrals are calculated forQuantile ± ΔN/Ntot • Symmetric error is assumedError = 0.5.((Q+ΔN/Ntot)–(Q-ΔN/Ntot)) Exaggerated! GLAST INFN-Pisa Workshop – 28-30 June, 2006

  6. D i r e c t i o n R e c o n s t r u c t i o n CalEnergyRaw • The sum of the raw energies in all the crystals • BeamTestMerits 20-23, 29-30 PS SPS 2 GeV, 0º0.96 T 20 GeV, 0º 0 T 10 GeV, 0º 0 T 2 GeV, 40º0.96 T 10 GeV, 40º 0 T 280 GeV, 0º 0 T GLAST INFN-Pisa Workshop – 28-30 June, 2006

  7. Selected events:95507/400000 failed reconstructions CalEnergyRaw > 5 MeV Selected events:5851/400000 Selected events:63482/400000 CalEnergyRaw > 1000 MeV CalEnergyRaw > 40 MeV tail disappears D i r e c t i o n R e c o n s t r u c t i o n Evolution of space angle distribution 2 GeV - 0º - 0.96 T Selected events:400000/400000 failed reconstructions CalEnergyRaw >= 0 MeV GLAST INFN-Pisa Workshop – 28-30 June, 2006

  8. D i r e c t i o n R e c o n s t r u c t i o n Space angle distributions • CalEnergyRaw > 40 MeV to avoid failed reconstructions PS SPS 2 GeV, 0º0.96 T 20 GeV, 0º 0 T 10 GeV, 0º 0 T 2 GeV, 40º0.96 T 10 GeV, 40º 0 T 280 GeV, 0º 0 T Exception:CalEnergyRaw > 50 GLAST INFN-Pisa Workshop – 28-30 June, 2006

  9. D i r e c t i o n R e c o n s t r u c t i o n CalEnergyRaw threshold dependence • 68% containment space angle dependence on the lower cut in CalEnergyRaw 46794* 1036* 99738* 5851* *counts 2 GeV - 0º - 0.96 T 10 GeV - 0º - 0.0 T • The decreasing of the curve at 2 GeV could be related to the long tail. No tail in 10 GeV gives flat curve. GLAST INFN-Pisa Workshop – 28-30 June, 2006

  10. D i r e c t i o n R e c o n s t r u c t i o n Statistics dependence of relative error 2 GeV - 0º - 0.96 T • Relative space angle error as a function of the selected number of counts • Statistics needed at 2 GeV: • 11 000 . 400 000 / 63 482 ≈≈ 69 000 Total numberof counts Remaining numberof counts afterCalEnergyRaw>40 science requirement? ~11000 counts GLAST INFN-Pisa Workshop – 28-30 June, 2006

  11. D i r e c t i o n R e c o n s t r u c t i o n Statistics dependence of relative error 10 GeV - 0º - 0.0 T • Relative space angle error as a function of the selected number of counts • Statistics needed at 10 GeV : • 1100 . 100 000 / 99 960 ≈≈ 1100 Total numberof counts Remaining numberof counts afterCalEnergyRaw>40 science requirement? ~1100 counts GLAST INFN-Pisa Workshop – 28-30 June, 2006

  12. Monte Carlo CAL P o s i t i o n R e c o n s t r u c t i o n Background • Study the difference between the generated particle position and recorded particle position in the calorimeter • Mc[X/Y]0 – position of photon conversion or charged particle origin • Cal[X/Y]0 – recorded position of CAL track at the energy centroid GLAST INFN-Pisa Workshop – 28-30 June, 2006

  13. P o s i t i o n R e c o n s t r u c t i o n Positional difference distribution 2 GeV - 0º - 0.96 T x-coord. • Distribution looks fairly symmetric  look at absolute value and calculate with quantiles again • Need to find dependence on statistics Absolute value FWHM: ~30 mm Relative bias: ~0.2 % GLAST INFN-Pisa Workshop – 28-30 June, 2006

  14. P o s i t i o n R e c o n s t r u c t i o n Positional difference distribution 2 GeV - 0º - 0.96 T y-coord. • Same thing for the y-coordinate Absolute value FWHM: ~30 mm Relative bias: ~0.2 % GLAST INFN-Pisa Workshop – 28-30 June, 2006

  15. E n e r g y D e p o s i t i o n L a y e r – w i s e Energy deposition as a function of layer number • Mean energy is calculated in each layer from CalELayer[0-7] 2 GeV - 0º - 0.96 T 10 GeV - 0º - 0.0 T GLAST INFN-Pisa Workshop – 28-30 June, 2006

  16. S u m m a r y Summary of reconstruction results • In all of the above (except 2 GeV 40º), CalEnergyRaw>40 • Should compare CalDir to direction from ancillary detectors instead of Monte Carlo direction, since the former is the one that comes from the beam test. When do we get systematics dominated? GLAST INFN-Pisa Workshop – 28-30 June, 2006

  17. D i s c u s s i on Suggestions • Monte Carlo & Beam test: n runs along crystal to plot asymmetry • Energy calibration runs could be used (Eduardo’s talk in beam test meeting June 20, slide 5) ? • Cal-tuple must be used for analysis n runs B. Atwood et al. (1999) GLAST INFN-Pisa Workshop – 28-30 June, 2006

  18. D i s c u s s i on Questions • How is the coordinate system of dir_rec_[x/y/z] defined? z x Anc.Det. CAL x z dir_rec_y dir_rec_z dir_rec_x 0 deg 90 deg 90 deg counts cos θx? cos θy? cos θz? GLAST INFN-Pisa Workshop – 28-30 June, 2006

  19. C o n c l u s i o n s Conclusions and next steps • Relative error of Ψ68% goes down with statistics as expected • Statistics should be ok for gamma/electron runs • Looking for the time being at three variables for beam test simulation validation: Ψ68%, ΔX, ΔY • Propose layer-wise energy deposition • Propose asymmetry curve • Propose layer-wise “center-of gravity” position • Suggestions for more observables welcome! GLAST INFN-Pisa Workshop – 28-30 June, 2006

  20. C o n c l u s i o n s More next steps • Continue to study the position and direction reconstructions for different energies, angles and particle types • Compare CalDir to the reconstructed directions and positions from the ancillary detectors • Variables available already?dir_rec_[x/y/z], position[x/y/z] • Or use tracker values as reference? Or both? • Start with the calibration studies of the individual crystals • Look at other observables? Suggestions welcome GLAST INFN-Pisa Workshop – 28-30 June, 2006

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