C4: Particle Physics Major Option

Particle Detectors

Author : William Frass Lecturer : Dr. Roman Walczak Michaelmas 2009

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Contents
1 Introduction 4
1.1 The aims of particle detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2 Momentum determination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Energy determination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4 Spatial resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.5 Temporal resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.6 Typical spatial and temporal resolutions for common detectors . . . . . . . . . . . . . . . 5

2 Gaseous ionisation detectors 6

2.1 Principle of operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 Applied detector voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 Detectors working in the ionisation region: ionisation chambers . . . . . . . . . . . . . . . 8
2.4 Detectors working in the proportional region . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.4.1 Proportional chambers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.4.2 Multi-wire proportional chambers (MWPCs) . . . . . . . . . . . . . . . . . . . . . 11
2.4.3 Drift chambers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.4.4 Time projection chambers (TPCs) . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.4.5 Brief history of improvements to the proportional chamber . . . . . . . . . . . . . 14
2.5 Detectors working in the Geiger-Müller region . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.5.1 Geiger-Müller tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.5.2 Multi-wire chambers (MWCs) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.6 Detectors working in the continuous discharge region: spark chambers . . . . . . . . . . . 15

3 Solid state detectors 16

3.1 Silicon semiconductor detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.1.1 Principle of operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.1.2 Energy resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.1.3 Radiation degradation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.2 Scintillators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.2.1 Principle of operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.2.2 Organic versus inorganic scintillators . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.2.3 Organic scintillator photon yields and luminescence . . . . . . . . . . . . . . . . . 18
3.3 Čerenkov detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.3.1 Particle identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.3.2 Calorimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

4 Calorimeters 20
4.1 Electromagnetic versus hadronic calorimeters . . . . . . . . . . . . . . . . . . . . . . . . . 20
4.2 Homogeneous versus heterogeneous calorimeters . . . . . . . . . . . . . . . . . . . . . . . . 20
4.3 Energy resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.3.1 Electromagnetic calorimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.3.2 Hadronic calorimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4.4 Typical energy resolutions for some calorimeters . . . . . . . . . . . . . . . . . . . . . . . 22

5 Hermetic detectors 23
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
5.2 Layout and purpose of layers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
5.3 Propagation of particles through the layers . . . . . . . . . . . . . . . . . . . . . . . . . . 24

6 Case studies 25
6.1 Drift chamber – barrel muon chambers at DELPHI . . . . . . . . . . . . . . . . . . . . . . 25
6.2 Drift chamber with magnetic field – central tracking chamber at ZEUS . . . . . . . . . . . 26
6.3 Sampling calorimeter – uranium-scintillator calorimeter at ZEUS . . . . . . . . . . . . . . 27
6.4 Hermetic detector – Compact Muon Solenoid (CMS) . . . . . . . . . . . . . . . . . . . . . 28
6.5 Ring imaging Čerenkov detector – Super-Kamiokande . . . . . . . . . . . . . . . . . . . . 29

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7 Particle identification 30
7.1 Characteristics of particle events in hermetic detectors . . . . . . . . . . . . . . . . . . . . 30
7.2 Identifying particles from the DELPHI detector at CERN’s LEP collider . . . . . . . . . . 31
7.2.1 e− e+ → e− e+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
7.2.2 e− e+ → µ− µ+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
7.2.3 e− e+ → 2 jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
7.2.4 e− e+ → 3 or 4 jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
7.2.5 e− e+ → ΛΛ̄ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
7.3 Identifying particles from Super-Kamiokande events . . . . . . . . . . . . . . . . . . . . . 36
7.3.1 Electron events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
7.3.2 Muon events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
7.3.3 Muon decay to electron event . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
7.4 Identifying particles from the spark chamber at CERN’s SPS . . . . . . . . . . . . . . . . 37

w.frass@seh.oxon.org

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1 Introduction
1.1 The aims of particle detectors
The aim of a particle detector is to quantify the momenta and discover the identity of the particles that
pass through it after being produced in a collision or a decay - an ‘event’.

The event might be a collision deliberately engineered to occur within the detector leading to many
particles which in turn decay into many more, or it could be a decay that occurs naturally (in the upper
atmosphere, for example), which is then detected on Earth. The exact position in space where the event
occurs is known as the interaction point.

In order to identify every particle produced by the collision, and plot the paths they take - to ‘completely
reconstruct the event’ - it is necessary to know the mass and momentum of the particles. The mass
can be found by measuring the momentum and either the velocity or the energy.

The modern large-scale detectors used today at places such CERN, including ATLAS and LCHb, which
encompass many forms of tracking chambers and calorimeters that completely surround the interaction
point are known as ‘hermetic detectors’.

1.2 Momentum determination

A tracking detector reveals the path, or ‘track’, taken by a particle. Momentum measurements can
be made by applying a magnetic field perpendicularly to the direction of travel in a tracking detector,
this causes the particle to curve into a circular orbit with a radius proportional to the momentum of the
particle; consider the Lorentz force on the particle:

F = qvB (1)

ma = qvB (2)

v2
 
m = qvB (3)
r
mv
= qB (4)
r
mv p
Figure 1: A particle with velocity v entering a mag- r= = (5)
qB qB
netic field. In unit time the particle travels a distance
v around the circle and turns through an angle ω. r∝p (6)

The radius is also proportional to the mass-charge-ratio, m/q, so if two particles have the same speed,
and one is half as heavy as the other, but has twice the charge, they will both orbit with the same radius.

Since the magnetic field exerts a force perpendicular to the direction of the particle’s direction, it can do
no work on the particle, hence the particle does not lose energy as a result of this process.

Thus having established the momentum, the energy can be measured by a calorimeter and the mass of
the particle, and hence its identity, deduced.

The direction the particle curves in the magnetic field reveals its charge, since positive and negative
charges curve in opposite directions.

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1.3 Energy determination
Calorimeters rely on energy loss phenomena in order to determine the energy of the particles pass-
ing through them. In the case of detectors built specifically for calorimetry, the energy deposition is
usually in the form of electromagnetic or hadronic showers, however calorimeters exist that exploit com-
pletely different forms of energy loss. In addition, a tracking detector is sometimes also able to provide
information on energy loss.

1.4 Spatial resolution

The term spatial resolution has a dual meaning in the context of tracking detectors:

• The precision with which a tracking detector reports the true location of a particle. The usual
measure of this precision is the square root of the variance of the probability density function that
gives the probability of getting a signal for a particle at x when it has crossed the detector at x0 :

Z 1/2 Z 1/2
σ(x0 ) = (x − x0 )2 P (x, x0 )dx ≈ (x − x0 )2 × r0 (x − x0 )dx (7)

• The ability of a tracking detector to distinguish the signals it receives due to two different particles
passing very close to each other.

Spatial resolution is also significant, albeit slightly less important, in calorimeters. This is because in
large hermetic detectors it is often necessary to associate a particle’s calorimeter hits with the track it
has left in tracking detectors - for this to work, the calorimeter has to be able to report fairly accurately
where the energy was deposited.

1.5 Temporal resolution

The time resolution of a detector determines how well it is able to distinguish two events which happen
in quick succession. It is important to have good time resolution for fast-triggering applications such as
time of flight measurements. As in the case of the spatial resolution, the temporal resolution is measured
using the standard-deviation (the square root of the variance).

The temporal resolution can be influenced by many properties of the detector, not limited to the material
it is made from, the size and the surface of the scintillation counter and the properties of the light guide.

1.6 Typical spatial and temporal resolutions for common detectors

Typical values of spatial and temporal resolutions for various common detectors are given below: 1

Detector type Spatial resolution [µm] Temporal resolution [ns]

Bubble chamber 10 – 150 1 × 106

Spark chamber 300 2000

Proportional chamber 50 – 300 2

Drift chamber 50 – 300 2

Liquid argon drift chamber 175 – 450 200

Scintillator (refractive index n) — 0.1/n

The bubble chamber is now obsolete, but has been included in a few tables for comparative purposes.
1 Source: Table 28.1 of Particle Data Group 2008.

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2 Gaseous ionisation detectors
2.1 Principle of operation
The principle on which gaseous ionisation chambers work is outlined below:

Figure 2: Circuit diagram for a gaseous ionisation chamber.

A voltage is applied to the central anode (positive) and the chamber walls / cathode (negative) to create
an electric field between them. When a charged particle passes through the chamber it ionises the gas
molecules inside, along the path it takes, creating negative electrons (anions) and positive ions (cations).

The collection of these charged particles reduces the voltage across the capacitor - this in turn increases
the voltage across the resistor. This ‘pulse’ across the resistor is recorded electronically, registering a hit.

The height of the pulse can be calculated as follows:

• The charge, Q on a capacitor of capacitance C under voltage V is given by:

Q = CV (8)
• As mentioned above, a change in the charge causes a change in the voltage:

∆Q
∆V = (9)
C
• The change in charge is equal to the number of electrons collected by the anode. This is related to
the number of ionising events that occur, n, as the charged particle being detected passes through
the gas. If the ionisation products have sufficient energy to cause secondary ionisations, then the
charge due to the primary ionisation events (n × e) must be multiplied by the gas amplification
factor A:

Ane
Pulse height = ∆V = (10)
C
• The gas amplification factor, A, is dependent on the voltage applied.
Many different elements or compounds can be used to fill the chamber2 - but they are always gases
because the ionisation products can move to the relevant electrodes more easily in a gas than they can
in a liquid or solid.

As shown in equation (10), the pulse height is dependent on the number of ion pairs collected by the
anode. However, the number of ion pairs collected varies hugely depending on the applied voltage. So
much so, that the way a detector behaves is different in each of the voltage ranges.

2 Examples include helium, argon and boron triflouride.

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2.2 Applied detector voltage
The number of ion pairs collected varies hugely as the voltage applied to the detector (see Figure 2) is
increased. The graph below shows two curves, the curve for alpha-particles is higher than the curve for
beta-particles because of the greater number of initial ion pairs an alpha-particle is able to produce due
to its larger mass.

Figure 3: Number of ion pairs collected versus applied voltage in a gaseous ionisation chamber.

Recombination region

In this region, the voltage is insufficient to create an electric field strong enough for collection of all
the ions produced. Instead they drift too slowly towards the electrodes and recombine back to neutral
molecules before they can be collected. Obviously as the voltage is increased - more ions are collected,
but until the saturation value is reached, not all ions will be prevented from recombining. For this reason
gaseous ionisation chambers are not operated at these voltages.

Ionisation region

Somewhere around 100 V a saturation value is reached: the voltage is now sufficient to ensure collection
of all the ion pairs that the charged particle creates. However, the voltage is not yet strong enough to
cause secondary ionisation - there is no gas amplification here, hence there is no rise in the number of
ions collected.

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Proportional region

The voltage in this region produces a large potential gradient near the anode. Gas amplification is now
possible because the electrons produced by ionisation are accelerated up to speeds where they can cause
secondary ionisation - this is a Townsend avalanche. In this region the voltage pulse is proportional
to the amount of ionisation.

Region of limited proportionality

As the voltage is increased further, the strength of the electric field causes electrons to be released from
the cathode. This results in the Townsend avalanche spreading along the anode, whilst the positive
ions then tend to remain near where they were created. This reduces the electric field to a point where
further ionisation events are impossible: the number of ions pairs collected begins to level off again. This
is another range of voltages not used for detectors.

Geiger-Müller region

By this point the voltage is so high that once an avalanche is initiated, it continues to spread until gas
amplification becomes impossible due to a build-up of positive ions around the anode forming a dense
shield. Once the threshold has been crossed and the dense shield is formed, no more ions can be col-
lected and the graph reaches the Geiger plateau.

The number of ions required to shield the anode depends on the detector and not the charged particle
passing through it. Therefore both alpha- and beta-particles have the same Geiger plateau because once
the ion shield is in place, no more ionisation events can occur, irrespective of the charged particle under
detection.

Region of continuous discharge

Finally, if the voltage is increased further it is so high that once ionisation occurs there is a continuous
discharge of electricity. The Geiger plateau is the last useful range for continuously applied voltages -
anything above this cannot be used for particle detection.

Spark chambers do operate at voltages above those shown on the graph - but there is a single discharge
onto the plates - not a continuous voltage supply.

2.3 Detectors working in the ionisation region: ionisation chambers

Ionisation chambers operate at the lowest possible voltages, in the ionisation region. Voltages lower
than these are not sufficient for collection of all the electrons and some recombine with ions to form
neutral atoms. The gas filling the chamber is often simply air. There are two types of ionisation
chambers:

• Pulse counting ionisation chambers: each individual particle traversing the detector creates
a pulse, which is counted.
• Integrating ionisation chambers: all the pulses add and the integrated total of all the ionisation
events over a period of time is measured. This type is more commonly used.

There are also two possible geometries for ionisation chambers:

• Parallel plates: this design is preferred because it has a well-defined active-volume.

• Concentric cylinders: this design necessitates some insulator to support the central anode. A
build-up of ions on this insulator will distort the electric field; this variation in the field means
there is not a well-defined active-volume.

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Ionisation chambers primarily detect charged particles through their ionisation losses. However they can
also detect neutral photons and neutrons:
• Photons can be detected because the interactions they undergo, namely photoelectric emission,
Compton scattering and pair production, all lead to the production of electrons, which are then
detected in exactly the same way as the electrons resulting from an ionisation event.

• Neutron detection is not possible in an ordinary ionisation chamber because neutrons are not
ionising. However, with the addition of a thin boron coating on the inner chamber walls, or the
use of boron triflouride gas, the following reaction takes place:

10 1 7 4
5 B + 0 n → 3 Li + 2 He + 5 e (11)
The neutron is captured by the boron atom and an energetic alpha particle is emitted along with
some electrons. The alpha particle is heavily ionising - losing all its energy in a just a few centimetres
- allowing the neutron to be detected.
Such ionisation counters are widely used in the nuclear industry. By reducing the volume or decreasing
the pressure inside the chamber, the active-volume is too small to contain the electrons produced by
gamma radiation, so only the alpha-particles due to the presence of neutrons are counted.

Ionisation chambers are not really useful for modern particle physics experiments because they need
heavy ionisation in order to receive a signal, yet fast particles create little ionisation according to (12),
and they have a slower response time than proportional chambers. They do however, have a longer
life-time than both proportional chambers and Geiger-Müller tubes because the gas in these tends to
break down eventually.

2.4 Detectors working in the proportional region

2.4.1 Proportional chambers
Increasing the voltage from the ionisation region to the proportional region means gas amplification
becomes possible. Amplification factors can be as high as 104 , making proportional detectors much
more sensitive than ionisation chambers because low energy (E < 10 keV) particles will still register due
to the Townsend avalanches they create.

The voltage is large enough to collect all the electrons within microseconds. The height of the voltage
pulse in a proportional chamber provides information about the energy of the incident charged particle:
       
pulse charge number of primary energy deposited by 1
∝ ∝ ∝ ∝ 2 (12)
height collected ionisation electrons the charged particle β
This is the biggest advantage proportional chambers have over other gaseous ionisation detectors - in
addition to tracking, they can provide information on the energy deposited by particles, which can be
used for particle identification. This works because the geometry of the detector is such that the
electric-field is insufficient to accelerate the electrons until they are micrometres from the anode: this
way all electrons generate the same sized avalanche - no matter how far they have drifted before getting
close to the anode.

The energy a particle deposits is, of course, proportional to 1/β 2 according to the Bethe formula. Once
the value of β is known, the energy can be found, if the momentum is deduced from magnetic curvature.

Unfortunately, for every electron there is an ion of chamber gas, which will gain an electron at the
cathode and thus emit a photon. All these emitted photons release electrons from the cathode via the
photoelectric effect, which will create unwanted pulses and could result in a current strong enough to
melt the wire. These photons must be absorbed by a quencher gas, typically carbon dioxide or
an organic molecule such as methane. A typical gas composition for proportional chambers is P-10
comprising 90% argon and 10% methane.

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Spatial dependence of the voltage pulse
• The work done (∆W = Force × distance), by a charge q moving through an electric-field, E is:
Z end
∆W = qE · dr (13)
start

• This change in energy is the source of the voltage pulse, ∆V . Voltage is the energy per unit charge,
therefore the change in energy equals Q × ∆V :
Z end
Q∆V = qE · dr (14)
start

• The total charge a capacitor of capacitance C can store is Q = CV0 , with V0 the applied voltage:
Z end
q
∆V = E · dr (15)
start CV0
• E is sometimes expressed as the gradient of the potential, and in any case is given by Gauss’ law:

Z start
q dV0
Voltage pulse = ∆V = dr (16)
end CV0 dr
• Recall the electric-field is not strong enough to cause an avalanche until the initial electrons are a
small distance from the anode - call this distance λ. Integrating along their paths, it can be shown
that the voltage pulse due to the electrons moving from λ to the anode is small compared to the
pulse due to the ions moving from λ to the cathode: the pulse is almost all due to the motion
of the positive ions.
Time dependence of the voltage pulse
• To find the temporal variation of the voltage pulse, substitute dV0 /dr for the electric field in (16).
• Now integrate (16), in general this time, using a boundary condition to find the constant of inte-
gration. This gives the voltage pulse in terms of r, hereby referred to as ∆V (r).
• The variable of time is introduced by considering the drift velocity. In a proportional chamber
the drift velocity is proportional to the electric-field:

dr
= v = µE (17)
dt
• Substitute for the electric field, E, in (17) and integrate (17) with respect to time; this yields a
new expression for r in terms of t. Now substitute this new expression into ∆V (r) giving ∆V (t).
• For the specific case of concentric cylinders of length l, with an inner cylinder having radius a:
   
−Q µCV0 t
∆V (t) = ln 1 + t ∆V (t) ∝ ln 1 + (18)
4π0 l π0 a2 t0
• The constant t0 is typically a few nanoseconds and depends on the geometry and ion mobility.
Dead time
• The longer the pulse, the longer the time before an individual wire can be used to detect another
particle - the wire’s dead time. The table below shows the dead time of some common detectors: 3

Bubble chamber Spark chamber Proportional chamber Drift chamber Scintillator

Dead time 50 ms 100 ms 200 ns 100 ns 10 ns

3 Source: Table 28.1 of Particle Data Group 2008.

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2.4.2 Multi-wire proportional chambers (MWPCs)
The detectors discussed so far have primarily been counters - they merely detect the presence of a par-
ticle. The proportional chamber advances this by virtue of the fact the voltage pulse it measures is able
to provide information on the particle’s energy as well.

The multi-wire proportional chamber or MWPC advances this further - instead of having one anode
wire surrounded by a cathode wall or plate, multiple ‘sense wires’ are equidistantly spaced symmet-
rically between two parallel plates. Wire spacings are typically a few millimetres. A nearly uniform
electric-field develops between the cathode plates, distorted only near the sense wires.

Each wire acts as a separate counter - when a charged particle passes through the chamber leaving a
trail of electron-ion pairs, the electrons drift to the nearest wire and cause a voltage pulse. By placing
another such configuration at 90◦ to the first, thus forming a grid, and marking off the wires that produce
a pulse, the path of the charged particle is revealed.

As explained in Chapter 1, applying a magnetic field perpendicular to the direction the particle is trav-
elling in, will cause it to spiral due to the Lorentz force. This will reveal how the particle is charged and
what its momentum is.

A typical gas composition for multi-wire proportional chambers is the ‘magic gas’ mixture comprising
75% argon + 24.5% isobutane + 0.5% freon.

2.4.3 Drift chambers

The resolution of multi-wire proportional chambers can be dramatically enhanced by taking into consid-
eration the time the electrons take to drift from the point where they were liberated to the sense
wire, where they are detected. Thus one can infer the distance at which the charged particle passed the
wire. This improves the spatial resolution and allows for wider wire spacings on the order of centime-
tres. Wider wire spacings distort the uniform field less, but increase the drift time, hence these ‘drift
chambers’ are not ideal for use in colliders with high collision rates, or in triggers.

In order to calculate the distance an electron has travelled it is necessary to understand its velocity in
the electric-field. The uniformity of the field must be more carefully controlled than it is in a multi-
wire proportional chamber: to this end, the anode sense wires are alternated with cathode field wires
that ‘correct’ the field distortion caused by the sense wires, restoring uniformity throughout the chamber.

Drift velocities under electric-fields

The graph below shows the drift velocities of common drift chamber gases as a function of the applied
electric-field:

Figure 4: Computed electron drift velocity

as a function of electric field in several
gases at standard temperature and pres-
sure. Taken from Figure 28.4 of the Par-
ticle Data Group 2008.

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If the average momentum relaxation time is τ , then an electron moving in an electric-field E
experiences a force:
dp mvdrift
F = = = eE (19)
dt τ
Here, vdrift is the drift velocity of the electrons in an electric-field only:

eEτ
vdrift = (20)
m
Drift velocities under electric- and magnetic-fields

The situation becomes more complex upon the application of a uniform magnetic-field. The electrons now
drift at an angle ψ with respect to the electric-field. If the electric- and magnetic-fields are perpendicular:

tan(ψ) = ωτ (21)
The angle ψ is known as the Lorentz angle, with the cyclotron frequency, ω, given by:
eB
ω= (22)
m
In order to prove the relationship in (21), it is necessary to solve the equation of motion for an electron
in both electric- and magnetic-fields. To avoid confusion with the electric-field-only drift velocity, vdrift ,
the symbol u will be used for the electric- plus magnetic-field case.

In addition to the Lorentz force, a particle in a gas filled drift chamber is also subjected to a retarding
force proportional to its velocity −Ku:
du
m = eE + e[u × B] − Ku (23)
dt
The constant K is defined such that τ = m/K. In steady-state (23) reduces to:
e 1 e
E = u + [u × B] (24)
m τ m
Writing out the x, y and z components of the above in a matrix equation gives:
    
E 1/τ −ωz ωy ux
e  x 
Ey = ωz 1/τ −ωx  uy  (25)
m
Ez −ωy ωx 1/τ uz
The ω components are defined according to (22). Solve for the drift velocity, u, by inverting this matrix:

1 + ωx2 τ 2 ωz τ + ωx ωy τ 2 −ωτ + ωx ωz τ 2
    
ux Ex
τ −ωz τ + ωx ωy τ 2 2 2 2 e
 uy  = 1 + ω y τ ωx τ + ω ω
y z τ Ey  (26)
1 + (ωτ )2 2 2 2 2 m
uz ωy τ + ωx ωz τ −ωx τ + ωy ωz τ 1 + ωz τ Ez
This can be written in a more accessible form with the use of the unit vectors Ê and B̂:

eEτ /m h i
u= 2
Ê + ωτ (Ê × B̂) + (ωτ )2 (Ê · B̂)B̂ (27)
1 + (ωτ )
When Ê is perpendicular to B̂ their scalar product is zero, so the last term vanishes:

eEτ /m h i
u= Ê + ωτ (Ê × B̂) (28)
1 + (ωτ )2
Remember, ψ is the angle the electrons are drifting at with respect to the electric-field, in other words
it is the angle between u and E, readily found from u · E:

eEτ /m h i
u · E = uE cos(ψ) = Ê · E + ωτ ( Ê × B̂) · E (29)
1 + (ωτ )2

12
The scalar product of a vector with its own unit vector returns the modulus of that vector (Ê · E = E).
The second term is a triple-scalar-product, eligible for a cyclic-permutation:

eEτ /m h i
uE cos(ψ) = E + ωτ ( Ê × Ê) · B (30)
1 + (ωτ )2
The vector-product of a vector with itself is zero (Ê × Ê = 0), hence the last term vanishes and some
factors of E can be cancelled:

eEτ /m
u = sec(ψ) (31)
1 + (ωτ )2
Since electrons solely under the influence of an electric-field move in the direction of E and the Lorentz
angle is the angle between u and E – ψ is also the angle between u and vdrift :

u = cos(ψ) vdrift (32)

Finally, substitute for u using (31) and for vdrift using (20):

eEτ /m eEτ
sec(ψ) 2
= cos(ψ) (33)
1 + (ωτ ) m
1
sec(ψ) = cos(ψ) (34)
1 + (ωτ )2

sec2 (ψ) = 1 + (ωτ )2 (35)

1 + tan2 (ψ) = 1 + (ωτ )2 (36)

tan(ψ) = ωτ (37)
This has important practical design consequences. For a typical gas the mean free path is 0.1 µm, and
the argon-methane mix in Figure 4 has a drift velocity peaking at 5.5 cm/µs. This gives τ ≈ 0.55 ps.
With a magnetic-field of 1 Tesla, tan(ψ) = 0.1 or ψ ≈ 6◦ . Drift chambers used with magnetic fields are
often structured to follow the Lorentz angle.

2.4.4 Time projection chambers (TPCs)

A truly tridimentional reconstruction of an event can be made by recording both the radial (r) and
azimuthal (θ) coordinates at which a charged particle enters and leaves a gas filled chamber using a
multi-wire proportional grid arrangement at each end.

If a high-voltage cathode disc is placed at the centre of the chamber an electric-field can be established
between the disc and the end-plates. The electrons that result from ionisation events in the chamber
will drift to the multi-wire end-plates - a typical drift length is around 2 metres. The arrival times of
the electrons at the end-plates determine how far they have travelled and hence the axial (z) coordinate
of the charged particle, thus allowing it to be tracked along its journey through the chamber.

Additionally, a magnetic-field is often applied in the axial direction to minimise the diffusion of the
electrons produced by the ionisation.

Finally, the velocity of the particle can

be found if the two end-plates are used
to trigger a timing device that records
the time taken for the particle to travel
the known length of the chamber. For
this reason such detectors are called time
projection chambers or TPCs.
Figure 5: A time projection chamber. Those wires
receiving hits are shown highlighted.

13
2.4.5 Brief history of improvements to the proportional chamber

Chamber type Drift volume Invented Inventors

Georges Charpak then at CERN was awarded the
Multi-wire
1992 Nobel Prize in Physics “for his invention and
proportional ∼ mm 1968
development of particle detectors, in particular the
chamber
multi-wire proportional chamber”.

Bressani, Charpak, Rahm and Zupancic added a 3cm

Drift chambera ∼ cm 1969 long drift space to a conventional 12 × 12 cm multi-
wire proportional chamber at CERN.

The time projection chamber was invented by David

Time
Nygren at the Lawrence Berkeley Laboratory. Its
projection ∼m 1979
first major application was in the PEP-4 detector,
chamber
which studied 29 GeV e+ e− collisions at SLAC.

a Useful resource at Google Books: Particle Detection with Drift Chambers (W. Blum, W. Riegler & L. Rolandi)

2.5 Detectors working in the Geiger-Müller region

2.5.1 Geiger-Müller tubes
After the proportional region, a further increase in the applied voltage takes the graph into the region
of limited proportionality, as the number of ion pairs begins to flatten out. The final useful region of
applied voltage is the Geiger plateau - this is the region of operation of the Geiger-Müller tube.

Traditional Geiger-Müller tubes have a window at one end, trapping the noble gas 4 , through which
the charged particle may enter. Geiger-Müller tubes are only really used for nuclear work so are largely
concerned with alpha, beta and gamma radiation. The window is made of either:

• Glass-mantle: thicker window, which is cheaper and stronger. However, alpha particles cannot
penetrate the glass, so are not detected.
• Mica: thinner window, which is more expensive and fragile. But alpha radiation may be detected.

Neutron detection is possible using the boron trifluoride gas techniques discussed in conjunction with
ionisation chambers.

For any given detector working in the Geiger-Müller region, all particles have the same Geiger plateau.
Therefore the same number of ions are collected irrespective of the charged particle passing through the
tube. This means the voltage pulse is the same height for all particles, making particle identification im-
possible. Despite this disadvantage Geiger-Müller tubes do produce many more electrons than detectors
working in the proportional region and are thus more sensitive.

As with all detectors working above the ionisation region a quencher gas is necessary because of the
positive ions produced by gas amplification.

2.5.2 Multi-wire chambers (MWCs)

Multi-wire chamber, or often just wire chamber, is the name used to refer to a multi-wire arrangement
operated in the Geiger-Müller region, hence it can be considered an advancement on the Geiger-Müller
tube. However, there is little point in building such a detector and then operating it in the Geiger-
Müller region, when it could be operated at a lower voltage and have all the benefits of the multi-wire
proportional chamber.

4 Helium, neon and argon are all used.

14
2.6 Detectors working in the continuous discharge region: spark chambers
Spark chambers (or streamer chambers) are usually filled with helium or neon. They are gaseous
ionisation chambers, but do not have a continuous supply of electricity. Instead a charged particle
will trigger its own detection by passing through a scintillator at either end of the chamber. When
the coincidence unit receives a signal from both of the scintillators’ neighbouring photomultiplier tubes
(PMTs) it triggers the discharge of many kilovolts onto the plates. Meanwhile the particle has left a trail
of electrons and ions in the spark chamber itself. The now highly charged plates will seek to discharge
themselves via the easiest route - in this case along the trail of electrons just left by the charged particle.
Sparks fly between the plates with a loud crack showing the path the particle took.

Figure 6: A spark chamber.

A more detailed explanation of spark formation is now given. The huge voltage difference across the
plates accelerates the electrons so they are able to cause multiple secondary ionisations; an avalanche
quickly forms. The electrons move to the head of the avalanche, positive ions move to the tail.

When sufficient electron-ion pairs have been created

an electric-field forms within the avalanche itself, ex-
cept this field points in the opposite direction to the
one between the plates.

When the avalanche’s field is strong enough, the elec-

trons and ions recombine, leading to isotropic photon
emission from the site of the avalanche. These pho-
tons cause ionisation in the vacinity of the avalanche -
hence new avalanches rapidly form, merging with the
original and eventually forming a conducting plasma
between the two plates known as a streamer. Fi-
nally a spark travels between the two plates allowing Figure 7: The electric field inside the avalanche
the path the charged particle took to be visualised. points in the opposite direction to the chamber’s
electric field; eventually leading to recombination.

15
3 Solid state detectors
3.1 Silicon semiconductor detectors
3.1.1 Principle of operation
Most modern particle detectors use silicon detectors as their central tracking detector - the position
resolution possible far exceeds that which is possible in gaseous ionisation chambers:
• An individual detector module comprises silicon that has been doped to form a diode.
• When the module is reverse-biased, a depletion region is set up with an electric-field that sweeps
charge-carriers to the electrodes.
• When a charged particle passes across the silicon strip it will liberate electrons from their atoms
creating electron-hole pairs. This is analogous to a charged particle creating electron-ion pairs
when traversing a gas.
• The electric-field in the depletion region sweeps the new electron-hole pairs to the electrodes where
they are collected and that particular module records a ‘hit’.
• In contrast to gaseous detectors, silicon detectors do not track the charged particle through the
entire body of silicon - instead individual, isolated mm sized strips or µm sized pixels record
hits.
• Those modules that record hits trace out the path followed by the charged particle. The smaller
the modules, the better the spatial resolution: around 5 µm for a 300 µm thick module.
The time taken for collection decreases as the bias voltage is increased. Increasing the voltage beyond
that necessary for complete collection - over-biasing - reduces the collection time further. In a silicon
detector 300 µm thick, electrons are collected in about 10 ns and holes in about 25 ns.

Figure 8: Left: schematic diagram of a silicon detector; Right: an array of silicon detector pixels - those
which detected hits are shown highlighted and trace out the particle’s trajectory..

In constrast to gasesous ionisation detectors, the active material in solid-state detectors is much denser,
therefore every effort is made to make the silicon as thin as possible - otherwise any improvement in
resolution gained by using silicon, is negated by the effects of increased multiple scattering.

Hence the increased spatial resolution possible with silicon detectors (compared to gaseous ionisation
detectors) comes at an increased cost.

16
3.1.2 Energy resolution
If the band-gap energy required to promote an electron into the conduction band and create an electron-
hole pair is Egap , the number of electron-hole pairs produced by a particle despositing energy E is:
E
N= (38)
Egap
Assuming a Poisson distribution for the number of electron-hole pairs, the fractional variance of N is:
√
σN N
= (39)
N N
The actual variance is affected by both electronic and lattice excitations. This is accounted for by the
Fano factor, F (FSi ≈ 0.1):
√ r
σN FN F
= = (40)
N N N
This can be used to find the energy resolution by substituting from (38):
r
σE F Egap
= (41)
E E
In actual fact, since silicon is an indirect semiconductor5 , Egap should also include phonon excitation to
provide the necessary momentum change. Taking this into account, at room temperature Egap = 3.67
eV. Therefore a 1 MeV charged particle will produce about 272,000 electrons. This gives σE /E = 0.06%.

However, the energy resolution is dominated by electrical noise and energy loss fluctuations in the
detector, hence the need for expensive cooling and low-noise electronics.

3.1.3 Radiation degradation

There are two ways that radiation can degrade individual modules or clusters of modules:

Damage Cause of damage and effect on module Critical factors

Displacement damage results from atoms being displaced
from their lattice sites, leading to current leakage, free-
Displacement Particle type + energy
carriers becoming trapped and a build-up of space charge
(changing the required operating voltage).

Surface damage results from charge building up in surface

Surface layers, leading to surface current leakage meaning separate Radiation dose
strips or pixels are no-longer isolated.

3.2 Scintillators
3.2.1 Principle of operation
A charged particle passing through matter will create electron-ion pairs in a gas and electron-hole pairs
in a semiconductor. In more complex substances however, the energy is manifest in excited molecules.
Those substances in which the molecules de-excite by emiting a photon are known as scintillators.

If a photon excites the molecules of a substance, which then de-excite by emitting a lower energy photon,
the substance is said to fluoresce. Absorption and emission occur over a wide range of photon energies,
which can overlap, leading to unwanted self-absorption. The greater the difference between the main
absorption and main emission energies (the Stokes’ shift), the less the amount of self-absorption.

5 The maxima of the valence band does not have the same k-space momentum as the minima of the conduction band

17
The organic substances used in detectors comprise a mixture of both scintillators and fluors. This is
because typical scintillators emit ultraviolet light which is rapidly attenuated by the scintillator itself
before it can ever be detected. The fluor acts as a wavelength-shifter: absorbing the ultraviolet light
and re-radiating it as blue light (a wavelength at which the scintillator is more transparent). Sometimes
secondary or even tertiary fluors are added to step-down the wavelength in stages.

If the fluor is added in high concentration the distance between the scintillator and the fluor is shorter
than the wavelength of light. In these cases the energy transfer from scintillator to fluor occurs by
dipole-dipole interactions, which are faster than absorption and emission, thus reducing the decay time
by an order of magnitude.

3.2.2 Organic versus inorganic scintillators

The two main classes of scintillator are compared below:

Scintillator Composition Density Examples Notes

Nearly all organic scintilla-
Carbon-based 1.03 – 1.20 Polystyrene
Organic tors are plastic since it is
(often with benzene) g cm−3 polyvinyltoluene
cheap and easily moulded.

Higher density makes these

Non-carbon-based 4–8 Sodium iodide
Inorganic useful for total absorption
crystals g cm−3 Barium fluoride
EM calorimeters (see § 4.2).

3.2.3 Organic scintillator photon yields and luminescence

On average one photon is emitted for every 100 eV of energy deposited in the scintillator. Therefore, a
particle depositing 1 MeV will produce 10,000 photons. This gives σE /E = 1%.

The luminescence of a scintillator, L, is given by Birk’s Law:

 
dL dE/dx
= L0 (42)
dx 1 + kB (dE/dx)
Here, L0 is the luminescence at low specific ionization density and kB is the Birks constant for that
particular scintillator.

3.3 Čerenkov detectors

3.3.1 Particle identification
By using a carefully chosen medium with the correct refractive index, particles can be distinguished by
whether or not they emit Čerenkov radiation. The refractive index of a gas can be adjusted accordingly
by varying the pressure.

There is a threshold velocity, and hence a threshold momentum below which particles do not radiate.
This threshold is different for different particles. This is the principle of the threshold Čerenkov
detector:
mβc
p = γmv = p (43)
1 − β2
Using the condition for Čerenkov radiation, β = 1/n, gives:

mc/n
pthreshold = √ (44)
1 − n−2

18
In an air filled detector (nair = 1.0003) the threshold for pions is 5 GeV/c, but the threshold for kaons
is 20 GeV/c. Therefore in the range 5 – 20 GeV/c pions radiate but kaons do not, allowing them to be
distinguished. Below 5 GeV/c neither pions nor kaons radiate, and above 20 GeV/c they both radiate.
The detector is therefore only useful in the range 5 – 20 GeV/c.

Modern Čerenkov detectors have 4π coverage of the radiating material with photomultiplier tubes. These
detectors produce rings where the light-cone intersects the PMT-lined wall of the chamber and are known
as Ring Imagining Čerenkov detectors (RICH), see Section 7.3.

3.3.2 Calorimetry
Čerenkov detectors can be used as calorimeters because the amount of light produced is proportional to
the total energy of the incident particle, E0 :
Z track length  
Number of emitting
(Amount of light) ∝ dL (45)
0 particles at distance L
The number of particles after N radiation lengths is 2N . Convert the integral over dL to an integral over
dN using the fact that the track length is the number of radiation lengths (L = X0 N → dL = X0 dN ).
The integral’s upper limit is now the number of radiation lengths at which the shower stops, NC :

Z NC
(Amount of light) ∝ 2N X0 dN (46)
0
NC
2N

(Amount of light) ∝ X0 (47)
ln 2 0

X0  NC 
(Amount of light) ∝ 2 −1 (48)
ln 2
The critical value of N , namely NC , can be converted into a critical energy. The initial energy E0 is
shared between however many particles there are after N radiation lengths:
E0 E0
EN = → EC = (49)
2N 2NC
This means equation (48) can be re-written as:
 
X0 E0
(Amount of light) ∝ −1 (50)
ln 2 EC
Finally, since E0  EC :

(Amount of light) ∝ E0 (51)

 
Energy of
(Amount of light) ∝ (52)
incident particle

19
4 Calorimeters
4.1 Electromagnetic versus hadronic calorimeters
Calorimeters use partial or total absorption of particles and their showers to measure their energy.
Calorimeters are typically composed of small cells aligned along the direction of the incident particle,
stacked up in towers. The alignment of these towers usually varies around the detector in order to
maximise the probability of encompassing the shower at a given angle.

Electrons, photons, and indeed π 0 mesons, which decay into photons, all produce electromagnetic show-
ers. These showers are relatively compact and have a short shower-depth, therefore they are readily con-
tained in a short distance by electromagnetic calorimeters. The size of an electromagnetic shower,
and hence an electromagnetic calorimeter, is governed by the radiation length, X0 .

Hadronic showers are generally much larger and their shape fluctuates hugely from one event to another,
hence hadronic calorimeters are larger than their electromagnetic counterparts. Indeed, the response
is lower and the resolution is worse for hadrons in a hadronic calorimeter compared to electrons of the
same energy in an electromagnetic calorimeter.

Most hermetic detectors use a calorimetry system that comprises both types of calorimeter. In such a
composite calorimeter the electromagnetic calorimeter is always the first layer the particles encounter
because whilst the heavy hadrons can pass through to the hadronic calorimeter beyond, electrons and
photons would never reach their designated calorimeter if the hadronic calorimeter came first.

Although hadrons might start showering in the electromagnetic calorimeter, they can only be fully con-
tained by the hadronic calorimeter. This is where all but the tiny fraction of energy hadrons lost in the
electromagnetic calorimeter, is deposited.

In light of the above, the absorber material in an electromagnetic calorimeter should ideally maximise
the hadronic interaction length (so as many hadrons can pass through with minimal interaction as
possible) and minimise the radiation length (so the electromagnetic shower is fully developed within the
electromagnetic calorimeter). The ratio λ/X0 approximately satisfies: λ/X0 ∝ Z 1.3 . Maximising this
ratio means using high-Z materials like tungsten (Z = 74), lead (Z = 82) or uranium (Z = 92).

4.2 Homogeneous versus heterogeneous calorimeters

There are two parts to any calorimeter:
• Active signal generators: the active material that measures the shower energy.
• Passive particle absorbers: the material that causes the particles to shower.
Calorimeters can incorporate these two aspects in two different ways, contrasted below:

Hetrogeneous or sampling calorimeters Homogeneous calorimeters

The active layers are interleaved with passive ab- The roles of the active mate-
Design sorbers. However, it is only the small fraction of energy rial and the passive absorber
deposited in the active layers that is measured. are combined.

The length and width of hadronic showers means The materials suitable for both
Particles hadronic calorimeters have to be of the sampling type, these roles can only be used in
but electromagnetic calorimeters can also be sampling. electromagnetic calorimeters.

Solid or liquid scintillating material or some form of

Active Crystals like NaI, Bi4 Ge3 O12
gaseous proportional counter.
(‘BGO’) and CsI or composite
materials such as lead-glass.
Passive Sheets of high-Z materials such as lead or uranium.

20
4.3 Energy resolution
The accuracy with which a calorimeter reports the energy of a particle is usually expressed as a fraction
of the particle’s energy, E, and comprises four separate contributions added in quadrature:

σ σ σ σ σ

= ⊕ ⊕ ⊕ (53)
E total E statistical E instrumental E systematic E sampling

The term energy resolution applies to the constant σ.

Contribution Scales as Origin of errors and their scaling Energy range

Statistical ∝ √1 Showers are inherently statistical processes, This contribution is the

E
thus the energy deposited varies according
√ most significant and domi-
a Poisson distribution: σ/E = N /N =
to √ nates over most of the use-
1/ N . Since the energy deposited is pro- ful range of calorimeters.
portional to the number of hits √ (N ∝ E),
this can be written as σ/E ∝ 1/ E.

1
Instrumental ∝ E The effect of noise and stray capacitance is This contribution tends to
largely energy independent, hence the rela- dominate at low energies.
tive contribution (σ/E) scales as 1/E.

Systematic constant Systematic errors include calibration er- This contribution usually
rors and non-uniformity of the calorime- sets the limit for perfor-
ter. Non-uniformity at high energies can mance at high energies.
limit accuracy to no-better than 2%. Usu-
ally, some average fraction of the energy
leaks out of the calorimeter as it fails to
completely contain the shower. These scale
with energy, hence the relative contribution
is energy independent.
q
∆E
Sampling ∝ E In sampling calorimeters the sampling fluc- This is only of significance
tuations have to be added, with ∆E the in sampling calorimeters.
energy loss of one particle in one layer.

4.3.1 Electromagnetic calorimeters

In electromagnetic calorimeters the statistical errors result from variations in the track length of the
charged particles:
 σ electromagnetic 0.5%
≈ √ (54)
E statistical E
Some electromagnetic calorimeters are sampling calorimeters, for these the sampling fluctuations are
given by:

 σ electromagnetic r
1000∆E
≈ 4% (55)
E sampling E
√
Total energy resolution below σ/ E = 1% is easily achieved in homogeneous electromagnetic calorime-
ters. Such results are more difficult to achieve in an electromagnetic sampling calorimeter.

21
4.3.2 Hadronic calorimeters
In hadronic calorimeters the statistical errors result from fluctuations in energy deposition due to energy
loss through non-hadronic mechanisms such as photons and leptons from pion decay and slow neutrons.
These fluctuations that arise in hadronic calorimeters are much larger than the main statistical errors in
electromagnetic calorimeters:
 σ hadronic 45%
≈ √ (56)
E statistical E
Compensating calorimeters are hadronic calorimeters with enhancements such as adjusted absorber
layer and active layer widths and U-238 absorbers for slow neutron capture. These calorimeters reduce
the statistical errors by around 20%:
 σ compensating 25%
≈ √ (57)
E statistical E
All hadronic calorimeters are sampling, but the contribution to the total energy resolution due to sam-
pling effects is small compared to the statistical errors:

 σ hadronic r
1000∆E
≈ 9% (58)
E sampling E

4.4 Typical energy resolutions for some calorimeters

Typical values of energy resolutions for various electromagnetic calorimeters are given below: 6

Electromagnetic detector Experiment Energy resolution

√
Lead glass OPAL 5%/ E
√
Liquid krypton NA48 3.2%/ E ⊕ 0.42% ⊕ 0.09/E
√
Liquid argon and lead NA31 7.5%/ E ⊕ 0.50% ⊕ 0.10/E
√
Liquid argon and lead ATLAS 10%/ E ⊕ 0.40% ⊕ 0.30/E
√
Depleted uranium scintillator ZEUS 18%/ E

Typical values of energy resolutions for various hadronic calorimeters are given below: 7

Absorber and thickness Plastic scintillator Experiment Energy resolution

√
6 mm uranium and 5 mm copper 2.5 mm AFS 35%/ E
√
80 mm marble 30 mm CHARM 45%/ E
√
25 mm iron 5 mm CDHS 58%/ E
√
50 mm iron 10 mm UA-1 80%/ E
√
15 mm iron 5 mm UA-2 60%/ E

6 Source: Table 28.9 of Particle Data Group 2008.

7 Source: Table 11.3 of Introduction to Experimental Particle Physics (R. Fernow).

22
5 Hermetic detectors
5.1 Introduction
The modern particle detectors in use today in accelerators such as the Large Electron Positron collider at
CERN8 or HERA9 at DESY10 are hermetic detectors. These are detectors designed to cover as much
of the solid angle around the interaction point (IP) as possible – to hermetically encompass it. This is
nearly always accomplished with a cylindrical barrel around the beam-pipe along which the accelerated
particles travel with end-caps sealing in both ends of the barrel. The accelerators and detectors are
often situated underground in order to provide the maximal shielding possible from natural radiation
such as cosmic rays that would otherwise mask the events taking place inside the detector.

5.2 Layout and purpose of layers

Hermetic detectors combine many of the detectors discussed so far, such as the drift chambers, Čerenkov
detectors, electromagnetic calorimeters and hadronic calorimeters. These are built up in concentric
layers, with each layer designed to measure a specific aspect of the jets of particles produced after the
collision at the interaction point. Starting with the innermost layer the successive layers in a hermetic
detector are:
• Central tracking detector (CTD): this is designed to track all the charged
particles and allow for complete event reconstruction.

• Large magnet: this produces a magnetic field strong enough to curve the tracks of
charged particles in the tracking detector, allowing their momentum to calculated.
• Electromagnetic calorimeter (ECAL): this measures the shower energy of elec-
trons and photons.

• Hadronic calorimeter (HCAL): this measures the hadronic shower energy.

• Muon tracking chamber: any particle registering on these tracking detectors
(often drift chambers) has necessarily travelled through all the other layers and can
only be a muon.

Figure 9: ATLAS (A Toroidal LHC ApparatuS) detector at CERN, a transverse slice is shown above.
8 French:
Conseil Europeen pour la Recherche Nucleaire (European Council for Nuclear Research)
9 German:
Hadron-Elektron-RingAnlage (Hadron-Electron Ring Accelerator)
10 German: Deutsches Elektronen Synchrotron (German Electron Synchrotron)

23
5.3 Propagation of particles through the layers
Particles can be identified by their energy loss, curvature in magnetic fields and Čerenkov radiation.
However, the identity of a particle can be significantly narrowed down by simply examining which parts
of the detector it deposits energy in:

• Photons (γ): Neutral photons leave no tracks in the CTD but produce an electromagnetic shower
in the ECAL.
• Electrons and positrons (e− , e+ ): Charged electrons and positrons leave tracks in the CTD
and produce a shower in the ECAL.
• Muons (µ− , µ+ ): Muons leave tracks in all the detectors - they are the only particles to reach
the muon chambers.

• Charged hadrons (p, π ± , K ± ): Charged hadrons leave tracks in all the detectors up to the
HCAL where they shower and deposit all their energy.
• Neutral hadrons (n, KL0 ): Neutral hadrons leave no tracks in any of the detectors and then they
shower in the HCAL. KS0 mesons are not listed here because they decay before ever reaching the
hadronic calorimeter.

A full description of the signature characteristic of all types of particle can be found in Section 7.1. For
now, the above facts are summarised in the diagram below:

Figure 10: Overview of the signatures left in a hermetic detector by detectable particles.

24
6 Case studies
6.1 Drift chamber – barrel muon chambers at DELPHI

Figure 11: Diagram of a single sector showing the relative positions of the three layers in the barrel.

Overview of the barrel muon sector:

Dates: Construction: 1983 – 1988

Operation: 1989 – 2000

Drift chambers: 1372 chambers arranged

into 24 sectors. Each
sector contains an inner,
outer and peripheral layer.

Details of the individual drift chambers:

Active volume: 363 × 20 × 1.6 cm3

Gas mixture: argon (84.6%)

methane (8.9%)
carbon dioxide (6.5%)

Field-strength: 400 V cm−1 Figure 12: The DELPHI detector. Some of the
muon chamber detectors are visible. These are the
Drift velocity: 46 µm ns−1 long, flat, pieces of aluminium outside the hadron
calorimeter.
Spatial σrφ = 1 mm (drift time)
resolution: σz = 10 mm (delay line)

25
6.2 Drift chamber with magnetic field – central tracking chamber at ZEUS

Figure 13: Diagram of the two types of superlayer within ZEUS’ central tracking chamber.

Overview of the central tracking detector:

Dates: Operation: 1992 – 2007

Drift chambers: 576 drift cells arranged into 9

‘superlayers’. Each drift cell has
8 sense wires and 34 field wires,
giving a total of 4608 sense wires
and 19,584 field wires.

5 axial Wires in these superlayers are

superlayers: parallel to the chamber axis.

4 stereo Wires in these superlayers are

superlayers: tilted by a small angle (5◦ or 6◦ )
with respect to the beam and
can thus provide information on
the z-coordinate of the hits.

Active volume: Length: 241 cm, inner radius:

16.2 cm, outer radius: 85 cm Figure 14: Installation of the central tracking
detector at the heart of the ZEUS detector.
Hermiticity: Angles covered: 15◦ < θ < 164◦

Gas mixture: argon (90%)

carbon dioxide (8%)
ethane (2%)

Drift velocity: 50 µm ns−1

Magnetic-field: 1.8 Tesla ⇒ Lorentz ψ ≈ 45◦

Spatial σrφ (θ) = 0.1 − 0.2 mm

resolution: σz = 2 mm
σp
Momomentum p = 0.005p ⊕ 0.007 ⊕ 0.001
p Figure 15: A view inside the chamber after the
resolution: for p measured in GeV.
first of the superlayers had been ‘strung’.

26
6.3 Sampling calorimeter – uranium-scintillator calorimeter at ZEUS

Overview of the uranium-scintillator calorimeter:

Dates: Operation: 1992 – 2007

Active material: 2.6 mm of plastic scintil-

lator (SCSN38).

Passive material: 3.0 mm of uranium ab-

sorber (98.1% 238 U).

Chambers: The UCAL comprises

three main sections, di-
vided into a total of 80
modules, further divided
into towers - see the table
below.

Hermiticity: 99.7%

σE 18%
Electromagnetic E = √
E
⊕ 1%
energy resolution:

σE 35%
Hadronic E = √
E
⊕ 2%
energy resolution:
σtiming 1.5
Time resolution: E =√ E
⊕ 0.5 ns
for E measured in GeV.
Figure 16: A ZEUS FCAL module.

Figure 17: Wavelength shifter installation of a Figure 18: The ZEUS barrel calorimeter after
central calorimeter module. dismantling had started.

Overview of the three main sections of the calorimeter. Remember, λ is the absorption length:

Section Name Dimensions Depth in terms of λ Angles covered

Forward end-cap FCAL + 234.4 cm from IP 7.1 λ 2.2◦ < θ < 36.7◦
Barrel BCAL Inner radius 134.5 cm 5.1 λ 36.7◦ < θ < 129.1◦
Rear end-cap RCAL – 160.2 cm from IP 4.0 λ 129.1◦ < θ < 176.2◦

27
6.4 Hermetic detector – Compact Muon Solenoid (CMS)

Figure 19: The arrangement of the CMS. In the middle, under the so-called barrel there is a man for
scale. (HCAL = hadron calorimeter, ECAL = electromagnetic calorimeter)

Figure 20: A slice of the CMS showing how e± , µ± , hadrons, neutrons and photons traverse the detector.

Overview of the Compact Muon Solenoid:

Construction dates: 1998 – 2008

Overall length: 21.5 m

Overall diameter: 15.0 m

Total weight: 12,500 tons

Magnetic field: 4 Tesla

Figure 21: The Compact Muon Solenoid.

28
6.5 Ring imaging Čerenkov detector – Super-Kamiokande

Figure 22: View of the Super-Kamiokande detector in the Mozumi Mine in Hida’s Kamioka area.

Overview of the Super-Kamiokande detector:

Overall dimensions: height: 41.4 m, diameter: 39.3 m

Inner detector: height: 36.2 m, diameter: 33.8 m

11,146 PMTs (diameter: 50.8 cm)

Outer detector: that volume which remains

1,885 PMTs (diameter: 20.3 cm)

Depth: 1000 m underground

Ultra-pure water: 50,000 tons

Energy resolution: σE = 2.5% (for particles at 1 GeV)

σE = 16% (for particles at 10 MeV)

The detector has undergone numerous alterations:

1983 Kamioka NDE An attempt to observe proton decay.

1985 Kamioka NDE-II Upgraded to observe solar neutrinos.

Figure 23: Super-Kamiokande
1996 Super-K Observed neutrino oscillations.
construction: checking photo-
multiplier tubes (1993 – 1996).
2001 Super-K-II PMTs repositioned after 6600 imploded.

2006 Super-K-III About 6000 PMTs were restored.

29
7 Particle identification
7.1 Characteristics of particle events in hermetic detectors
The table below outlines the tracks and shower types expected for a variety of different particle events:

Particles Signature of event Tracks Showers

Neutral photons leave no track in tracking chambers: there
γ — Small EM
will be a small shower without a matched track.

Electrons and positrons leave a track in tracking chambers

e− and e+ P Small EM
that matches a small electromagnetic calorimeter shower.

These heavier charged particles make it through all the

other detectors, leaving minimum ionising signals pointing
µ− and µ+ P+µ —
at the interaction point, eventually stopping at the muon
chambers where they deposit their energy.

Neutrinos are the only particles to leave no evidence of

their passage through a hermetic detector. Their existence
must be inferred by looking for ‘missing momentum’: con-
servation of momentum requires that the momentum of the
νe , νµ and ντ — —
initial colliding beams equals the total momentum of the
particles produced, hence the momentum unaccounted for
when the momenta of all the visible particles is added up
must be the momentum of the neutrino.

These light neutral particles will leave no track in tracking

π 0 and η chambers: there will be a small calorimeter shower without — Small hadronic
a matched track.

These heavier neutral particles again leave no track them-

selves, but soon decay into pair of oppositely charged par-
ticles: K 0 → π + π − and Λ0 → p π − . This results in a pair
KS0 and Λ0 of diverging tracks that begin a distance away from the in- S Particle decayed
teraction point equal to the path travelled by the neutral
particle: a secondary, or displaced vertex is observed. Dis-
placement of ∼ cm is tracked with proportional chambers.

Much heavier charged particles deposit very little energy

Hadronic jets in the tracking chambers, most of their energy is lost in — Large hadronic
large hadronic calorimeter showers.

b-tagging: obviously b quarks are not produced as free par-

ticles, they are bound in B-mesons, which have a suffi-
ciently long lifetime that they are able to travel some dis-
tance before decaying within the detector, hence the decay
b + c quarks jet is displaced from the interaction point. The b quark S Wide hadronic
is much heavier than anything it decays into, thus the de-
cay products tend to have higher transverse momentum -
making the decay jets wider than usual hadronic showers.
Displacement of ∼ mm is tracked with silicon detectors.

In the ‘Tracks’ column the abbreviations used are: P for Primary vertices in the central tracking chamber,
S for Secondary vertices in the central tracking chamber and µ for vertices in the muon chamber.

30
7.2 Identifying particles from the DELPHI detector at CERN’s LEP collider
The images below are real events from the DEtector with Lepton, Photon and Hadron Identification
(DELPHI) at the Large Electron Positron (LEP) collider at CERN. 11

7.2.1 e− e+ → e− e+

TD TE TS TK TV ST PA
DELPHI Interactive Analysis Act
1 20 0 2 0 0 0
Beam: 45.6 GeV Run: 39265 DAS : 5-Jul-1993 ( 41) ( 22) ( 0) ( 3) ( 0) ( 0) ( 0)
14:21:08 0 0 0 0 0 0 0
Proc: 4-May-1994 Evt: 4754 Scan: 2-Jun-1994 Deact
( 0) ( 2) ( 0) ( 4) ( 0) ( 0) ( 0)

Z
X

Figure 24: e− e+ → e− e+

Detector Observation
Central vertex detectors Two tracks back to back

Electromagnetic calorimeters Hits that match the tracks

11 Source: http://delphiwww.cern.ch/delfigs/events/z0ps/z0maxen.html

31
7.2.2 e− e+ → µ− µ+

TD TE TS TK TV ST PA
DELPHI Interactive Analysis Act
26 29 0 2 0 0 0
Beam: 45.6 GeV Run: 26154 DAS : 25-Aug-1991 ( 28) ( 29) ( 0) ( 2) ( 3) ( 0) ( 0)
21:36:22 0 0 0 0 0 0 0
Proc: 1-Oct-1991 Evt: 1417 Scan: 19-Feb-1992 Deact
( 0) ( 2) ( 0) ( 2) ( 0) ( 0) ( 0)

Z
X

Figure 25: e− e+ → µ− µ+

Detector Observation
Central vertex detectors Two tracks back to back

Electromagnetic calorimeters Nothing

Hadronic calorimeters Minimum ionising hits

Muon chambers Hits that match the tracks

32
7.2.3 e− e+ → 2 jets

TD TE TS TK TV ST PA
DELPHI Interactive Analysis Act
14 72 0 17 0 0 0
Beam: 45.6 GeV Run: 26154 DAS : 25-Aug-1991 ( 93) (133) ( 0) ( 23) ( 18) ( 0) ( 0)
21:47:02 0 0 0 0 0 0 0
Proc: 1-Oct-1991 Evt: 3018 Scan: 19-Feb-1992 Deact
( 0) ( 13) ( 0) ( 23) ( 12) ( 0) ( 0)

Z
X

Figure 26: e− e+ → 2 jets

Detector Observation
Central vertex detectors Two narrow jets in opposite directions

Electromagnetic calorimeters Hits that match the tracks

Hadronic calorimeters Considerable amount of energy deposited

33
7.2.4 e− e+ → 3 or 4 jets

TD TE TS TK TV ST PA
DELPHI Interactive Analysis Act
1 207 0 26 0 0 0
Beam: 45.6 GeV Run: 26154 DAS : 25-Aug-1991 (158) (207) ( 0) ( 40) ( 0) ( 0) ( 0)
21:37:20 0 0 0 0 0 0 0
Proc: 1-Oct-1991 Evt: 1580 Scan: 27-May-1994 Deact
( 0) ( 6) ( 0) ( 27) ( 0) ( 0) ( 0)

Z
X

Figure 27: e− e+ → 3 or 4 jets

Detector Observation
Central vertex detectors A total of 21 different particles seen

Electromagnetic calorimeters Hits that match the tracks

Hadronic calorimeters Considerable amount of energy deposited

34
7.2.5 e− e+ → ΛΛ̄

+
+ ++ +
+
+

+ +++
+
++ +

+ +
++++ +

+ +
+
O + +
+
+
+

+
+ +
+
+

Figure 28: e− e+ → Λ Λ̄

In this event there is a high momentum Λ Λ̄ pair with a small rapidity difference. The lambdas are shown
as dashed lines, the outgoing pions as red solid lines and the protons as blue ones. Although there were
no track elements reconstructed in the inner detector (intermediate precision tracking) for the Λ that
decayed within it (at a radius of 17.9 cm), the vertex has been reconstructed.

The tracks belonging to the other Λ decaying at a radius of 4.4 cm have three associated vertex detector
hits.

Three other tracks which are very close to the two lambdas have been erased to make the lambda vertices
easier to see.

35
7.3 Identifying particles from Super-Kamiokande events
The colours in the images 12 below represent the time of arrival of light to individual photomultiplier
tubes (PMTs). Short wavelengths (violet and blue) correspond to early arrival times and long wave-
lengths (orange and red) to late arrival times. A window on the time of light of 30 ns has been applied
to eliminate noise and scattered reflected light. The histogram on the right shows the time charge dis-
tribution before the applying the window on the time of flight. The size of a given square representing
a PMT corresponds to the amount of observed light. There is a maximum size such that squares are
always smaller than the distance between PMTs.
7.3.1 Electron events
The fuzzy ring with all signals received at
roughly the same time (the ring is more or less
all the same green colour) is an electron event.

Since σscatter ∝ 1/m, electrons scatter more

than muons. So the incident electron produces a
shower of photons, electrons and positrons, when
it hits the target.

Whilst the photons dont emit any Čerenkov

radiation the electrons and positrons all create
smaller circles of Čerenkov radiation at an
approximately fixed distance from where the
electron hit the target.

This gives rise to the fuzzy ring, made up of lots

of smaller Čerenkov rings. Since all the electrons
and positrons produced started from the same
point with roughly the same energy, the PMT
signals all occur at the same time; hence the ring Figure 29: An electron event at Super-K.
is a homogeneous green colour.

7.3.2 Muon events

The sharply defined ring with signals occur-
ring at differing times from top left to bottom
right is a muon event.

The ring is sharply defined compared to the

ring from the electron event due to the reduced
scattering since σscatter ∝ 1/m and mµ  me .

The muon in this image is not quite travelling

along the line of sight instead it is moving from
the top left, where the blue points (early times)
are to the bottom right where the red points
(late times) are.

Figure 30: A muon event at Super-K.

12 Source: http://www.ps.uci.edu/~tomba/sk/tscan/compare_mu_e/

36
7.3.3 Muon decay to electron event
The mean lifetime of a muon is around 2 µs.
Since PMTs can record on the nanosecond scale,
muons could be observed to decay into electrons
and neutrinos according to: µ → e− + ν̄e + νµ .

So if there is an electron event around 2 µs later,

it was probably caused by muon decay.

The image to the right shows a muon event,

as the sharp blue ring in the top left. Then at
a later time a fuzzy green ring appears in the
bottom right signifying an electron event.

Figure 31: A muon decay event at Super-K.

7.4 Identifying particles from the spark chamber at CERN’s SPS

Figure 32: A proton-antiproton interaction at 540 GeV observed using a spark chamber at CERN’s Super
Proton Synchrotron (SPS) facility in 1982. The identity of the particles produced is anyone’s guess.

37
References
Gaseous ionisation detectors
Data sources: D. Green, The Physics of Particle Detectors (Cambridge University Press, 2000)

W. Blum, W. Riegler & L. Rolandi, Particle Detection with Drift Chambers (Springer-Verlag, 2008)

http://ikpe1101.ikp.kfa-juelich.de/briefbook_part_detectors/PH14pp.html

Spark chambers
Data source: http://www.ep.ph.bham.ac.uk/general/outreach/SparkChamber/text4h.html

Hermetic detectors
Data source: http://www.lancs.ac.uk/users/spc/teaching/py364/introduction.html

Diagram source: http://visits.web.cern.ch/visits/guides/tools/manual/english/Atlas.html

Drift chamber – barrel muon chambers at DELPHI

Data source: http://hepunx.rl.ac.uk/~adye/thesis/html/node14.html
http://delphiwww.cern.ch/delphi$specific/cp/monitor/presenter/help_files/mub_descrip.html

Photo source: http://hands-on-cern.physto.se/hoc_v21en/page_pict/de_muon1.html

Drift chamber with magnetic field – central tracking chamber at ZEUS

Data sources: http://www.pd.infn.it/~longhin/tesidott/html/node30.html
http://www-zeus.desy.de/public/zeus.php3

Photo source: http://www.hep.ucl.ac.uk/~tjf/zctdinst.html

Sampling calorimeter – uranium-scintillator calorimeter at ZEUS

Data sources: http://www.pd.infn.it/~longhin/tesidott/html/node32.html
http://www-zeus.desy.de/public/cal.php3

Photo sources: http://www-zeus.desy.de/img/wls_inst.gif

http://en.wikipedia.org/wiki/File:Zeus_calorimeter.JPG

Hermetic detector – Compact Muon Solenoid (CMS)

Data source: http://en.wikipedia.org/wiki/Compact_Muon_Solenoid

Diagram sources: http://en.wikipedia.org/wiki/File:CMScollaborationPoster.png

http://en.wikipedia.org/wiki/File:CMS_Slice.gif

Photo source: http://www.nytimes.com/2007/05/15/science/15cern.html

Ring imaging Čerenkov detector – Super-Kamiokande

Data source: http://en.wikipedia.org/wiki/Super-Kamiokande

Diagram source: http://atropos.as.arizona.edu/aiz/teaching/a204/lecture11.html

Photo source: http://www-sk.icrr.u-tokyo.ac.jp/sk/gallery/index-e.html

38