1. Particle Conservation Laws

What Is a Conservation Law?

When particles interact, decay, or transform, some properties may change. A neutron can become a proton, particles can be created, and matter and antimatter can annihilate.

However, certain physical quantities must remain balanced.

These rules are called conservation laws.

For the particle reactions in this topic, three especially useful quantities are:

• electric charge
• baryon number
• lepton number

A proposed reaction is allowed only if the relevant conservation laws are satisfied, along with other requirements such as conservation of energy and momentum.

A useful way to think about it is:

Total before reaction = Total after reaction

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Conservation of Electric Charge

Electric charge is conserved in every known physical interaction.

This means:

Total charge before = Total charge after

Particles can exchange charge or transform into different particles, but the total electric charge of an isolated system cannot change.

---

Common Particle Charges

Quarks have fractional charges:

Antiquarks have the opposite electric charge of their corresponding quarks.

---

Example 1: Checking Charge

Consider beta-minus decay:

n → p + e⁻ + ν̄ₑ

Check the charge.

Before

Neutron:

Q = 0

After

Proton:

+1

Electron:

−1

Antineutrino:

0

Total:

+1 − 1 + 0 = 0

Therefore:

0 = 0

Charge is conserved.

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Conservation of Baryon Number

Particles called baryons are assigned a quantity called baryon number.

Ordinary baryons have:

B = +1

Antibaryons have:

B = −1

Particles that are not baryons have:

B = 0

For the processes considered here:

Total baryon number before = Total baryon number after

---

Common Baryon Numbers

Protons and neutrons are both baryons because they are made from three valence quarks.

Electrons and neutrinos are leptons, not baryons.

Photons are bosons.

---

Baryon Number and Quarks

At a deeper level, each quark is assigned:

B = +⅓

Each antiquark has:

B = −⅓

A proton contains:

uud

Therefore:

B = ⅓ + ⅓ + ⅓

B = +1

A neutron contains:

udd

Again:

B = ⅓ + ⅓ + ⅓

B = +1

A meson contains a quark and an antiquark:

B = +⅓ − ⅓ = 0

This is why mesons are hadrons but are not baryons.

---

Example 2: Checking Baryon Number

Consider again:

n → p + e⁻ + ν̄ₑ

Before:

B = +1

After:

Proton:

B = +1

Electron:

B = 0

Antineutrino:

B = 0

Therefore:

+1 = +1

Baryon number is conserved.

---

Conservation of Lepton Number

Leptons are assigned a lepton number.

Ordinary leptons have:

L = +1

Antileptons have:

L = −1

Non-leptons have:

L = 0

Therefore:

Total lepton number before = Total lepton number after

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Common Lepton Numbers

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Why Is the Antineutrino Needed?

Consider an incomplete version of beta-minus decay:

n → p + e⁻

Check lepton number.

Before:

L = 0

After:

Electron:

L = +1

Therefore:

0 ≠ +1

Lepton number would not be conserved.

The complete reaction includes an electron antineutrino:

n → p + e⁻ + ν̄ₑ

Now:

L = 0 + (+1) + (−1)

L = 0

So lepton number is conserved.

The neutrino or antineutrino is therefore essential when writing many weak-interaction reactions.

---

Three Checks for a Particle Reaction

For introductory particle reactions, we can perform three quick checks:

1. Charge

Qbefore = Qafter

2. Baryon number

Bbefore = Bafter

3. Lepton number

Lbefore = Lafter

A convenient table is:

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Example 3: Beta-Minus Decay

Consider:

n → p + e⁻ + ν̄ₑ

Charge

Before:

0

After:

+1 − 1 + 0 = 0

Conserved.

Baryon number

Before:

+1

After:

+1 + 0 + 0 = +1

Conserved.

Lepton number

Before:

0

After:

0 + 1 − 1 = 0

Conserved.

Therefore, this reaction passes all three tests.

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Example 4: Beta-Plus Decay

In a suitable nucleus, beta-plus decay can be represented at the nucleon level as:

p → n + e⁺ + νₑ

Check each conservation law.

Charge

Before:

+1

After:

0 + 1 + 0 = +1

Conserved.

Baryon number

Before:

+1

After:

+1 + 0 + 0 = +1

Conserved.

Lepton number

Before:

0

After:

0 − 1 + 1 = 0

Conserved.

Therefore, the particle identities satisfy these three conservation laws.

Note that an isolated free proton cannot spontaneously undergo this decay because the reaction would also fail the energy requirement. Beta-plus decay occurs in suitable proton-rich nuclei where the overall nuclear energy balance permits it.

---

Conservation Laws Do Not Tell the Whole Story

Passing charge, baryon-number, and lepton-number tests does not automatically prove that a reaction will occur.

Other quantities must also be conserved, including:

• energy
• momentum
• angular momentum

Other quantum rules can also restrict particle interactions.

Therefore:

Failing a conservation law → reaction is forbidden

but:

Passing these three tests → reaction may be possible, but further checks may be required

This is an important distinction.

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Example 5: Is This Reaction Possible?

Consider:

n → p + γ

Let's test it.

Charge

Before:

0

After:

+1 + 0 = +1

Charge is not conserved.

Therefore, the reaction is not possible as written.

We do not need to continue checking the other conservation laws because one violation is enough to rule it out.

---

Example 6: A Missing Particle

Suppose we are given:

n → p + e⁻ + X

Determine particle X.

Charge

Before:

0

Known products:

+1 − 1 = 0

Therefore X must have:

Q = 0

Baryon number

Before:

+1

Known products already contain:

B = +1

Therefore:

BX = 0

Lepton number

Before:

0

The electron contributes:

L = +1

Therefore X must contribute:

L = −1

A neutral particle with:

Q = 0

B = 0

L = −1

is an antineutrino.

More specifically:

X = ν̄ₑ

Therefore:

n → p + e⁻ + ν̄ₑ

---

Matter and Antimatter

Conservation laws become particularly useful when dealing with antimatter.

An antiparticle has the same mass as its corresponding particle but opposite values of certain quantum numbers.

For example:

This allows particle-antiparticle pairs to be created or annihilated while preserving the total conserved quantities.

---

Electron-Positron Annihilation

An electron and positron can annihilate:

e⁻ + e⁺ → γ + γ

Check the conservation laws.

Charge

Before:

−1 + 1 = 0

After:

0 + 0 = 0

Conserved.

Baryon number

Before:

0

After:

0

Conserved.

Lepton number

Before:

+1 − 1 = 0

After:

0

Conserved.

The electron and positron disappear as particles, but their energy and momentum are carried away by photons.

For annihilation at rest in the centre-of-momentum frame, two photons are required so that momentum can also be conserved.

---

Pair Production

The reverse process can also occur under suitable conditions:

γ → e⁻ + e⁺

However, a single photon cannot produce an electron-positron pair in otherwise empty space while conserving both energy and momentum.

Pair production therefore occurs in the presence of another object, commonly a nucleus:

γ + nucleus → e⁻ + e⁺ + nucleus

The nucleus can recoil and help conserve momentum.

The photon must also have sufficient energy to create the rest mass of both particles.

The minimum rest-energy required for the pair itself is:

2 × 0.511 MeV = 1.022 MeV

---

Conservation Laws at the Quark Level

Particle transformations can also be examined using quarks.

A neutron has:

udd

A proton has:

uud

During beta-minus decay:

n → p + e⁻ + ν̄ₑ

one down quark changes into an up quark:

d → u + W⁻

The W⁻ then decays:

W⁻ → e⁻ + ν̄ₑ

Charge remains conserved throughout.

Initially:

d charge = −⅓

After the first step:

u = +⅔

W⁻ = −1

Total:

+⅔ − 1 = −⅓

The charge is exactly the same as before.

---

A More Precise Look at Lepton Number

At an introductory level, we often use one total lepton number L.

Particle physics can also distinguish between different lepton flavours:

• electron lepton number
• muon lepton number
• tau lepton number

For example:

electron and electron neutrino → electron family

muon and muon neutrino → muon family

tau and tau neutrino → tau family

In many basic particle interactions, these family numbers provide another useful way to track reactions.

Neutrino oscillations make the full picture more subtle, so total lepton number is the most useful starting point for this course.

---

Worked Reaction Analysis

Consider:

p + e⁻ → n + νₑ

This represents electron capture at the particle level.

Charge

Before:

+1 − 1 = 0

After:

0 + 0 = 0

Conserved.

Baryon number

Before:

+1 + 0 = +1

After:

+1 + 0 = +1

Conserved.

Lepton number

Before:

0 + 1 = +1

After:

0 + 1 = +1

Conserved.

Therefore, the reaction passes all three conservation tests.

---

Try Comparing These Reactions

Consider:

A. n → p + e⁻ + ν̄ₑ

B. n → p + e⁻

C. e⁻ + e⁺ → γ + γ

Reaction A conserves charge, baryon number, and lepton number.

Reaction B conserves charge and baryon number but violates lepton number.

Reaction C conserves all three.

This demonstrates why conservation laws are useful: they allow us to test proposed reactions without needing to observe every reaction experimentally.

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A Particle Conservation Table

This table is useful when solving problems:

For many introductory questions, this table is enough to determine whether a proposed reaction violates one of the major conservation laws.

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A Reliable Problem-Solving Method

When analyzing a particle reaction:

Step 1: Write down every particle.

Identify all particles before and after the reaction.

Step 2: Check charge.

Calculate:

Qbefore

and:

Qafter

They must be equal.

Step 3: Check baryon number.

Calculate:

Bbefore

and:

Bafter

They must be equal.

Step 4: Check lepton number.

Calculate:

Lbefore

and:

Lafter

They must be equal.

Step 5: Look for a missing particle.

If one quantity does not balance, determine what properties a missing particle would require.

Step 6: Remember energy and momentum.

Even if Q, B, and L balance, the reaction must also satisfy conservation of energy and momentum and any other relevant quantum rules.

---

Did You Know?

Conservation laws played an important role in the discovery of the neutrino.

During beta decay, physicists found that the observed electron did not carry all of the expected energy and momentum.

Wolfgang Pauli proposed that another very light, electrically neutral particle must also be produced.

That particle became known as the neutrino.

The neutrino allowed conservation laws to remain satisfied and was later detected experimentally.

This is a powerful example of physicists using conservation laws not only to describe reactions, but also to predict the existence of previously unknown particles.

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Connecting the Ideas

Particle conservation problems can be approached as a balancing system:

Particle reaction

↓

Check electric charge

↓

Check baryon number

↓

Check lepton number

↓

Check energy and momentum

↓

Determine whether the reaction is physically possible

Conservation laws therefore act as fundamental rules controlling which particle transformations can occur.

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Key Terms

Conservation law – A physical rule stating that a particular quantity remains constant in an isolated system.

Electric charge – A conserved property that determines electromagnetic interactions.

Baryon number – A quantum number used to distinguish baryons and antibaryons.

Lepton number – A quantum number associated with leptons and antileptons.

Baryon – A hadron such as a proton or neutron with baryon number +1.

Lepton – A fundamental particle such as an electron, muon, tau, or neutrino.

Antiparticle – A particle corresponding to another particle but with opposite values of certain quantum numbers.

Annihilation – A process in which a particle and antiparticle disappear and their mass-energy is transformed into other particles.

Pair production – The creation of a particle-antiparticle pair from energy under suitable conditions.

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Key Takeaways

• Particle reactions must obey fundamental conservation laws.
• Electric charge is conserved: total charge before equals total charge after.
• Ordinary baryons such as protons and neutrons have B = +1.
• Antibaryons have B = −1, while non-baryons have B = 0.
• Leptons have L = +1 and antileptons have L = −1.
• Beta-minus decay requires an antineutrino to conserve lepton number.
• Conservation laws can be used to identify missing particles.
• Particle-antiparticle annihilation can conserve charge, baryon number, and lepton number.
• A reaction that violates a required conservation law is forbidden.
• A reaction that passes these three tests is not automatically guaranteed to occur; energy, momentum, angular momentum, and other quantum requirements must also be satisfied.
• Conservation laws are powerful tools for analyzing and predicting nuclear and particle interactions.

2. Particle Decays

3. Particle Collisions

What Is a Particle Collision?

Particle physicists investigate matter by accelerating particles to very high speeds and causing them to collide.

During a collision, particles exchange energy and momentum through the fundamental interactions. If enough energy is concentrated in the collision, entirely new particles can be produced.

A simple collision can be represented as:

A + B → C + D

The particles on the left are the initial particles.

The particles on the right are the products.

Unlike an ordinary macroscopic collision, high-energy particle collisions may change the identities and even the number of particles involved.

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Ordinary Collisions vs Particle Collisions

Imagine two billiard balls colliding.

Before the collision:

2 balls

After the collision:

2 balls

The balls may change direction and speed, but they remain billiard balls.

At the subatomic level, something much more interesting can happen.

For example:

particle A + particle B → particle C + particle D + particle E

The initial particles may disappear and new particles may form.

This is possible because energy and mass are equivalent.

---

Creating Particles from Energy

Einstein's mass-energy relationship is:

E = mc²

This means mass represents a form of energy.

In a high-energy collision, some of the kinetic energy of the incoming particles can be transformed into the rest mass-energy of newly created particles.

We can think of the process as:

kinetic energy → mass-energy of new particles + kinetic energy of products

Mass alone is not conserved separately.

Instead, the total energy and momentum of the system are conserved.

---

A Simple Example

Suppose two particles collide:

A + B → C + D

Before the collision, the system contains:

• rest mass-energy of A
• rest mass-energy of B
• kinetic energy of A and B

After the collision, the energy may be distributed among:

• rest mass-energy of C
• rest mass-energy of D
• kinetic energy of C and D

Therefore, if sufficient collision energy is available, C and D can be more massive than the original particles individually.

---

Why Are High Energies Required?

Creating a massive particle requires energy.

From:

E = mc²

a particle with mass m requires at least its rest energy:

E₀ = mc²

For example, the electron has a rest energy of approximately:

0.511 MeV

Creating an electron and its antiparticle, the positron, requires at least:

2 × 0.511 MeV

= 1.022 MeV

This is the minimum energy associated with the rest masses of the pair.

In an actual collision, additional energy may be required to satisfy momentum conservation and may appear as kinetic energy of the products.

---

Particle-Antiparticle Pair Production

One important example of particle creation is pair production.

Energy can produce a particle and its antiparticle.

For example:

energy → e⁻ + e⁺

The electron has:

Q = −1

The positron has:

Q = +1

Therefore the total charge created is:

−1 + 1 = 0

Charge is conserved.

This illustrates why new particles are commonly produced in particle-antiparticle pairs.

---

Conservation Laws Still Apply

High-energy collisions can produce many new particles, but they cannot violate fundamental conservation laws.

Important conservation principles include:

• energy
• momentum
• electric charge
• angular momentum
• applicable particle quantum numbers

At the introductory level, we can often test collisions using:

charge

baryon number

lepton number

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Example 1: Checking Charge

Consider:

e⁻ + e⁺ → μ⁻ + μ⁺

Before:

Electron:

−1

Positron:

+1

Total:

Q = 0

After:

Muon:

−1

Antimuon:

+1

Total:

Q = 0

Therefore:

Charge is conserved.

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Checking Lepton Number

For:

e⁻ + e⁺ → μ⁻ + μ⁺

Before:

Electron:

L = +1

Positron:

L = −1

Total:

L = 0

After:

Muon:

L = +1

Antimuon:

L = −1

Total:

L = 0

Total lepton number is conserved.

All particles involved have:

B = 0

so baryon number is also conserved.

If sufficient energy is available and the other conservation requirements are satisfied, this reaction is possible.

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Heavier Particles Require More Energy

A muon is much heavier than an electron.

Electron rest energy:

≈ 0.511 MeV

Muon rest energy:

≈ 105.7 MeV

Therefore, producing a muon-antimuon pair requires at least:

2 × 105.7 MeV

≈ 211.4 MeV

of centre-of-mass energy just to provide their rest mass-energy.

This is why high-energy accelerators are required to study heavy particles.

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Centre-of-Mass Energy

Not all of the energy of a particle beam is necessarily available to create new particles.

The most useful quantity is the centre-of-mass energy.

This is the energy available in the reference frame where the total momentum of the colliding system is zero.

If two equal-energy particles collide head-on, a large fraction of their energy can be available for creating new particles.

This is one reason modern particle accelerators often use colliding beams.

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Fixed-Target Experiments

In a fixed-target experiment, a fast particle strikes a stationary target:

fast particle → stationary target

After the collision, the total momentum cannot simply disappear.

Some of the incoming energy must therefore remain as motion of the products.

This reduces the amount of energy available to create new particle mass.

---

Collider Experiments

A collider sends two beams toward each other:

particle → ← particle

If their momenta are equal and opposite, the total momentum before the collision can be close to zero.

This means much more of the beam energy is available as centre-of-mass energy.

Therefore:

colliding beams are especially effective for producing very massive particles.

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Particle Accelerators

A particle accelerator uses electric fields to increase the energy of charged particles.

Magnetic fields can be used to:

• bend particle paths
• steer beams
• focus beams
• keep particles moving around circular accelerators

Large accelerators can bring particles to extremely high energies before causing them to collide.

One famous example is the Large Hadron Collider (LHC) at CERN.

It collides high-energy proton beams and allows physicists to study the particles produced in those collisions.

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What Happens in a Proton Collision?

A proton is not a fundamental particle.

It contains quarks and gluons.

Its valence quark structure is:

uud

At very high energies, a proton-proton collision is better understood as interactions between the quarks and gluons inside the protons.

A simplified picture is:

proton + proton → many particles

But at a deeper level:

quark/gluon + quark/gluon → new particles

The collision energy can produce particles that were not present as constituents of the original protons.

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Collision Diagrams

A simple particle collision diagram often shows incoming particles entering an interaction region and outgoing particles leaving it.

For example:

e⁻ → → μ⁻
** X**
e⁺ → → μ⁺

The central point represents the interaction.

Incoming lines represent particles before the collision.

Outgoing lines represent particles after the collision.

More advanced particle physics uses diagrams called Feynman diagrams to represent interactions.

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Reading a Simple Collision Diagram

When interpreting a collision diagram:

Step 1: Identify the incoming particles

Which particles enter the interaction?

Step 2: Identify the outgoing particles

Which particles are produced?

Step 3: Check electric charge

Does:

Qbefore = Qafter?

Step 4: Check baryon and lepton numbers

Are they conserved where applicable?

Step 5: Consider energy

Is enough centre-of-mass energy available to create the products?

Step 6: Consider momentum

Can momentum be conserved?

These steps allow us to test whether a proposed interaction is physically possible.

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Example 2: Is This Collision Possible?

Consider:

e⁻ + e⁺ → p + p̄

where:

p = proton

p̄ = antiproton

Check the conservation laws.

Charge

Before:

−1 + 1 = 0

After:

+1 − 1 = 0

Charge is conserved.

Baryon Number

Before:

0

After:

+1 − 1 = 0

Baryon number is conserved.

Lepton Number

Before:

+1 − 1 = 0

After:

0

Total lepton number is conserved.

Therefore, the reaction passes these conservation tests.

But there is another requirement:

enough energy must be available to create the proton and antiproton masses.

A proton has a rest energy of approximately:

938 MeV

Therefore, creating the pair requires at least approximately:

2 × 938 MeV = 1876 MeV

or:

1.876 GeV

of centre-of-mass energy.

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Example 3: An Impossible Collision

Consider:

e⁻ + e⁺ → p

Check charge.

Before:

−1 + 1 = 0

After:

+1

Charge is not conserved.

Therefore, this reaction is impossible as written.

It also violates baryon number:

Before:

B = 0

After:

B = +1

Multiple conservation laws are violated.

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Matter and Antimatter Creation

When energy creates matter, conservation laws often require corresponding antimatter.

For example:

energy → proton + antiproton

Baryon number:

0 → +1 + (−1)

Therefore:

0 → 0

Similarly:

energy → electron + positron

Lepton number:

0 → +1 + (−1)

Again:

0 → 0

Particle-antiparticle pair creation allows new particles to appear without changing the total conserved quantum numbers.

---

Annihilation

The reverse process can also occur.

A particle and its antiparticle can annihilate.

For example:

e⁻ + e⁺ → γ + γ

The mass-energy and kinetic energy of the original particles appear as photon energy.

Pair production and annihilation provide a clear demonstration of:

energy ↔ particle mass

while total energy and momentum remain conserved.

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Energy Units in Particle Physics

The joule is inconveniently large for individual particles.

Particle physicists commonly use the electronvolt (eV).

Useful units include:

1 keV = 10³ eV

1 MeV = 10⁶ eV

1 GeV = 10⁹ eV

1 TeV = 10¹² eV

Modern particle accelerators can operate at energies measured in GeV and TeV.

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Example 4: Can the Particle Be Produced?

Suppose a collision has:

500 MeV

of available centre-of-mass energy.

Could it produce a particle-antiparticle pair in which each particle has a rest energy of:

180 MeV?

Required rest energy:

2 × 180 = 360 MeV

Available energy:

500 MeV

Since:

500 MeV > 360 MeV

there is enough energy, in principle, to provide the rest mass-energy of the pair.

Remaining energy:

500 − 360 = 140 MeV

can appear as kinetic energy of the products, provided all other conservation laws and reaction requirements are satisfied.

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Example 5: Not Enough Energy

Suppose a collision has:

700 MeV

of available centre-of-mass energy.

Scientists want to create two particles, each with a rest energy of:

500 MeV

Required energy:

2 × 500 = 1000 MeV

Available:

700 MeV

Since:

700 < 1000

the pair cannot be produced.

The collision does not contain enough centre-of-mass energy.

---

Threshold Energy

The minimum energy required for a particular reaction to occur is called the threshold energy.

Below the threshold:

reaction cannot occur

At or above the threshold:

reaction may occur

provided all other conservation laws and interaction requirements are satisfied.

For simple centre-of-mass examples, we can estimate the threshold from the total rest energy of the required products.

Real collision calculations can be more complicated because energy and momentum must be conserved simultaneously.

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Collision Products

A high-energy collision can produce many particles.

Some may be stable.

Others may exist for extremely short times before decaying.

For example:

collision → unstable particle → decay products

Scientists may therefore never detect the original short-lived particle directly.

Instead, they reconstruct it from the particles produced by its decay.

---

Particle Detectors

Particle detectors surround collision points and measure properties such as:

• particle trajectories
• electric charge
• momentum
• energy
• particle type

A high-energy collision may produce many tracks spreading outward from the interaction point.

By analyzing these tracks and energy deposits, physicists can reconstruct what happened during the collision.

---

Reconstructing a Particle

Suppose an unstable particle is produced:

collision → X → A + B

Particle X may decay almost immediately.

Scientists measure particles A and B.

Using their energies and momenta, they can calculate properties of the original particle X.

One particularly important quantity is the invariant mass of the decay products.

A peak in the reconstructed mass distribution can provide evidence that a particular unstable particle was produced.

This technique has played a major role in particle discoveries.

---

The Higgs Boson

The Higgs boson provides a famous example.

High-energy proton collisions can produce processes involving a Higgs boson.

The Higgs boson is extremely short-lived and decays almost immediately.

Scientists therefore identify it by studying its possible decay products and reconstructing the properties of the original collision.

This demonstrates why particle physics requires both:

high-energy accelerators

and

highly sophisticated detectors.

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Why Build More Powerful Accelerators?

Increasing collision energy allows scientists to:

• produce heavier particles
• investigate physics at smaller distance scales
• study rare interactions
• test predictions of particle theories
• search for previously unknown particles

There is an important connection between energy and scale:

higher energy → shorter effective wavelength → smaller structures can be investigated

Particle accelerators therefore act somewhat like extremely powerful microscopes.

---

A Reliable Method for Collision Problems

When analyzing a simple particle collision:

1. Identify the initial particles.

2. Identify the products.

3. Calculate total charge before and after.

4. Calculate baryon number before and after.

5. Calculate lepton number before and after.

6. Check whether sufficient energy is available.

7. Remember that momentum must also be conserved.

A reaction that violates a required conservation law cannot occur.

A reaction that satisfies the basic conservation laws may occur if sufficient energy and an appropriate interaction are available.

---

Did You Know?

When physicists say that a collider has reached a higher energy, they are not simply trying to make particles move "faster."

Once particles are already moving extremely close to the speed of light, adding more energy produces only a very small increase in speed.

Instead, the additional energy greatly increases the particles' energy and momentum.

When they collide, that energy can be used to create heavier particles.

This is why particle accelerators continue to benefit from higher energies even though their particles are already travelling extremely close to the speed of light.

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Connecting the Ideas

High-energy particle collisions connect several major ideas from nuclear and particle physics:

Particles accelerated to high energy

↓

High-energy collision

↓

Energy concentrated in a tiny region

↓

E = mc²

↓

New particles can be created

↓

Unstable particles may decay

↓

Detector records decay products

↓

Conservation laws are applied

↓

Original particles and interactions are reconstructed

Particle collisions therefore allow scientists to investigate both the fundamental particles of matter and the forces acting between them.

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Key Terms

Particle collision – An interaction between particles in which energy and momentum can be exchanged and new particles may be produced.

Particle accelerator – A machine that increases the energy of charged particles using electromagnetic fields.

Centre-of-mass energy – The collision energy available in the reference frame where the system's total momentum is zero.

Pair production – The creation of a particle and its antiparticle from energy under suitable conditions.

Annihilation – A process in which a particle and antiparticle transform into other particles.

Threshold energy – The minimum energy required for a particular reaction to occur.

Collision product – A particle produced during a collision.

Particle detector – Equipment used to measure particles and their interactions.

Invariant mass – A quantity calculated from the energy and momentum of particles that can be used to reconstruct the mass of a parent particle.

Feynman diagram – A graphical representation used to describe particle interactions in quantum field theory.

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Key Takeaways

• High-energy particle collisions allow physicists to investigate the fundamental structure of matter.
• Collision energy can be converted into the rest mass-energy of new particles.
• The relationship E = mc² explains how energy can produce massive particles.
• New particles are often created as particle-antiparticle pairs, helping conserved quantum numbers remain balanced.
• Particle collisions must conserve energy, momentum, electric charge, angular momentum, and applicable particle quantum numbers.
• Charge, baryon number, and lepton number are useful tools for analyzing introductory collision problems.
• Producing heavier particles requires greater centre-of-mass energy.
• Colliding beams are generally more effective for particle production than fixed-target experiments because more energy can be available in the centre-of-mass frame.
• Protons contain quarks and gluons, so high-energy proton collisions involve interactions between their internal constituents.
• Many newly created particles decay almost immediately and are identified through their decay products.
• Particle detectors allow scientists to reconstruct collision events from tracks, energies, and momenta.
• Higher collision energies allow physicists to investigate heavier particles and smaller distance scales.

4. Antimatter

What Is Antimatter?

Antimatter is made of antiparticles.

For many known particles, there is a corresponding antiparticle with:

• the same mass
• the same spin
• opposite electric charge, if the particle is charged
• opposite values of certain quantum numbers

For example:

electron → positron

proton → antiproton

neutron → antineutron

The positron is the antimatter counterpart of the electron.

---

Matter and Antimatter

Ordinary matter is made from particles such as:

• electrons
• protons
• neutrons

Antimatter is made from the corresponding antiparticles.

For example:

The bar above a symbol often indicates an antiparticle.

---

The Positron

The antiparticle of the electron is the positron.

The electron has:

charge = −1

The positron has:

charge = +1

Both have exactly the same mass:

0.511 MeV/c²

Both are leptons.

However, their lepton numbers are opposite:

electron: L = +1

positron: L = −1

---

The Antiproton

The proton contains three valence quarks:

uud

The antiproton contains the corresponding antiquarks:

ūūd̄

The proton has:

charge = +1

baryon number = +1

The antiproton has:

charge = −1

baryon number = −1

Their masses are the same.

---

The Antineutron

The neutron has:

charge = 0

The antineutron also has:

charge = 0

So how are they different?

Their internal quark structures are different.

Neutron:

udd

Antineutron:

ūd̄d̄

Their baryon numbers are also opposite:

neutron: B = +1

antineutron: B = −1

This shows that an antiparticle is not always distinguished by electric charge alone.

---

Antiparticles and Quantum Numbers

Antiparticles have opposite values of several additive quantum numbers.

For example:

This is important because conservation laws must still be obeyed when matter and antimatter interact.

---

Matter and Antimatter Are Not "Opposite Mass"

A common misconception is that antimatter has negative mass.

It does not.

An antiparticle has the same positive mass as its corresponding particle.

For example:

electron mass = positron mass

proton mass = antiproton mass

The word "anti" refers to opposite quantum properties, not negative mass.

---

Annihilation

When a particle meets its antiparticle, they can undergo annihilation.

During annihilation, the original particle-antiparticle pair disappears and new particles are produced.

For example:

e⁻ + e⁺ → γ + γ

An electron and positron can annihilate to produce two gamma-ray photons.

---

Why Are Two Photons Produced?

Suppose an electron and positron annihilate while their total momentum is zero.

Producing only one photon would not work because a photon always carries momentum.

Two photons travelling in opposite directions can satisfy:

total momentum before = total momentum after

Therefore:

e⁻ + e⁺ → γ + γ

allows both energy and momentum to be conserved.

---

Energy Released During Annihilation

The electron and positron each have a rest energy of:

0.511 MeV

Therefore, if they annihilate while essentially at rest:

total rest energy = 0.511 + 0.511

= 1.022 MeV

If two photons are produced equally:

energy per photon = 0.511 MeV

So:

e⁻ + e⁺ → 2γ

with each photon carrying approximately:

511 keV

in the centre-of-momentum frame when the pair begins essentially at rest.

---

Conservation Laws in Annihilation

Consider:

e⁻ + e⁺ → γ + γ

Charge

Before:

−1 + 1 = 0

After:

0 + 0 = 0

Charge is conserved.

Baryon Number

Before:

0

After:

0

Lepton Number

Before:

+1 − 1 = 0

After:

0

All three are conserved.

---

Proton-Antiproton Annihilation

A proton and antiproton can also annihilate.

A simplified representation is:

p + p̄ → other particles

Because protons contain quarks and antiprotons contain antiquarks, annihilation often produces several particles rather than just two photons.

The products commonly include hadrons such as pions.

The important principle is still:

matter + antimatter → other particles and energy

while all relevant conservation laws remain satisfied.

---

Pair Production

Annihilation can be considered the reverse of pair production.

During pair production, energy creates a particle-antiparticle pair.

For example:

energy → e⁻ + e⁺

A high-energy photon can produce an electron-positron pair in the presence of another object, such as a nucleus:

γ + nucleus → e⁻ + e⁺ + nucleus

The nearby nucleus helps conserve momentum.

At least:

1.022 MeV

of photon energy is needed to provide the rest mass-energy of the electron and positron pair, with additional energy needed for recoil and kinetic energy.

---

Matter-Antimatter Symmetry

The laws of physics treat particles and antiparticles in closely related ways.

For example:

electron and positron have equal masses

proton and antiproton have equal masses

Experiments have tested many particle-antiparticle properties to extremely high precision.

However, matter and antimatter are not perfectly interchangeable in every process.

Certain weak-interaction processes show small differences between the behaviour of matter and antimatter, known as CP violation.

---

Why Is the Universe Mostly Matter?

One of the biggest unanswered questions in physics is why the observable universe contains much more matter than antimatter.

According to our current understanding, the early universe should have produced matter and antimatter in nearly equal amounts.

If exactly equal amounts had survived and annihilated, very little ordinary matter would remain.

Yet stars, planets, and living organisms are made overwhelmingly of matter.

Scientists are still investigating why this imbalance developed.

This problem is known as the matter-antimatter asymmetry.

---

Is There an "Antimatter Periodic Table"?

In principle, antimatter could form structures similar to ordinary matter.

An antihydrogen atom, for example, consists of:

• one antiproton
• one positron

This mirrors ordinary hydrogen:

• one proton
• one electron

Scientists have successfully produced and trapped antihydrogen atoms for research.

---

Antimatter and Gravity

Because antimatter has positive mass-energy, it is expected to respond to gravity.

Experiments with antihydrogen are used to test this directly.

Current measurements are consistent with antimatter falling downward in Earth's gravitational field rather than behaving as if it had negative mass.

This is an active area of precision experimental physics.

---

Practical Application: PET Scanning

One of the most important practical uses of antimatter is positron emission tomography, or PET.

PET is a medical imaging technique.

A radioactive tracer containing a positron-emitting isotope is introduced into the body.

The isotope undergoes beta-plus decay and emits a positron.

The positron travels a short distance before meeting an electron.

Then:

e⁺ + e⁻ → γ + γ

Two gamma photons are produced.

---

How PET Detects Annihilation

In PET imaging, the two annihilation photons typically travel in nearly opposite directions.

Detectors around the patient detect the photons.

If two detectors register photons at nearly the same time, the system can infer that the annihilation occurred somewhere along the line between them.

Many such detections are combined by computers to construct an image.

PET can help reveal patterns of biological activity in the body.

---

Why PET Uses 511 keV Photons

When an electron and positron annihilate approximately at rest:

electron rest energy = 511 keV

positron rest energy = 511 keV

Therefore, the two photons each have approximately:

511 keV

This characteristic energy is fundamental to PET imaging.

---

Antimatter in Scientific Research

Antimatter is also used in fundamental physics research.

Scientists study antimatter to investigate:

• matter-antimatter symmetry
• properties of antiparticles
• CP violation
• the behaviour of antimatter in gravity
• the origin of the matter-antimatter imbalance
• tests of the Standard Model

Antiprotons and antihydrogen are especially useful in these experiments.

---

Antimatter Is Difficult to Store

Antimatter cannot simply be placed in an ordinary container.

If it touches ordinary matter, annihilation occurs.

Scientists therefore use combinations of:

• electric fields
• magnetic fields
• extremely high vacuum

to keep charged antiparticles away from the walls of a container.

Neutral antimatter such as antihydrogen requires specially designed magnetic traps.

---

Why Antimatter Is Not a Practical Energy Source

Matter-antimatter annihilation converts a very large fraction of the initial rest mass-energy into other forms of energy.

That may make antimatter sound like an ideal fuel.

However, there is a major problem:

We must first produce the antimatter.

Producing antimatter requires much more usable energy than can presently be recovered from it.

Antimatter is also extremely difficult to manufacture in significant quantities and difficult to store.

Therefore, antimatter is currently a research tool and medical technology component, not a practical energy source.

---

Comparing Matter and Antimatter

---

Example 1: Identify the Antiparticle

What is the antiparticle of an electron?

Electron:

e⁻

The antiparticle must have:

• same mass
• opposite charge
• opposite lepton number

Therefore:

e⁺

The antiparticle is the positron.

---

Example 2: Identify the Antiparticle

What is the antiparticle of a proton?

The proton has:

Q = +1

B = +1

The antiparticle has:

Q = −1

B = −1

Therefore:

p̄

The particle is the antiproton.

---

Example 3: Check an Annihilation Reaction

Consider:

p + p̄ → γ + γ

Check charge:

Before:

+1 − 1 = 0

After:

0

Check baryon number:

Before:

+1 − 1 = 0

After:

0

So charge and baryon number are conserved.

However, actual proton-antiproton annihilation commonly produces multiple hadrons because protons and antiprotons are composite particles.

The simplified equation still illustrates the conservation principles.

---

Example 4: Energy from Electron-Positron Annihilation

An electron and positron annihilate at rest.

Each has rest energy:

0.511 MeV

Total:

0.511 + 0.511 = 1.022 MeV

If two equal-energy photons are produced:

1.022 ÷ 2 = 0.511 MeV

Each photon has:

0.511 MeV = 511 keV

---

Did You Know?

Antimatter occurs naturally.

Positrons can be produced during some radioactive decays, cosmic-ray interactions, and other high-energy processes.

Antimatter is therefore not purely artificial.

However, large concentrations of antimatter are not normally found around us because contact with ordinary matter leads to annihilation.

---

Connecting the Ideas

Antimatter connects many topics in particle physics:

Fundamental particles

↓

Each particle may have an antiparticle

↓

Opposite charges and quantum numbers

↓

Matter-antimatter interaction

↓

Annihilation

↓

Mass-energy converted into other particles and radiation

↓

Conservation laws remain satisfied

This connects antimatter directly to:

• mass-energy equivalence
• particle collisions
• particle decays
• conservation laws
• medical imaging
• the Standard Model

---

Key Terms

Antimatter – Matter composed of antiparticles.

Antiparticle – A particle with the same mass as its corresponding particle but opposite values of certain quantum properties.

Positron – The antiparticle of the electron.

Antiproton – The antiparticle of the proton.

Antineutron – The antiparticle of the neutron.

Antiquark – The antiparticle corresponding to a quark.

Annihilation – A process in which a particle and its antiparticle transform into other particles.

Pair production – The creation of a particle-antiparticle pair from energy.

Antihydrogen – An antimatter atom consisting of an antiproton and a positron.

PET – Positron emission tomography, a medical imaging technique that uses positron-emitting radioactive tracers.

Matter-antimatter asymmetry – The observed dominance of matter over antimatter in the universe.

---

Key Takeaways

• Antimatter is made of antiparticles.
• Most particles have corresponding antiparticles with the same mass but opposite values of certain quantum numbers.
• The antiparticle of the electron is the positron.
• The antiparticle of the proton is the antiproton.
• Antimatter does not have negative mass.
• When a particle meets its antiparticle, they can undergo annihilation.
• Electron-positron annihilation can produce two gamma-ray photons.
• Mass-energy, momentum, charge, baryon number, and lepton number must remain conserved during antimatter interactions.
• The reverse of annihilation is pair production, in which energy produces a particle-antiparticle pair.
• Antimatter can form structures such as antihydrogen.
• Antimatter has important practical use in PET medical imaging.
• Antimatter is difficult and energy-intensive to produce and store, so it is not currently a practical energy source.
• The reason the observable universe contains much more matter than antimatter remains one of the major open questions in modern physics.

5. Particle Accelerators

What Is a Particle Accelerator?

A particle accelerator is a machine that increases the energy of charged particles and directs them into targets or into other particle beams.

Scientists use particle accelerators to investigate the structure of matter at extremely small scales.

Accelerators can be used to:

• study fundamental particles
• investigate nuclear structure
• create unstable particles
• test particle-physics theories
• search for previously unknown particles
• produce radioactive isotopes
• support medical and industrial applications

In particle physics, accelerators are especially important because higher particle energies allow scientists to investigate smaller distance scales and create heavier particles.

---

Why Accelerate Particles?

There are two major reasons for giving particles very high energies.

1. Higher energy can create new particles

Einstein's mass-energy relationship tells us:

E = mc²

During a high-energy collision, some kinetic energy can be converted into the rest mass-energy of new particles.

Therefore:

higher collision energy → possibility of producing heavier particles

---

2. Higher energy allows smaller structures to be investigated

Particles also behave as waves.

Their wavelength is related to momentum.

Very high-momentum particles have extremely short wavelengths.

Shorter wavelengths can probe smaller structures.

Therefore:

higher momentum → shorter wavelength → smaller distance scale

This is similar to using shorter-wavelength light to obtain greater detail with a microscope.

---

How Are Charged Particles Accelerated?

Charged particles gain energy from electric fields.

An electric field exerts a force on a charged particle.

The force is:

F = qE

where:

F = electric force

q = particle charge

E = electric field strength

When a charged particle moves through a potential difference, its energy changes.

The electrical energy gained is:

ΔE = qV

where:

q = charge

V = potential difference

This is the basic principle behind particle acceleration.

---

Example: Accelerating an Electron

An electron moving through a potential difference of:

1000 V

gains an energy of:

1000 eV

because the magnitude of the electron charge is one elementary charge.

Therefore:

1 electron through 1 volt → 1 eV

This is why the electronvolt is such a convenient unit in particle physics.

---

What Is an Electronvolt?

An electronvolt (eV) is the amount of energy gained by a particle with one elementary charge moving through a potential difference of one volt.

Useful units include:

1 keV = 10³ eV

1 MeV = 10⁶ eV

1 GeV = 10⁹ eV

1 TeV = 10¹² eV

Modern research accelerators can reach energies measured in GeV and TeV.

---

Linear Accelerators

A linear accelerator, often called a linac, accelerates particles along a straight path.

The particles pass through a sequence of accelerating regions.

Each region increases their energy.

A simplified sequence is:

particle source → accelerating sections → high-energy beam

Electric fields repeatedly push the charged particles forward.

---

Radio-Frequency Cavities

Modern accelerators often use radio-frequency cavities, or RF cavities.

These cavities create rapidly changing electric fields.

The timing is arranged so that particles receive a forward push each time they pass through an accelerating region.

Repeated pushes gradually increase the particle energy.

We can think of it as repeatedly giving the particles carefully timed boosts.

---

Circular Accelerators

Another major design uses a circular or nearly circular path.

Particles move around the accelerator many times.

Each time they pass through accelerating cavities, they gain more energy.

This allows particles to be accelerated repeatedly without requiring an impossibly long straight accelerator.

Two important types are:

• cyclotrons
• synchrotrons

---

Magnetic Fields and Particle Motion

Electric fields primarily increase particle energy.

Magnetic fields are used mainly to:

• bend the path of charged particles
• steer the beam
• focus particles into a narrow beam

A moving charged particle experiences a magnetic force.

For motion perpendicular to a magnetic field:

F = qvB

where:

q = charge

v = particle speed

B = magnetic field strength

The magnetic force can make the particle follow a curved path.

---

Why Strong Magnets Are Needed

As particles gain momentum, they become harder to bend.

The relationship for a charged particle moving perpendicular to a magnetic field can be written:

p = qBr

where:

p = momentum

q = charge

B = magnetic field strength

r = radius of curvature

To keep very high-momentum particles moving around a circular accelerator, scientists need:

• stronger magnetic fields
• larger accelerator rings
• or both

This is one reason high-energy accelerators can be enormous.

---

Particle Beams

A particle accelerator does not usually accelerate just one particle.

Instead, particles are grouped into bunches.

These bunches travel through the accelerator at extremely high speeds.

In a collider, two beams may travel in opposite directions.

At selected locations, the beams are made to cross.

That produces high-energy collisions.

---

Fixed-Target Accelerators

In a fixed-target experiment, a high-energy beam strikes a stationary target.

For example:

high-energy proton → stationary target

The collision can produce many particles.

Fixed-target experiments are useful for many types of nuclear and particle research.

However, some of the incoming energy must remain as motion of the final system because momentum must be conserved.

---

Particle Colliders

In a particle collider, two beams travel toward each other.

For example:

proton → ← proton

If the two particles have equal and opposite momentum, the total momentum of the system can be approximately zero.

This means a much larger fraction of their energy is available for creating new particles.

Therefore, colliders are particularly useful when searching for very massive particles.

---

Particle Detectors

Producing particles is only part of the experiment.

Scientists must also determine what was created.

A particle detector measures the products of particle collisions.

Different detector systems can measure:

• particle tracks
• electric charge
• momentum
• energy
• speed
• particle type

Modern particle detectors often contain several layers, with each layer performing a different job.

---

Tracking Detectors

A tracking detector records the paths of charged particles.

Charged particles passing through detector material leave signals along their trajectories.

If the detector is placed in a magnetic field, charged particles follow curved paths.

The curvature helps determine:

• the sign of the particle's charge
• its momentum

Positive and negative particles curve in opposite directions.

Higher-momentum particles curve less strongly.

---

Calorimeters

A calorimeter measures particle energy.

A particle enters the detector and interacts with the material, producing a cascade or shower of secondary particles.

The detector measures the energy deposited.

Different types of calorimeters are designed for different particles.

For example:

• electromagnetic calorimeters measure electrons and photons
• hadronic calorimeters measure particles such as protons, neutrons, and pions

---

Muon Detectors

Muons can pass through large amounts of matter more easily than many other charged particles.

For this reason, muon detectors are often placed in the outer layers of a detector.

If a charged particle passes through the inner detector and calorimeters and continues into the outer muon system, it may be identified as a muon.

---

Detecting Neutrinos

Neutrinos interact extremely weakly with matter.

They usually pass through particle detectors without leaving a direct signal.

Scientists therefore infer their presence from missing energy and momentum.

For example, if the measured particles do not account for all the momentum in an event, an undetected neutrino may have carried some away.

---

Putting Detector Layers Together

A simplified multipurpose detector may contain:

collision point

↓

tracking detector

↓

electromagnetic calorimeter

↓

hadronic calorimeter

↓

muon detector

Each system contributes different information.

Scientists combine the measurements to identify particles.

---

How Can a Detector Identify a Particle?

Suppose a collision produces an unknown charged particle.

Scientists may examine:

• how much its path curves
• which detector layers it reaches
• how much energy it deposits
• whether it produces an electromagnetic or hadronic shower
• how quickly it travels

Combining this information allows physicists to distinguish among particles such as:

• electrons
• muons
• protons
• pions
• photons

No single detector component usually provides the complete answer.

---

Bubble Chambers and Early Particle Detection

Before modern electronic detectors, scientists often used bubble chambers.

A bubble chamber contained a superheated liquid.

Charged particles passing through the liquid created trails of bubbles.

Photographs of these tracks allowed physicists to study particle paths and interactions.

Curved tracks in magnetic fields revealed information about particle charge and momentum.

---

Discoveries Made with Particle Accelerators

Particle accelerators have played a major role in the development of modern physics.

They have helped scientists discover or investigate many particles, including:

• new mesons and baryons
• antimatter particles
• quarks
• W and Z bosons
• the tau lepton
• the Higgs boson

Accelerators have also provided evidence supporting the Standard Model of particle physics.

---

Discovering Quarks

Quarks cannot normally be observed as isolated particles because of quark confinement.

However, high-energy scattering experiments revealed that protons and neutrons contain smaller point-like constituents.

Experiments in which high-energy electrons were scattered from protons provided important evidence for internal structures later understood as quarks and gluons.

This was similar in principle to Rutherford's earlier use of scattering to investigate the atomic nucleus.

---

W and Z Bosons

The W and Z bosons carry the weak interaction.

They were discovered in accelerator experiments at CERN in the early 1980s.

Their discovery strongly confirmed the electroweak theory, which connects electromagnetic and weak interactions within the Standard Model.

The particles are:

W⁺

W⁻

Z⁰

They are much more massive than particles such as electrons, so high-energy collisions were necessary to produce them.

---

The Higgs Boson

One of the most famous accelerator discoveries is the Higgs boson.

The Higgs boson is associated with the Higgs field.

The Higgs mechanism helps explain why fundamental particles such as the W and Z bosons, quarks, and charged leptons have mass.

The Higgs boson was discovered in 2012 by experiments at the Large Hadron Collider.

---

The Large Hadron Collider

The Large Hadron Collider, or LHC, is a very large particle accelerator at CERN.

It is located in a circular underground tunnel approximately:

27 km in circumference

near Geneva, on the border between Switzerland and France.

The LHC is primarily designed to collide high-energy proton beams.

---

Why Is It Called the Large Hadron Collider?

The name describes what it does.

Large

It has a circumference of roughly 27 km.

Hadron

It accelerates hadrons, particularly protons.

Protons are baryons and therefore belong to the larger family of hadrons.

Collider

Two particle beams travel in opposite directions and are brought into collision.

---

How the LHC Works

A simplified sequence is:

1. Protons are produced.

2. Smaller accelerators increase their energy.

3. The protons are injected into the LHC.

4. Two proton beams travel in opposite directions.

5. RF cavities increase their energy.

6. Powerful magnets steer and focus the beams.

7. The beams cross at detector locations.

8. Collision products are measured.

This entire process requires extremely precise control.

---

Superconducting Magnets

The LHC uses powerful superconducting magnets.

When some materials are cooled to extremely low temperatures, they can conduct electrical current with essentially no resistance.

This allows very large currents to flow and produce strong magnetic fields.

These magnetic fields bend the high-energy proton beams around the accelerator ring.

The magnets are cooled using liquid helium systems to temperatures close to absolute zero.

---

Major LHC Experiments

Several large experiments are located around the LHC.

Two of the best known are:

ATLAS

and

CMS

Both are general-purpose detectors designed to investigate many different types of particle interactions.

Other experiments specialize in particular areas of particle physics.

---

ATLAS and CMS

ATLAS and CMS independently analyze proton-proton collisions.

Having two different experiments study similar physics is valuable.

If both experiments observe the same phenomenon independently, confidence in the result increases.

This was important in the discovery of the Higgs boson.

---

Why Was the Higgs Discovery Important?

The Standard Model predicted the existence of the Higgs boson.

Before 2012, scientists had strong indirect evidence for the Higgs mechanism but had not observed the Higgs boson itself.

The LHC produced enough high-energy collisions for Higgs bosons to be created.

The Higgs bosons decayed almost immediately.

Scientists identified them by analyzing their decay products.

In July 2012, the ATLAS and CMS collaborations announced the discovery of a new particle consistent with the Higgs boson.

---

Why Didn't Scientists Simply See the Higgs?

The Higgs boson is extremely short-lived.

It decays before it can travel through a detector as an observable particle.

Instead:

collision → Higgs boson → decay products

Scientists measure the decay products.

They then reconstruct the mass and properties of the original particle.

A concentration of events near a particular reconstructed mass provides evidence for the particle.

This is similar to solving a puzzle from the pieces left behind.

---

What Else Does the LHC Study?

The LHC is not just a "Higgs machine."

Scientists use it to study:

• properties of the Higgs boson
• quarks and gluons
• top quarks
• matter-antimatter differences
• heavy-ion collisions
• conditions similar to the early universe
• possible physics beyond the Standard Model

Researchers also search for evidence of particles that might help explain dark matter or other unresolved questions in physics.

---

Heavy-Ion Collisions

The LHC can also collide heavy atomic nuclei, such as lead nuclei.

At extremely high collision energies, these interactions can produce a state of matter known as a quark-gluon plasma.

Scientists believe the early universe contained similar conditions shortly after the Big Bang.

Studying this state helps researchers understand how quarks and gluons behave under extreme conditions.

---

Why Are Particle Accelerators So Large?

Higher-energy particles have greater momentum.

That makes them harder to bend around a circular path.

From:

p = qBr

increasing momentum requires either:

• stronger magnetic field B
• larger radius r
• or both

There are practical limits to magnetic-field strength.

Therefore, increasing accelerator size can allow particles to reach higher energies.

---

Why Can't Particles Be Accelerated Beyond the Speed of Light?

As a particle with mass gains energy, its speed approaches the speed of light.

However, it never reaches or exceeds:

c = 3.00 × 10⁸ m/s

Adding more energy continues to increase its total energy and momentum, but the increase in speed becomes extremely small.

This is why accelerator physicists focus on particle energy, not simply particle speed.

---

Medical Uses of Particle Accelerators

Particle accelerators are not used only for fundamental physics.

They also have important medical applications.

Examples include:

• X-ray production
• radiation therapy
• proton therapy
• production of medical radioisotopes

Hospitals commonly use smaller linear accelerators for cancer treatment.

---

Proton Therapy

In proton therapy, accelerated protons are directed toward a tumour.

Protons can deposit a large fraction of their energy near the end of their path.

This allows doctors to target some tumours while reducing radiation exposure to surrounding tissue.

Particle-accelerator technology therefore has direct medical applications.

---

Industrial and Scientific Applications

Accelerators are also used for:

• materials research
• semiconductor manufacturing
• sterilization
• isotope production
• archaeological analysis
• studying the structure of materials
• synchrotron light production

This makes particle accelerators valuable far beyond particle physics.

---

Example 1: Why Use Electric Fields?

A student says:

"Magnetic fields are what speed particles up in an accelerator."

This is generally incorrect.

A magnetic force acts perpendicular to the velocity of a charged particle, so it mainly changes the direction of motion.

Electric fields can do work on charged particles and increase their kinetic energy.

Therefore:

electric fields → accelerate

magnetic fields → steer and focus

---

Example 2: Why Use a Collider?

Suppose two identical high-energy particles travel toward each other with equal and opposite momentum.

Their total momentum can be approximately:

0

If they collide, a large fraction of their total energy is available for creating new particles.

By contrast, if one strikes a stationary target, the products must carry substantial momentum away.

This is why high-energy research often uses colliders.

---

Example 3: Detecting Charge

Suppose two charged particles pass through the same magnetic field.

One curves left.

The other curves right.

The particles must have opposite signs of electric charge, assuming they are travelling in the same initial direction.

The direction of curvature therefore gives information about charge.

---

Example 4: Detecting Momentum

Two particles with equal charge travel through the same magnetic field.

Particle A curves strongly.

Particle B curves only slightly.

Since:

p = qBr

the particle with the larger radius has greater momentum.

Therefore:

Particle B has the greater momentum.

---

Did You Know?

Particle accelerators do not only help us study extremely small objects.

Accelerator technology has produced tools used in medicine, industry, chemistry, biology, materials science, and engineering.

Only a relatively small fraction of the world's particle accelerators are dedicated to high-energy particle physics.

Many are used for practical research, manufacturing, and healthcare.

---

Connecting the Ideas

Particle accelerators bring together many concepts from this course:

Charged particles

↓

Electric fields increase energy

↓

Magnetic fields steer and focus

↓

High-energy particle beams

↓

Collisions

↓

E = mc² allows new particles to be created

↓

Unstable particles decay

↓

Detectors measure the products

↓

Conservation laws help reconstruct the interaction

↓

New particles and physical laws can be investigated

The accelerator and detector therefore work together as one experimental system.

---

Key Terms

Particle accelerator – A machine that increases the energy of charged particles.

Linear accelerator (linac) – An accelerator in which particles travel mainly along a straight path.

Synchrotron – A circular accelerator in which magnetic fields and accelerating systems are synchronized with the particles.

Electric field – A field that can exert a force and do work on charged particles.

Magnetic field – A field used to bend and focus moving charged particles.

Particle beam – A directed group of high-energy particles.

Collider – An accelerator designed to bring two particle beams into collision.

Fixed-target experiment – An experiment in which an accelerated beam strikes a stationary target.

Particle detector – Equipment used to measure particles produced in interactions.

Calorimeter – A detector designed to measure particle energy.

Tracking detector – A detector that records the paths of charged particles.

Large Hadron Collider (LHC) – A large particle collider at CERN used to study high-energy particle interactions.

Higgs boson – A particle associated with the Higgs field, discovered at the LHC in 2012.

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Key Takeaways

• Particle accelerators increase the energy of charged particles.
• Scientists use accelerators to investigate matter at extremely small scales and to create new particles.
• Electric fields increase particle energy.
• Magnetic fields steer and focus moving charged particles.
• Linear accelerators move particles mainly along straight paths, while circular accelerators allow repeated acceleration.
• High-energy collisions can convert kinetic energy into the mass-energy of new particles.
• Colliders allow more energy to be available for particle production than comparable fixed-target experiments.
• Particle detectors identify particles using information such as tracks, charge, momentum, and energy.
• Tracking detectors, calorimeters, and muon systems perform different roles.
• Neutrinos are often identified indirectly through missing energy and momentum.
• Particle accelerators have contributed to major discoveries, including the W and Z bosons and the Higgs boson.
• The Large Hadron Collider is one of the most important tools for testing the Standard Model and searching for new physics.
• Accelerator technology also has important applications in medicine, industry, and materials research.