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Mandy Kiburg

Undergraduate Lecture Series

10 June 2021

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Physics of Particle Detectors

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Outline

  • What are we interested in seeing?
    • Individual particles
    • Interactions between particles
  • How do we detect these?
    • Particles interact with various mediums, lose energy
    • Use basic physics principles
    • Detector technologies
  • Full experiment
  • Detectors at Fermilab
  • Further reading

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What do we know about?

  • **Full Intro Lecture on 6/1**
  • Standard Model
    • Matter is made of quarks and leptons
    • Interactions are mediated by gauge bosons
  • For detectors we care about:
    • Strong Interactions
    • EM Interactions
  • Most commonly detected: e+/-, mu+/-, pi+/-, protons, neutrons, gamma, K0, K+/-

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How can we identify particles?

  • We know that particles have a unique set of numbers that define them.
    • Mass, charge, etc.
  • Momentum conservation
    • Momentum before is the same as the momentum after a collision
  • Energy conservation
    • Same energy before and after collision
  • We can observe electromagnetic interactions and strong interactions
  • We can tell types of particles based on their lifetime
    • Muons, kaons, pions all decay at different times and into different things

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In theory…

  • Theory tells us that an electron and a positron interact via a Z boson and produce a quark-antiquark pair

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  • We produce a beam of electrons and positrons at a certain energy and we detect the end products via energy/momentum loss

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Physics Principles

  • Energy loss

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  • Motion in a magnetic field

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  • Ionization

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  • Scintillation

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Energy Loss

  • Energy loss happens in a variety of ways
  • EM Interactions:
    • Bremsstrahlung
    • Pair productions
    • Photo electric effect
    • Cherenkov radiation
    • Scattering (inelastic, elastic)
    • Ionization/Scintillation
  • Strong Interactions
    • Hadronic showers
  • Weak Interactions
    • Neutrinos

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Bethe-Bloch Equation – Energy loss for “heavy particles”

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  • Relativistic Formula: Bethe (1932), others added more corrections later
  • Gives “stopping power” (energy loss = dE/dx) for charged particles passing through material:

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where

A, Z: atomic mass and atomic number of absorber

z: charge of incident particle

β,γ : relativistic velocity, relativistic factor of incident particle

δ(βγ): density correction due to relativistic compression of absorber

I: ionization potential

Tmax: maximum energy loss in a single collision;

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dE/dx has units of MeV cm2/g

x is ρ s, where ρ is the material density, s is the path length

**Note that this is NOT for electrons, that requires more math**

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Minimum Ionizing Particles

  • Bethe-Bloch has same shape regardless of material
  • The minimum is about the same regardless of material: occurs around p/Mc = 3-3.5
  • dE/dx can be used to identify particle type along with an energy or momentum measurement

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Uniform circular motion in a magnetic field

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Ionization

  • Definition: Ionization is the removal or addition of an electron to an atom to make it positive or negative.

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How does this help us?

  • After ionization, you are left with a free electron (negative) and a positively charged atom
  • Adding an electric field – we can separate the different types of charges.
  • Electrons will leave a charge on a s sensor that we can read out.

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Scintillation Light

  • Sometimes, in some materials, a particle moving through does not knock out an electron

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What can we do with scintillation light?

  • The photon emitted will have a very specific energy
  • We can count the number of photons that go to our readout tools

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How to build a detector

  • In order to fully understand an interaction, we should use multiple detectors. There are 2 classic geometries: fixed target and collider.

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Fixed Target Geometry

Collider Geometry

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What do events look like?

  • We can use the different detectors to figure out the signals

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Particle Detectors

  • Tracking Detectors
    • Scintillation
    • Ionization
    • Pair production
  • Calorimeters
    • Hadronic showers
    • Pair production
    • Bremsstrahlung
  • Transition Radiation Detectors
    • Transition radiation
    • Cherenkov radiation

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Tracking Detectors

  • Used for:
    • momentum measurements (p)
    • charge determination
    • particle production position (primary and secondary)
  • Main Concepts
    • Motion in Magnetic field
    • Ionization / scintillation
    • Resolution
  • What are trackers made of?
    • Gaseous detectors
    • Silicon detectors
    • Scintillating fiber trackers

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Gaseous Trackers

  • Straws, Proportional Chambers, Drift chambers, GEMS, TPCs, and many others
  • Operate with high voltage, cathode/anode geometry, charge multiplication

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Solid State Detectors and Fibers

  • Vertex detectors, microstrips, pixel detectors, fibers
    • Radiation hard (very important!)
  • Silicon detectors have many nice features
    • Commercially produced
    • Can make fine granularity

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CMS

9.6M ch

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Tracking Summary

  • Three types of tracking detectors: gaseous, solid state, scintillating
  • Gaseous detectors rely on charge multiplication
    • Gas choice is a bit of “magic”
    • Covers large areas ”cheaply” with sensitive materials
  • Solid state/scintillating
    • Fine granularity, commercially produced
    • Can have problems with too much material in the beamline

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Calorimeters

  • Used for:
    • Energy measurements
    • Mass measurements

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  • Main concepts
    • Ionization
    • Nuclear interactions = “showering”

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  • What type of calorimeters are there?
    • Electromagnetic calorimeters
    • Hadronic calorimeters
    • Sampling vs homogeneous

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Lead Tungstate crystals

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EM Calorimetry

  • EM calorimeters measure response from coulomb interactions (EM force)
    • Used to determine photons and electrons
    • Hadronic showers also have an EM component

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How does a calorimeter work?

  • Particles have gone through the trackers with only minimal energy loss (they haven’t really slowed down).

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  • If they never stop- they can leave our detectors and we can’t tell the difference between them or how much energy they have.

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  • So we stop them.
    • Deposit all their energy
    • We can tell a lot from how they stop

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EMCal: Definitions of Important parameters

  • Radiation length: When a particle’s energy is reduced to 1/e. This is how we describe the thickness of an EMCal:
    • X0 = 180 (A/ Z2) (g/cm2)
  • Critical energy: When the loss of energy from Bremsstrahlung equals the ionization loss of Energy: Ec = 800/(Z + 1.2) (MeV)
  • Moliere radius: Contains 90% of the shower and characterizes the width of the shower
    • r = 21.2 (MeV) X0/Ec
  • Max shower: Smax = ln(Eincoming/Ec)

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Hadronic Calorimetry

  • Hadronic calorimeters
    • Contain both an EM component driven by EM interactions and a hadronic component driven by Strong interactions

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HCal: Definitions of Parameters

  • Defined by nuclear interaction lengths instead of radiation lengths

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    • Lambda = A / (cross section)*Number of atoms
  • Much more complicated, no easy formulas to use to define various concepts (shower max, etc)

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  • Several orders of magnitude bigger than EM interactions
    • Might need 25 cm to contain an EM shower, but need 2.5 meters to contain Hadronic shower

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Time Projection Chambers

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By Rlinehan - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=45798181

  • Uses ionization
  • Can be used for both position and energy measurements
  • Filled with either gas or liquid

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Cherenkov Detectors

  • In some materials, particles will travel faster than the speed of light
    • “Sonic boom” or a boat in the water

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    • Main parameter: Cherenkov angle
      • Cos(theta) = 1/(n*beta)
      • Dependent of velocity of particle and the index of refraction for the material

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Cherenkov and Transition Radiation detectors

  • Both used for Time of Flight and particle identification
    • Depending on mass and speed of particle, it will arrive in different places
  • Important piece of the whole detector

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Putting it all together

  • LHCb
  • NOvA

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  • CMS
  • ATLAS
  • sPHENIX

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Fixed Target Geometry

Collider Geometry

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What do events look like?

  • We can use the different detectors to figure out the signals

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More information on what they look like

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Signature Detector Type Particle

Jet of hadrons Calorimeter u, c, t→Wb,

d, s, b, g

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‘Missing’ energy Calorimeter νe, νμ, ντ

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Electromagnetic

shower, Xo EM Calorimeter e, γ, W→eν

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Purely ionization

interactions, dE/dx Muon Absorber μ, τ→μνν

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Decays,cτ ≥ 100μm Si tracking c, b, τ

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DAQ and electronics

  • Okay, the particles have interacted with our detectors – now what?
  • Final product is
    • A number: mass of the Higgs = 125 GeV
    • A plot:

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  • How do we get from trackers and calorimeters to this?

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Data Acquisition Process

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Detector

Triggering

Signal processing

Storing to tape

Slow controls

Analysis!

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Detector signals

  • Trackers, calorimeters, TPCs all have “eyes”
    • Photomultiplier tubes
    • Silicon Photomultiplier tubes
    • Sense wires that collect charge

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Example – Photomultiplier Tube

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Signal processing

  • Shape
    • Look at the shape of the signal – will tell you important information
  • Amplify
    • Make a small signal large enough to see
  • Discriminate
    • Only look at signals above a certain threshold.

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Processing signals

  • We’ve turned those particle interactions into electronic signals

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Trigger systems

  • Take the input from all the sub systems and detectors
    • Make a decision: keep or not?
  • Usually multi-level
    • Make decisions based on which detector sub systems have events.

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CMS Level 1 Trigger

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Detectors at Fermilab (A Sample)

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Summary

  • The physics of particle detectors comes down to matter interacting with matter
    • Could spend a lifetime studying these different effects
  • What I want you to remember:
    • Charged particle interactions are our main source of information
    • Use energy loss to determine what type of particles you are dealing with
  • Things not touched on at all
    • Readout electronics: extremely important!!!
    • Services: HV and gases, etc: also extremely important!!!
  • This is an active field
    • New experiments will have different configurations

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References

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Resolution – How good is your tracker?

  • Note that most trackers are in a magnetic field
    • pT (Gev/c) = 0.3 B R
    • How well can we measure R?

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  • Depends on a variety of things, including the magnetic field
    • For three hits in a tracker:

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    • Note this equation improves with length squared and improves with magnetic field. It degrades with position resolution and the momentum
    • A rough estimate of how well we can measure resolution:

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s

θ

B

x

L

R