Maria Laach Summer School Maria Laach Abbey 9

Maria Laach Summer School Maria Laach Abbey 9 -18 September, 2015 Principles of Detection for Particle Physics Part 2: Charged Particle Tracking Bruce A. Schumm Santa Cruz Institute for Particle Physics and the University of California, Santa Cruz

Charged Particle Tracking: Introduction Basic idea: • Place as many layers in the way of energetic particles as you can afford (cost, material) • Each layer should measure the position of the through-going particle as precisely as possible • Exploit curvature in a magnetic field (typically solenoidal) to measure momentum • We will discuss tracking sensors (gaseous, solid-state) as well as generic aspects of kinematic reconstruction Bruce Schumm Maria Laach 2015, Part 2: Charged Particle Tracking 2

Tracking in Cylindrical Geometry Typical application: cylindrical-geometry detector in colliding beam experiment (e. g. , the DELPHI Detector at LEP, 1980 s and 1990 s) Solenoidal magnetic field Particles emerging from the collision point execute helical trajectories Bruce Schumm Maria Laach 2015, Part 2: Charged Particle Tracking 3

Gaseous Detectors A little “old school”… but still many applications and R&D. Also, generic principles: F. Sauli, Principles of Operation of Multiwire Proportional Chambers, CERN Yellow Report 77 -09 (1977) Ionization Recall that primary mode of charged-particle energy loss is ionization; for almost all gases <Eion> is between 20 and 40 Ge. V ~5 x 104 e- per g/cm 2 of material Argon STP: ~10 e- per mm Helium STP: ~1 e- per mm Bruce Schumm Maria Laach 2015, Part 2: Charged Particle Tracking 4

Most Basic: Cylindrical Ionization Detectors V 0 b Rb a Anode (sense) wire Typical dimensions: • b of order cm • a of order 10 s of m (1. 2 mil = 30 m typical) Different regimes of operation as a function of V 0 Bruce Schumm Maria Laach 2015, Part 2: Charged Particle Tracking 5

Ionization Detectors: Regimes of Operation I In order of increasing sense wire (“bias”) voltage V 0 I. Recombination V 0 = 0. No net motion of electrons relative to ion. II. Ionization Chamber For V 0 high enough so that E ~10 V/cm over most of gaseous volume, each ionization will produce a 1 e- signal. Radiation detection (Accelerator PPS, diagnostics) Bruce Schumm Maria Laach 2015, Part 2: Charged Particle Tracking 6

Ionization Detectors: Regimes of Operation II number of primary ions Bruce Schumm Maria Laach 2015, Part 2: Charged Particle Tracking 7

Ionization Detectors: Regimes of Operation IV IV. Geiger-Muller Region For large voltage, avalanche is large, and creates significant UV light (electron-ion recombination) that creates ionization throughout gaseous volume (unless “quenched” by additive) Complete discharge, large signal, large dead time “Geiger counter” V. Discharge Tube For very large voltage, gas is unstable, leading to spontaneous discharge and emission of light, independent of passage of ionizing particle. Fluorescent light Bruce Schumm Maria Laach 2015, Part 2: Charged Particle Tracking 8

Regimes of Operation: Graphical Synopsis Signal (in equivalent electrons) as a function of bias voltage V 0 for our “typical” ionization chamber Note that Geiger counter signals are of order 1010 electrons (sensitive electronics not required) From: A. Melissinos, Experiments in Modern Physics Bruce Schumm Maria Laach 2015, Part 2: Charged Particle Tracking 9

Multiwire Proportional Chambers Charpak, 1968 E electron drift “Brute-force” approach to achieving position resolution Wires spaced with ~2 mm pitch ( ~1 mm resolution) E Bruce Schumm electron drift Exploits fact that avalanche is close to wire Maria Laach 2015, Part 2: Charged Particle Tracking 10

Drift Chambers electron drift E Exploit distance-time relationship between point of ionization and collection at anode wire. Multiple measurements along trajectory reconstruct helical trajectory Bruce Schumm Maria Laach 2015, Part 2: Charged Particle Tracking 11

Opal Precision Drift Chamber Bruce Schumm Maria Laach 2015, Part 2: Charged Particle Tracking 12

Drift Chamber Resolution Dominant phenomenon: Diffusion of ionization cloud as electrons drift through field • proportional to square root of drift distance • Depends on mean time between collision: sensitive to T, P • Can achieve better than 100 m resolution Bruce Schumm Maria Laach 2015, Part 2: Charged Particle Tracking 13

Mean Ionization Energy Loss In explicit form, the Bethe energy-loss form is • For incident particle, depends only on the velocity parameters , • If p is known independently (coming soon…) the mean ionization loss determines the mass of the incident particle via p/c = m Since a drift chamber (or any tracker; true for solid-state tracking as well!) makes multiple measurements of the energy loss, a mean may be calculated In principle, any tracker also provides particle ID Bruce Schumm Maria Laach 2015, Part 2: Charged Particle Tracking 14

Truncated Mean However, recall Landau Distribution: welldefined mean but infinite RMS An average of proportional-chamber pulse-heights over any number of depositions contains no information about the true mean! Landau Distribution Truncate SOLUTION: Truncated Mean Remove (truncate) the highest n% of the pulse height, eliminating the pathological tail What should n be? Optimization issue… 20% typical Bruce Schumm Maria Laach 2015, Part 2: Charged Particle Tracking 15

De. Dx and Particle ID Distribution of truncated means for 45 Gev muons Can be done for any repetitive tracking medium (e. g. solid-state) p K Each point is the truncated mean for a single traversing particle Bruce Schumm Opal Collaboration: The Opal Detector at LEP e , Maria Laach 2015, Part 2: Charged Particle Tracking 16

Gaseous Tracking Pulse Development I b +q V 0 Rb a dr Bruce Schumm Maria Laach 2015, Part 2: Charged Particle Tracking 17

Gaseous Tracking Pulse Development II Bruce Schumm Maria Laach 2015, Part 2: Charged Particle Tracking 18

Gaseous Tracking Pulse Development III Bruce Schumm Maria Laach 2015, Part 2: Charged Particle Tracking 19

Opal Precision Drift Chamber (again) Here, we remind ourselves of the typical drift chamber geometry, so that we can contrast it with that of a more recent idea: The TPC… Bruce Schumm Maria Laach 2015, Part 2: Charged Particle Tracking 20

The TPC David Nygren, Lawrence Berkeley National Laboratory The Time Projection Chamber (TPC) 3 D gaseous tracking: Z coordinate from drift, r coordinate from anode pads Well-suited for dense tracking environments, including heavy ion physics Bruce Schumm Maria Laach 2015, Part 2: Charged Particle Tracking The ALICE tracker 21

Precision Micro-Patterned Gaseous Tracking High fields produced by micro-patterned arrays lead to local gas gain; precision provided by segmentation of anode GEM Detectors e. g. , TPC end-plate readout Bruce Schumm Micro. Megas Maria Laach 2015, Part 2: Charged Particle Tracking 22

Helical Tracking Parameters Most prevalent application of charge-particle tracking is for cylindrical-geometry detectors with a solenoidal B-field Helical trajectories with five defining “track parameters” Bruce Schumm Maria Laach 2015, Part 2: Charged Particle Tracking 23

Helical Track Parameters: , d 0, 0 Consider projection in plane transverse to magnetic field (x, y or r, plane): Collision point N. B. : For track with p. T > ~1 Ge. V, only a small arc of the trajectory is visible in the tracking system 2 D point of closest approach Radius of curvature J. Strube, PNNL Three of the five track parameters are: d 0: 2 D distance of closest approach 0: angle at 2 D distance of closest approach = curvature = 1/R Bruce Schumm Maria Laach 2015, Part 2: Charged Particle Tracking y z x 24

Helical Tracking Parameters: , z 0 y x z z 0 2 D point of closest approach Collision point The two remaining track parameters are defined at the 2 D point of closest approach: : polar angle z 0: longitudinal displacement Bruce Schumm Maria Laach 2015, Part 2: Charged Particle Tracking 25

Billoir Algorithms Track parameter resolution can be calculated (in Gaussian approximation) in closed form, e. g. , Pierre Billoir, TRACK FITTING WITH MULTIPLE SCATTERING: A NEW METHOD, Nuclear Instruments and Methods in Physics Research 225 (1984) 352 -366 There are several (rather dusty) packages available that implement the Billoir method with a convenient driver. For high-energy experiments (LHC, ILC), I have written LCDTRK; see http: //scipp. ucsc. edu/~schumm/lcdtrk 20011204. tar. gz Not a commercial-grade product, but documentation and some support available! NOTE: For Gaussian layer-by-layer measurement uncertainties, curvature ( ) and not transverse momentum (p. T) is the Gaussiandistributed track parameter Bruce Schumm Maria Laach 2015, Part 2: Charged Particle Tracking 26

LCDTRK Example: Momentum Resolution Note: p. T in Ge. V/c (not Me. V/c) for this plot Bruce Schumm Maria Laach 2015, Part 2: Charged Particle Tracking 27

Momentum Uncertainty Scaling Behavior I Track of radius of curvature R measured in chamber of radius b R = 1/ b O x Not shown: N precision tracking layers filling tracking volume of radius b. Solenoidal magnetic field (into page) of strength B Typically, 0. 5<B<5 Tesla Bruce Schumm Maria Laach 2015, Part 2: Charged Particle Tracking 28

Momentum Uncertainty Scaling Behavior II s b O Bruce Schumm Maria Laach 2015, Part 2: Charged Particle Tracking 29

Momentum Uncertainty and MCS I 1/p. T: Note: p. T in Ge. V/c (not Me. V/c) for this plot MCS-dominated Geometrydominated Below some value of p. T, MCS will dominate the momentum resolution, leading to a regime for which p. T/p. T 2 is not constant. Example: For (proposed!) ultra-precise International Linear Collider tracking systems, break-point is between 50 and 100 Ge. V… Low-mass tracking technology is major focus of ILC R&D. Bruce Schumm Maria Laach 2015, Part 2: Charged Particle Tracking 30

A Modern Alternative: Solid State Tracking Consider adjoining two oppositely-doped semiconductors (circled charges fixed, uncircled are mobile) in a diode junction + + + - + + p-type ++ + + circled = fixed uncircled = free --xp -- + + V + + - + + + xn V 0 Depletion Zone + + - n-type + + - x Tradeoff between diffusion and energy minimization leads to finite junction potential V 0, with associated capacitance C 0. Bruce Schumm Maria Laach 2015, Part 2: Charged Particle Tracking 31

The Depletion Zone Maximize signal (and minimize capacitance) by maximizing d Bruce Schumm Maria Laach 2015, Part 2: Charged Particle Tracking 32

N- and P-Type Sensors Bruce Schumm Maria Laach 2015, Part 2: Charged Particle Tracking 33

Bias Voltage and Full Depletion Even for high-resistivity Si ( 104 -cm), d is only about 50 m. At about 80 e/h pairs per micron, signal about 4000 e/h pairs, or about 2/3 f. C Small signal (compare to gas gain of 105 or greater, and multiple ionizations) Solution: Reverse bias voltage (e. g. , N-type sensor) Metalization --- p n --- ++ + + + ++ VB Bruce Schumm Maria Laach 2015, Part 2: Charged Particle Tracking 34

Position-Sensitive Solid State Sensors Heavily-doped ptype “implant”; depletes N bulk. Metallization N bulk Heavily-doped ntype implant to reduce Schottky barrier To achieve position resolution, segment anode (N-type) or cathode (P-type) into strips (strip detector) or pixels (pixel detector) Typical “pitch” is around 50 m point resolution of between 5 and 15 m 5 -10 times better than gaseous tracking, but fewer layers. Which is “better”? I discuss in Nucl. Instrum. Meth. A 579 (2007) 595 -598. • Energy frontier: Si tends to show up more often. • Luminosity frontier (flavor physics): gaseous tracking if it can tolerate the radiation environment. Bruce Schumm Maria Laach 2015, Part 2: Charged Particle Tracking 35

Silicon Diode Pulse Development I p n+ p+ VB + x 0 d x E Time scale = Bruce Schumm Maria Laach 2015, Part 2: Charged Particle Tracking 36

Silicon Diode Pulse Development II -Q/e total signal electrons holes For high-resistivity silicon, = 1 nsec Bruce Schumm Maria Laach 2015, Part 2: Charged Particle Tracking t (units of ) 37

Readout Noise Response Weighting Functions RB Id RS CS ia, va (t) where is the amplifier rise time H. Spieler, Semiconductor Detector Systems, Oxford, 2005 For “lumped” elements, in electron-equivalent noise Bruce Schumm Maria Laach 2015, Part 2: Charged Particle Tracking 38

Lumped Elements vs. Distributed Network K. Collier et al. , Microstrip electrode readout noise for load-dominated long shaping-time systems, Nucl. Instr. & Meth. A 729 (2013), 127. Expectation (dotted) and measurement (red dashed) suggest that distributed sensor RC network shunts significant noise to ground… Bruce Schumm Maria Laach 2015, Part 2: Charged Particle Tracking 39

Monolithic Pixel Sensors (e. g. MAPS) Advanced microelectronic technology (sub 100 -nm feature size) allows significant processing and data-flow architecture to be developed local to pixel, e. g. , the MAPS (Monolithic Active Pixel Sensor) concept; now part of baseline designs. Bruce Schumm Maria Laach 2015, Part 2: Charged Particle Tracking 40

Next Stop Next stop: High-energy caloimetry… Bruce Schumm Maria Laach 2015, Part 2: Charged Particle Tracking 41