1. 26 Apr 2009Paul Dauncey1 Digital ECAL: Lecture 1 Paul Dauncey Imperial College London

2. 26 Apr 2009Paul Dauncey 2 DECAL lectures summary Lecture 1 – Ideal case and limits to resolution Digital ECAL motivation and ideal performance compared with AECAL Shower densities at high granularity; pixel sizes Effects of EM shower physics on DECAL performance Lecture 2 – Status of DECAL sensors Basic design requirements for a DECAL sensor Current implementation in CMOS technology Characteristics of sensors; noise, charge diffusion Results from first prototypes; verification of performance Lecture 3 – Detector effects and realistic resolution Effect of sensor characteristics on EM resolution Degradation of resolution due to sensor performance Main issues affecting resolution Remaining measurements required to verify resolution

3. 26 Apr 2009Paul Dauncey 3 DECAL lectures summary Lecture 1 – Ideal case and limits to resolution Digital ECAL motivation and ideal performance compared with AECAL Shower densities at high granularity; pixel sizes Effects of EM shower physics on DECAL performance Lecture 2 – Status of DECAL sensors Basic design requirements for a DECAL sensor Current implementation in CMOS technology Characteristics of sensors; noise, charge diffusion Results from first prototypes; verification of performance Lecture 3 – Detector effects and realistic resolution Effect of sensor characteristics on EM resolution Degradation of resolution due to sensor performance Main issues affecting resolution Remaining measurements required to verify resolution

4. 26 Apr 2009Paul Dauncey 4 DECAL: basics Requirements for linear collider ECAL Highly granular to allow particle flow Reasonable EM shower resolution Covers range of energies relevant to hadronic jets; 1-100 GeV Take typical energy as 10GeV Effect of DECAL on PFA not yet studied in detail Complex optimisation; depends on detector details Compared to analogue ECAL, DECAL presented here may have Improved energy resolution Improved position resolution Lower cost Assume this cannot harm PFA

5. 18 Sep 2008Paul Dauncey 5 DECAL: Motivation Average number of charged particles in an EM shower  incident energy Fluctuations around the average occur due to statistical nature of the shower Average energy deposited in the sensitive layers  number of charged particles Fluctuations around the average occur due to angle of incidence, velocity and Landau spread Number of particles is a better measure than energy deposited of the shower energy Sensitive Layers

6. 18 Sep 2008Paul Dauncey 6 Simulation study of concept Use simplified “typical” ILC calorimeter geometry 30 layers of silicon-tungsten 20×0.6X 0 + 10×1.2X 0 giving 24X 0 total 500  m thick silicon to give analogue energy deposit No electronics, noise, etc, effects included; “ideal” analogue case Count number of particles emerging from back of each silicon sensor DECAL energy measure 20×0.6X 0 + 10×1.2X 0

7. 18 Sep 2008Paul Dauncey 7 Shower depth dependence Number of particles and energy deposited closely related; both peak at layer ~11 Proportional with ~ 0.26MeV/particle Particles Energy

8. 18 Sep 2008Paul Dauncey 8 Energy spread per particle 0.26MeV is not a constant but an average Energy has extra spread due to fluctuations Dominated by Landau contribution Does not affect number of particles

9. 18 Sep 2008Paul Dauncey 9 Reconstruction of total shower energy E total = ∑ i=0,29 w i E i

10. 18 Sep 2008Paul Dauncey 10 Reconstruction of total shower energy ×1 ×2 ×1.5 E total = ∑ i=0,29 w i E i Why 1.5?!?

11. 18 Sep 2008Paul Dauncey 11 Example resolution E total for 10 GeV photons Counting particles gives better resolution Find mean and width for many different photon energies Particles Energy

12. 18 Sep 2008Paul Dauncey 12 EM shower mean = linearity Both number of particles and energy deposited show good linearity Particles Energy

13. 18 Sep 2008Paul Dauncey 13 EM shower width = resolution 20×0.6X 0 + 10×1.2X 0 a = 0.9, b = 12.8% a =1.1, b = 16.0%  E /E = a  b/  E(GeV) Particles Energy

14. 18 Sep 2008Paul Dauncey 14 Aside: Fischer discriminant Linear weighted combination of N variables Take number of particles per layer (or energy per layer) as 30 variables and find weights which minimise resolution Original weights Optimised weights

15. 18 Sep 2008Paul Dauncey 15 Fischer discriminant: resolution Only minor improvement... Original weights Optimised weights

16. 18 Sep 2008Paul Dauncey 16 Digital ECAL concept How can we measure the number of charged particles??? Make pixellated detector with small pixels and count pixels Probability of more than one charged particle per pixel must be small Allows binary (digital) readout = hit/no hit Analogue ECAL Digital ECAL

17. 18 Sep 2008Paul Dauncey 17 Pixel size Any realistic sensor has to be pixellated With digital (binary) readout, each pixel gives a single bit Two particles within one pixel will lead to undercounting and non-linearity Analogous to saturation effects in SiPMs and DHCAL How small do the pixels need to be? Compromise Non-linearity minimised by smaller pixels Channel count and power minimised by larger pixels Critical quantity is density of particles within EM showers Go for largest pixel size which does not harm resolution

18. 18 Sep 2008Paul Dauncey 18 Typical shower particles; 10GeV photon

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49. 18 Sep 2008Paul Dauncey 49 Particle density vs radius Core ~ 2000 particles/mm 2 Area of first bin  r 2 ~ 3×10 −4 mm 2 Only ~0.6 particles/event in this bin Density in other bins falls off exponentially

50. 18 Sep 2008Paul Dauncey 50 Core particle densities Core density is balance of Increasing number of particles Increasing transverse spread Spread wins; core density is highest in first few layers Absolute number of particles is low here Note, peak in density is NOT at shower maximum, layer ~11

51. 18 Sep 2008Paul Dauncey 51 Core particle density vs energy

52. 18 Sep 2008Paul Dauncey 52 Effect of pixellation If pixels too big, probability of two particles in one pixel is higher Small: N pixels = N particles Big: N pixels < N particles 

53. 18 Sep 2008Paul Dauncey 53 Effect of pixellation Compare original number of particles with number of hit pixels

54. 18 Sep 2008Paul Dauncey 54 Effect of pixellation Conclusion: 50  m is sufficiently small Factor 100 smaller than AECAL cells of 5mm Cross-check AECAL expects up to ~4000 particles per cell Roughly ~0.4 particles per 50  m pixel Assume 50  m for rest of lectures

55. 18 Sep 2008Paul Dauncey 55 Pixellation effect: linearity and resolution Small non-linearity ~1% a = 1.0, b = 12.9%  E /E = a  b/  E(GeV) Effectively unchanged

56. 18 Sep 2008Paul Dauncey 56 CLIC energies Typical hadrons not 1TeV but for fun, see what happens at these energies... 10% effect

57. 18 Sep 2008Paul Dauncey 57 Critical points Counting particles gives better resolution than energy deposited Core density is highest well before shower maximum Pixels of 50  m will give good performance up to at least 100GeV