Slope measurements from test-beam irradiations Crystal Detector Performance Group 18-09-07 Christopher Rogan California Institute of Technology

Test-beam Irradiations Normalized laser and electron responses Each xtal irradiated for ~10 hours 120 & 90 GeV electrons nominally ~50k events / 60 s ~15 rad/hour Ratio of electron (S(t)) and laser response (APD/PN R(t)) parameterized by Xtal response depends on radiation dose-rate and individual xtal characteristics SM22 - xtal 168 120 GeV e- 6k events / 60 s 4/26/2019 Christopher Rogan - Crystal Detector Performance Group 18-09-07

Christopher Rogan - Crystal Detector Performance Group 18-09-07 2006 Irradiation data sets Goals: Understand transparency change dynamics Look at distribution of xtal alpha values with more statistics Study alpha extraction systematics 6 different xtals irradiated SM22 - 120 GeV e- Xtal 168 Tighter beam-spot for single xtal alpha extraction SM06 - 90 GeV e- Xtals 88, 128, 148, 552, 672 Wider beam-spot allows for study of transparency change in groups of xtals (extracting neighbor xtal alpha values) Issues: Data quality - DAQ issues, lower than optimal rate (~6k / 60 s) Minimal transparency change vs. APD/PN stability 4/26/2019 Christopher Rogan - Crystal Detector Performance Group 18-09-07

Extracting ‘alpha’ values Previous strategy: use ‘correlation plot’ ‘alpha’ corresponds to the slope of the ratio of the electron and interpolated laser responses 4 mm x 4 mm hodoscope cut around point of maximum response ‘electron’ and ‘laser’ response values taken from distribution fit Requires many events at one level of xtal transparency (in situ?) Relative electron response SM22 - xtal 168 120 GeV e- Relative laser response Events 4/26/2019 Christopher Rogan - Crystal Detector Performance Group 18-09-07

Extracting ‘alpha’ values Fitted Sigma as function of Alpha RMS as function of Alpha Sigma / mean Sigma / mean New strategy: minimize xtal energy resolution with respect to alpha value Transparency changes affect electron responses - degrades energy resolution. Laser monitoring system (and optimal choice of alpha) is designed to minimize resolution Fitted (gaussian) sigma is not a smooth function of alpha Instead, use RMS of energy distribution with selected events - smooth function Problem become one dimensional minimization (for single xtal) E9 resolutions SM22 - xtal 168 120 GeV e- 4/26/2019 Christopher Rogan - Crystal Detector Performance Group 18-09-07

Energy resolution minimization Alpha vs. iteration Use iterative method to minimize energy resolution as a function of alpha For one xtal can, for example, use a parabolic interpolation minimization (Brent’s method) Algorithm converges quickly For selected events one can extract alpha with arbitrary precision Resolution vs. iteration SM22 - xtal 168 120 GeV e- 4/26/2019 Christopher Rogan - Crystal Detector Performance Group 18-09-07

Systematic error of the slope extraction Selects events within a ‘sigma window’ for fitted raw data Alpha value appears independent of ‘window’ size Small spread in alpha value distribution from different sets of events .008 .58% Alpha SM22 - xtal 168 120 GeV e- 4/26/2019 Christopher Rogan - Crystal Detector Performance Group 18-09-07

‘Correlation plot’ vs. ‘resolution minimization’ methods 25 independent 4 mm x 4 mm hodo bins One can look at xtal response for events incident on different parts of xtal face Statistics limited in non-central bins Plot is just an illustration (axis scales are different, etc.) Just an illustration SM22 - xtal 168 120 GeV e- 4/26/2019 Christopher Rogan - Crystal Detector Performance Group 18-09-07

‘Correlation plot’ vs. ‘resolution minimization’ methods Using ‘correlation plot’ method: ‘correlation plot’ method suffers in low statistics bins Error on alpha from linear fit doesn’t coincide with actual spread Still statistics limited in outer bins Alpha Mean 1.373 RMS 0.1468 SM22 - xtal 168 120 GeV e- 4/26/2019 Christopher Rogan - Crystal Detector Performance Group 18-09-07

‘Correlation plot’ vs. ‘resolution minimization’ methods Using ‘resolution minimization’ method: 25 independent samples corresponding to 4 mm x 4 mm hodo bins ‘resolution minimization’ statistically consistent with ‘correlation plot’ Spread in alpha distribution improved by a factor of 10 ‘correlation plot’: Mean 1.373 Sigma ~11% ‘resolution minimization’: Mean 1.384 Sigma ~1% 4/26/2019 Christopher Rogan - Crystal Detector Performance Group 18-09-07

E1 resolution minimization 25 independent samples corresponding to 2 mm x 2 mm hodo bins Algorithm minimizes the energy resolution of single xtal Does not require information from surrounding xtals Assumes relative xtal response over face of xtal is maintained during transparency change (containment correction) ~.7% percent spread 4/26/2019 Christopher Rogan - Crystal Detector Performance Group 18-09-07

E25 resolution minimization Algorithm minimizes the energy resolution of E25 object Requires information from surrounding xtals but no containment correction Slightly sensitive to surrounding xtal alpha values (fixed for this algorithm) Result consistent with E1 minimization 25 independent samples corresponding to 2 mm x 2 mm hodo bins ~.8% percent spread E1 Mean: 1.367 RMS: .0098 E25 Mean: 1.355 RMS: .011 4/26/2019 Christopher Rogan - Crystal Detector Performance Group 18-09-07

Magnitude of transparency change The spread in alpha distributions reflects how much the object (E1, E25) resolution depends on alpha ~1% As a result, more transparency change yields a better resolution on the parameter -- seen for xtals 168 and 128 ~3% 4/26/2019 Christopher Rogan - Crystal Detector Performance Group 18-09-07

Resolution minimization Minimization algorithms work for xtals with less transparency change Spread in alpha value greater for less transparency change Here: 25 independent event samples corresponding to 2 mm x 2 mm hodo bins E1 and E25 minimizations consistent E1 minimization: Mean 1.572 Sigma ~2% E25 minimization: Mean 1.589 Sigma ~2.5% SM06 - xtal 128 90 GeV e- 4/26/2019 Christopher Rogan - Crystal Detector Performance Group 18-09-07

Resolution minimization ~.2% .05% APD/PN instability ‘correlation plot’ SM06 - xtal 148 90 GeV e- Difficulties with xtal 148 result from lack of transparency change Regardless, resolution minimization yields (qualified) alpha vale 4/26/2019 Christopher Rogan - Crystal Detector Performance Group 18-09-07

Resolution minimization E1 method: Mean 1.541 Sigma ~9.5% E25 method: Mean 1.356 Sigma ~16% Appreciable spread in alpha; E1 and E25 minimizations still consistent E25 method further degrade due to transparency changes in neighbors with unknow alpha values Important to remember: Regardless of resolution of alpha parameter, the energy resolution is still minimized wrt alpha; spread reflects that energy resolution is relatively insensitive to alpha value 4/26/2019 Christopher Rogan - Crystal Detector Performance Group 18-09-07

Christopher Rogan - Crystal Detector Performance Group 18-09-07 ‘Neighbor’ xtals SM22 - xtal 167 120 GeV e- For ‘neighbor’ xtals in irradiation there is no hodoscope data to construct containment correction for E1 resolution minimization => can use E25 approach One can extract alpha value even without enough statistics for ‘correlation plot’ approach ~.8% change in xtal 167 laser response E25: Mean 1.186 Sigma ~5% 4/26/2019 Christopher Rogan - Crystal Detector Performance Group 18-09-07

Resolution minimization summary Resolution of alpha parameter is closely related to magnitude of transparency change - should be taken into consideration for future irradiations Appreciable spread in alpha values between xtals - must calculate alpha in situ Dispersion of  for 35 BTCP crystals 2002 # Crystals 2003 mean = 1.538 /mean  6% 2004 (fall) 2004 (spring) 2006 (center)  alpha vs. % transparency change 2006 (neighbor)  4/26/2019 Christopher Rogan - Crystal Detector Performance Group 18-09-07

Christopher Rogan - Crystal Detector Performance Group 18-09-07 Outlook ‘Resolution minimization’ approach appears more robust and powerful than ‘correlation plot’ method E1 & E25 minimization approaches can be used in situ to extract alpha values (in fact, in situ data is better suited for this approach than TB irradiation data) E25 minimization does not require containment correction - requires inter-calibration constants. Inter-calibration constants require xtal alpha values => Two sets of constants could be calculated simultaneously. Iterative resolution minimization algorithms are adaptable to all existing inter-calibration schemes Development of toy Monte Carlo in progress to demonstrate this scheme 4/26/2019 Christopher Rogan - Crystal Detector Performance Group 18-09-07

Christopher Rogan - Crystal Detector Performance Group 18-09-07 EXTRA SLIDES 4/26/2019 Christopher Rogan - Crystal Detector Performance Group 18-09-07

R-plot from previous studies SM06 xtal 552 R-plot from previous studies ~.6% change in xtal 552 laser response R-plot shows that a range of alpha values could be quoted depending only on which subset of data points is used -- error on the fit parameter certainly doesn’t reflect this fact 4/26/2019 Christopher Rogan - Crystal Detector Performance Group 18-09-07

Christopher Rogan - Crystal Detector Performance Group 18-09-07 SM06 xtal 552 E1 method: Mean 1.567 Sigma ~3% E25 method: Mean 1.491 Sigma ~7% 4/26/2019 Christopher Rogan - Crystal Detector Performance Group 18-09-07

Christopher Rogan - Crystal Detector Performance Group 18-09-07 Neighbor xtals: SM06 108 E25: Mean 1.186 Sigma ~17% E25 weighted: Mean 1.515 Sigma ~16% ~.6% change in xtal 108 laser response (comparable to level of APD/PN stability). Weighting done with number of events in sample bin. Resolution on central xtal (128) alpha not as good as for 167. E25 for neighbors is quite sensitive to central xtal alpha! 4/26/2019 Christopher Rogan - Crystal Detector Performance Group 18-09-07

Christopher Rogan - Crystal Detector Performance Group 18-09-07 Neighbor xtals: SM22 169 E25: Mean 1.786 Sigma ~18% E25 weighted: Mean 1.826 Sigma ~18% ~.3% change in xtal 169 laser response (comparable to level of APD/PN stability). Weighting done with number of events in sample bin. 4/26/2019 Christopher Rogan - Crystal Detector Performance Group 18-09-07

Alpha value distribution Using these minimization approaches to calculating alpha values has been yielding values consistent with previous picture It is extremely important that we understand the distribution of alpha values Dispersion of  for 35 BTCP crystals 2002 # Crystals 2003 mean = 1.538 /mean  6% 2004 (fall) 2004 (spring) 2006 (center) 2006 TB alpha 2006 (neighbor) Central Neighbor  4/26/2019 Christopher Rogan - Crystal Detector Performance Group 18-09-07