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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.