Detectors

Question 1

Particles’ passage through matter

What is the fundamental principle of particle detection?

Answer 1

Particles must interact with the detector material and lose energy in a measurable way. The detection is based on observing this energy loss, enabling measurement of properties like momentum, energy, and type (mass, charge, spin, parity, couplings, lifetime, etc.).

Question 2

Particles’ passage through matter

Which particles are considered stable in particle physics? How to detect unstable particles?

Answer 2

Stable particles: electron (e), proton (p [uud]), photon (γ), and neutrinos (ν). Other particles decay (after s = γvτ distance) and can only be observed through their decay products.

Question 3

Particles’ passage through matter

How do* short-lived* and long-lived particles differ in terms of detectability?

Answer 3

Relativistic particles with lifetimes ≳ 10^(–10) s (e.g., μ, n, π±, K±) travel measurable distances (few meters) in detectors and can be directly observed. Shorter-lived particles decay too quickly and are detected via their decay products.

Question 4

Particles’ passage through matter

What types of interactions are used to detect different particles?

Answer 4

Charged particles: ionisation, bremsstrahlung, Cherenkov radiation, and transition radiation

Photons: photoelectric effect, Compton scattering, and pair production

Hadrons: nuclear interactions

Neutrinos: (only) weak interaction

Question 5

Particles’ passage through matter

What is the Bethe-Bloch formula and what does it describe? What corrections are applied?

Answer 5

The Bethe-Bloch formula describes the energy loss per unit path length of heavy charged particles through a medium due to ionisation.

• valid for 0,1 < βγ < 1000 and mid-Z materials
• maximal energy transfer (W(max)) depends on particle mass and velocity

Corrections:

• high energy corrections: density corrections due to the density effect (density dependent polarization od medium)
• low energy corrections: shell corrections due to the breakdown of the stationary electron assumption (speed of the incident particle is close to the orbit speed of the electron)

heavy charged = M&raquo_space; m(e)

Question 6

Particles’ passage through matter

What is a Minimum Ionising Particle (MIP)?

Answer 6

A particle that loses the least energy per unit length while traversing a medium. This occurs around βγ ≈ 3–4, with energy loss ~1–2 MeV/(g·cm²).

• e.g.: pions, muons

Question 7

Particles’ passage through matter

How does the energy loss of a charged particle change with velocity?

Answer 7

At low velocities: energy loss decreases sharply (~1/β²)

At high velocities (βγ > 4, v ≈ c): relativistic rise, energy loss increases logarithmically (~ln(βγ)).

• saturation at large βγ due to density effect

Question 8

Particles’ passage through matter

How is dE/dx used for particle identification?

Answer 8

Energy loss per distance (dE/dx) is velocity-dependent and helps distinguish particles of different masses at the same momentum. This is useful in tracking detectors like ALICE TPC.

• momentum can be measured by the track radius in the magnetic field
• particles w/ diff. mass get separated on the plot (dE/dx histogram): typically π/K/p separation

Question 9

Particles’ passage through matter

What technique improves accuracy in dE/dx measurements?

Answer 9

The ‘truncated mean’ method excludes outliers caused by δ-electrons (tail in the Landau distribution that thin absorbers follow) to reduce the effect of fluctuations and improve resolution.

• it excludes the highest measured energy loss values from the average

The distribution is of the energy loss of single collisions.

Question 10

Particles’ passage through matter

What is the Bragg peak and why is it significant?

Answer 10

The Bragg peak is the point near the end of a particle’s range where it deposits maximum energy. This is exploited in medical applications like proton therapy.

The range is the mean penetration length that is not a sharp value but fluctuates statistically.

Question 11

Particles’ passage through matter

Why must Bethe-Bloch be modified for electrons?

Answer 11

Electrons are identical in mass to atomic electrons, making interactions indistinguishable and requiring a more complex treatment than for heavy particles. They are also highly relativistic.

Low energy positrons need different treatment in the calculation, as they are not identical (i.e. they are distinguishable).

Question 12

Particles’ passage through matter

What is bremsstrahlung and when is it important?

Answer 12

Bremsstrahlung is radiation emitted by accelerating charges, especially significant for electrons due to their small mass.

• arises if particles are accelerated in the Coulomb field of a nulceus
• dE/dx ~1/m²
• critical energy: where in a given material the bremsstrahlung starts to dominate over the ionization (where ionisation energy loss = radiation energy loss)
• at high energies, it always dominates over ionisation
• E = E0 exp(-x/X0) for electrons where X0 is the radiation length

Question 13

Particles’ passage through matter

How do muons interact with matter?

Answer 13

Muons mainly lose energy via ionisation. They can travel long distances through dense materials, making them easily detectable as they penetrate deeper than most particles.

• in particle accelerators, muons pass through the full detector leaving a long ionisation trail behind
• below 100 GeV, ionisation energy loss dominates

Question 14

Particles’ passage through matter

What is Cherenkov radiation and when does it occur?

Answer 14

It occurs when a charged particle moves faster than the phase speed of light in a medium. It produces a coherent conical light (shock) wave (while conserving energy and momentum) detected via photodetectors.

• coherent emission because it is in phase with the particle velocity
• threshold: β > 1/n
• Cherenkov angle: cos(θ(c)) = 1/(n·β)

Question 15

Particles’ passage through matter

How can Cherenkov detectors be used for particle ID?

Answer 15

By measuring the angle or presence of Cherenkov radiation, one can determine the velocity of the particle and, when combined with momentum data, infer its mass.

Question 16

Particles’ passage through matter

What are RICH and DIRC detectors?

Answer 16

RICH (Ring Imaging Cherenkov): detects Cherenkov photons forming rings for full 4π coverage

• all photons emitted at same Cherenkov angle
• from the radius of the ring, the velocity can be determined

DIRC (Detection of Internally Reflected Cherenkov light): preserves angle info via light-guiding elements using total reflection to guide photons

Question 17

Particles’ passage through matter

What is transition radiation and when is it emitted?

Answer 17

Transition radiation occurs when a charged particle crosses between inhomogenous materials with different dielectric properties, emitting X-ray photons, especially for highly relativistic particles (γ > 1000).

• the moving charged particle can be considered as an electric dipole with its mirror charge
• energy loss proportional to γ
• increase in energy loss primarily due to increase of photon energy
• low atomic number radiator needed to minimize photon absorption, otherwise TR photons won’t leave the material

Question 18

Particles’ passage through matter

How is transition radiation used for particle identification?

Answer 18

TR is used for electron-pion separation by detecting emitted X-ray photons (so, energy loss), typically 5–15 keV, in a high-Z gas detector (e.g., Xe) with a low-Z radiator (e.g., Mylar).

Question 19

Particles’ passage through matter

What types of interactions do neutral particles undergo in matter?

Answer 19

Neutrons, kaons, lambdas: strong interactions. Neutrinos: weak interactions (with a very small cross section)
Gamma photons: electromagnetic interaction

Question 20

Particles’ passage through matter

What are the main interaction mechanisms of gamma photons in matter?

Answer 20

1. Photoelectric effect: on an atomic electron
2. Compton scattering
3. Pair production: only in external EM field (= close to nucleus)

If none of these happen, the energy of the photon does not change! The photon does not lose energy when passing through matter, only the intensity of the radiation (radiation flux) decreases due to absorption processes, hence we talk about photon absorption not energy loss.

Photons are the only known long-range mediator particles and they are produced in the decay of short-lived particles and in ionisation interactions.

Question 21

Particles’ passage through matter

What is the mean free path in photon interactions?

Answer 21

λ = ρ/μ = ρ/(nσ), where μ is the linear attenuation coefficient, n is the number density and σ is the attenuation cross-section. It represents the average distance a photon travels before interacting and is a characteristic quantity of photons.

Question 22

Particles’ passage through matter

What is the Z-dependence of the photoelectric effect?

Answer 22

Probability(photoeff. from K shell) ~ Z^5. More likely with high-Z materials, especially involving tightly bound electrons (e.g. K-shell) where the innermost electron is closer to the nucleus.

Question 23

Particles’ passage through matter

Why can’t the photoelectric effect occur with a free electron?

Answer 23

Because of conservation of momentum; a nearby nucleus is needed to absorb excess momentum, since during the photoelectric effect a photon transfers all its energy to an atomic electron.

• therefore: most probable is an interaction with an electron on the 1s orbit, on the K shell

Question 24

Particles’ passage through matter

What are the characteristics of the Compton effect?

Answer 24

Photon scatters off an electron, losing energy and changing direction. Maximum energy transfer occurs at 180° scattering.

• energy transferred to electron depends on photon scattering angle
• when a 𝛾 radiation scatters in a scintillator and then leaves it, only a part of the photon energy is transferred to the material, thus measured by the detector

Question 25

# Particles' passage through matter How does the Compton cross section vary?

Answer 25

**It depends weakly on energy (compared to the photoelectric effect) and is proportional to *Z*. It also depends on angle and is described by the Klein-Nishina formula.** * at low energy: more uniform distribution * at high energy: point forward

Question 26

# Particles' passage through matter What is pair production and its requirements?

Answer 26

**A photon converts into an electron-positron pair and their kinetic energy near a nucleus. It requires at least 2×511 keV photon energy.** * in the center of mass system of the electron-positron pair the total momentumof the final state is 0, but the initial photon has a nonzero momentum —» nucleus or other electron needed to take away part of the momentum * cross section: ~*Z²* dependence and quick increase with energy * more energetic photons tend to produce more asymmetric energy sharing between the particles of the pair

Question 27

# Particles' passage through matter How likely is it for each photon interaction to happen compared to each other?

Answer 27

**The Z-dependence of the photoelectric effect and the pair production is stronger, compared to the Compton effect. At high energy always the pair production, at low energy always the photoelectric effect is most probable to happen.**

Question 28

# Particles' passage through matter What is the structure of a *monoenergetic gamma spectrum*?

Answer 28

Includes photopeak, Compton shoulder, backscatter peak depending on the photon interaction in the detector. **Back-scattering peak**: photon back-scatters from surrounding material with Compton scattering **Compton shoulder**: partial energy deposition due to scattered photons leaving the detector before full absorption (photon Compton scatters in scintillator) **Photopeak**: full absorption peak, *E(bs) + E(Cs) = E(peak)*

Question 29

# Detectors in HEP How do *detector systems* look in high energy physics?

Answer 29

**Onion-style structure: each layer brings new information.** Comparing the signals of the various detectors, one can identify the particles and measure their momentum, energy. _From innermost to outermost detector:_ * **charged particle trackers**: lightweight materials * **EM calorimeter**: high-*Z* materials * **hadron calorimeter**: heavy materials + active media * **muon detectors**: heavy absorbers where only muons and neutrinos remain

Question 30

# Detectors in HEP What is **pseudorapidity**?

Answer 30

**It's a spatial coordinate describing the angle of a particle relative to the beam axis: *η = –ln[tan(θ/2)]*.** * *θ* is the polar angle measured from the beam line * particle production distribution is roughly constant as a function of *η* * no energy-dependence (unlike rapidity) * if *m << p*: *η ≈ y* (rapidity)

Question 31

# Detectors in HEP Why do muons escape calorimeters while electrons and pions don't?

Answer 31

**Muons mainly lose energy via ionisation and require much more material (~meters) to stop.** Electrons/pions create showers and are absorbed quickly.

Question 32

# Detectors in HEP What is an **electromagnetic shower**?

Answer 32

**A cascade of particles initiated by an electron or photon, involving bremsstrahlung and pair production until energy falls below a critical value.** After the critical value absorption processes dominate. * photon induced showers somewhat longer, as the energy loss only starts after the first conversion to e+e- pair (*λ = 9X0/7* photon mean free path for pair production)

Question 33

# Detectors in HEP How is EM calorimeter depth determined?

Answer 33

To contain 95% of a 1 GeV photon’s energy in CsI (*E(crit) ~10 MeV*), ~*7-9 X0* is needed; typically, *≥15 X0* is used. **To contain an entire EM shower, the shower length and some plus length has to be taken into account.**

Question 34

# Detectors in HEP What is the **Molière radius**?

Answer 34

**The radius of an infinitely long cylinder containing 90% of an EM shower’s energy.** It characterizes the lateral shower size. * in different materials the lateral size scales with R(M) to good approximation * use: electrons change direction due to multiple Coulomb scattering, and lateral size is also increased by photons that loose their energy far from their birth place

Question 35

# Detectors in HEP What is the purpose of **calorimeters**?

Answer 35

**To stop particles, absorb and measure their full energy. They are thick, high-density materials placed to the particles’ path.** * destructive for all particles excepts muons and neutrinos —» helps with muon identification * detection of neutral particles * incoming charged or neutral particles interact electromagnetically with the detector material or create hadronic showers —» ECals and HCals * secondary particles ionise or produce excited states in the active material, giving measureable signal

Question 36

# Detectors in HEP What is the energy resolution formula for calorimeters?

Answer 36

(σE / E)^2 = (a/E)^2 + (b/√E)^2 + c, with noise (a), stochastic (b), and constant (c) terms.

Question 37

# Calorimeters What are **sampling calorimeters** and how do they work?

Answer 37

**Sampling calorimeters alternate dense absorber layers and active detector layers.** Only a fraction of the shower is sampled, leading to worse energy resolution compared to homogeneous calorimeters. * sampling coefficient = visible energy/total energy absorbed * active elements: gas counters, scintillators, etc.

Question 38

# Calorimeters What are the advantages of the *ATLAS LAr EM calorimeter*?

Answer 38

**Detector uniformity, stable response, high radiation hardness, high granularity, and precise energy measurement using liquid argon as active material. Also, the design is accordion-shaped leading to good signal extraction and shorter cables.**

Question 39

# Calorimeters Why is precise energy resolution important in Higgs boson searches (H -> γγ)?

Answer 39

**A tiny signal sits atop a large background; excellent resolution is critical for distinguishing the Higgs signal peak from background noise.** * *H —» γγ* is the best way for discovery: ATLAS provides good photon/jet separation to minimize the reducible background (photon pointing)

Question 40

# Calorimeters How do **hadronic showers** differ from electromagnetic showers?

Answer 40

**Hadronic showers are longer and wider, involve nuclear interactions, have large event-by-event fluctuations, and a significant non-visible energy component (~30-40%).** * large transverse momentum transfer in nuclear interactions * development of the shower based on *X0* **EM showers are narrower, start earlier and are more localized; they grow with the energy leading to a non-linear response.** * multiple scattering * only the EM energy and the energy of charged particles can be measured in the calorimeter * development of the shower based on *λ(I)* (*X0 << λ(I)*)

Question 41

# Calorimeters What challenges arise when detecting low energy neutrons in hadronic showers?

Answer 41

Low energy neutrons often escape detection because they don't ionize efficiently, contributing to invisible energy losses.

Question 42

# Calorimeters What are the characteristics of **hadron calorimeters**?

Answer 42

**They are thick and dense, operate similarly to EM calorimeters but on larger scales, and suffer from larger fluctuations and invisible energy losses.**

Question 43

# Calorimeters What are compensating calorimeters?

Answer 43

**Calorimeters designed to equalize the response for hadrons and electrons by enhancing the detection of hadronic components (which would not be detected otherwise), e.g., using uranium absorbers.** ## Footnote In a uranium absorber neutrons are also produced, inducing nuclear fission in the absorber material —» more neutrons and high-energy photons —» measuring these increases the hadron shower's signal.

Question 44

# Calorimeters What are the main features and characteristics of **scintillators**?

Answer 44

**They convert deposited particle energy into visible light and guide the light towards the photo-detector.** They have fast timing (~ns), are available in large sizes and masses, but need more energy (~50 eV) to produce a photon compared to semiconductors. _Characteristic quantities:_ photon yield, efficiency emission spectra, decay time, afterglow, stopping power, light collection, energy resolution

Question 45

# Calorimeters What factors influence scintillator *light yield* and *decay time*? How does *light collection* work?

Answer 45

Temperature (lower temperature improves both), doping (activators shift UV light to visible), and the intrinsic material properties. _Light collection_: **scintillation counters are usually read out only via one or two surfaces, this area is significantly smaller than the full surface of the scintillator**

Question 46

# Calorimeters What are the *types of scintillators*?

Answer 46

**Inorganic crystals**: pure or doped (e.g., NaI, PbWO4) * transparent for the emitted light * wide gap: electron-hole pairs form due to an incoming charged particle/gamma-radiation * electron-hole pairs recombine or form bound states (exciton) * exciton moves and de-excites after a collision with a phonon or recomines emitting a UV photon * scintillation due to the crystal structure **Organic materials**: (plastic scintillators) * organic molecules that have symmetry properties associated with the electron structure * fluorescence mechanism arises from transitions in the energy levels of a single molecule **Noble gases or liquids** (LAr, LKr, LXe).

Question 47

# Calorimeters What is a **photomultiplier tube** (PMT) and how does it work?

Answer 47

**PMTs detect weak light signals by converting photons into electrons using a photocathode and amplifying them through a series of dynodes, achieving gains >10^6.** * visible or UV light frees electrons from the photocathode via photoelectric effect * the large kinetic energy electron kicks out several electrons as it hits the dynode * **quantum efficiency**: mean number of photoelectrons created by an incoming photon (max. 50%) * currect amplification: *A = g^n* (n dynodes) | *g*: secondary emission coefficient

Question 48

# Calorimeters What are the *disadvantages* of PM tubes?

Answer 48

Dark current (signal without incoming photon), sensitivity to magnetic fields, after-pulsing (the ionised atoms arrive back to the cathode), and non-linear output at large signals.

Question 49

# Calorimeters What is particle flow calorimetry (PFCal)?

Answer 49

**Technique combining tracking and calorimetry to reconstruct individual particles, significantly improving energy resolution by measuring charged particles in trackers and neutral particles in calorimeters.**

Question 50

# Calorimeters How does time-of-flight (TOF) measurement aid particle identification?

Answer 50

**It is a direct method to measure the speed of a particle. By measuring the difference in flight time over a known distance, particles of different masses (but same momentum) can be distinguished.**

Question 51

# Calorimeters What are typical TOF detector setups?

Answer 51

**Scintillation counters read by photomultiplier tubes with ~100 ps resolution, or Cherenkov detectors with even better timing (~6 ps).**

Question 52

# Calorimeters How do **scintillating fibre tracking detectors** work?

Answer 52

Thin scintillator fibres produce light when hit by particles, allowing precise spatial and timing measurements when read out separately.