Particle Interactions
2. Particle Decays
Learning outcomes
- I can describe common particle decay processes.
- I can interpret particle decay equations.
- I can identify particles produced during decay.
- I can apply conservation laws to particle decays.
- I can compare nuclear decay and particle decay.
What Is Particle Decay?
Many particles in nature are unstable. An unstable particle can spontaneously transform into other particles.
This process is called particle decay.
The original particle is called the parent particle, while the particles produced are called decay products or daughter particles.
A general decay can be represented as:
Parent particle → decay products
For example, a free neutron can undergo beta decay:
n → p + e⁻ + ν̄ₑ
The neutron is the parent particle.
The products are:
- a proton
- an electron
- an electron antineutrino
Why Do Particles Decay?
A particle can decay when there is an allowed lower-energy combination of particles into which it can transform.
The decay must satisfy fundamental conservation laws.
These include:
- conservation of energy
- conservation of momentum
- conservation of electric charge
- conservation of angular momentum
- applicable particle quantum-number conservation laws
For the introductory reactions in this course, we will pay particular attention to:
charge
baryon number
lepton number
A particle cannot simply decay into any combination of particles.
Reading a Particle Decay Equation
Consider:
n → p + e⁻ + ν̄ₑ
The arrow means:
"decays into"
So we read this equation as:
A neutron decays into a proton, an electron, and an electron antineutrino.
The particle on the left is the parent.
The particles on the right are the products.
Common Symbols in Particle Decays
| Particle | Symbol | Charge |
|---|---|---|
| Proton | p | +1 |
| Neutron | n | 0 |
| Electron | e⁻ | −1 |
| Positron | e⁺ | +1 |
| Electron neutrino | νₑ | 0 |
| Electron antineutrino | ν̄ₑ | 0 |
| Muon | μ⁻ | −1 |
| Antimuon | μ⁺ | +1 |
| Muon neutrino | νμ | 0 |
| Muon antineutrino | ν̄μ | 0 |
| Photon | γ | 0 |
Recognizing these symbols makes particle-decay equations much easier to interpret.
Neutron Beta Decay
One of the most important particle decays is the decay of a free neutron.
A free neutron is unstable and can undergo beta-minus decay:
n → p + e⁻ + ν̄ₑ
At the quark level:
neutron = udd
proton = uud
One down quark changes into an up quark.
This transformation occurs through the weak interaction.
Beta Decay at the Quark Level
The process can be represented as:
d → u + W⁻
The W⁻ boson then decays:
W⁻ → e⁻ + ν̄ₑ
The overall result is:
n → p + e⁻ + ν̄ₑ
This is an important example of a particle changing identity through the weak interaction.
Applying Conservation Laws to Neutron Decay
Consider:
n → p + e⁻ + ν̄ₑ
We can check the reaction systematically.
| Quantity | Before | After |
|---|---|---|
| Charge | 0 | +1 − 1 + 0 = 0 |
| Baryon number | +1 | +1 + 0 + 0 = +1 |
| Lepton number | 0 | 0 + 1 − 1 = 0 |
All three quantities are conserved.
Therefore, the reaction passes these conservation tests.
Why Is the Antineutrino Important?
Imagine writing neutron decay incorrectly as:
n → p + e⁻
Charge works:
0 = +1 − 1
Baryon number also works:
+1 = +1
But lepton number does not.
Before:
L = 0
After:
L = +1
Adding an electron antineutrino fixes the problem because:
L(ν̄ₑ) = −1
Therefore:
+1 + (−1) = 0
The antineutrino is an essential part of the reaction.
Muon Decay
The muon is a heavier relative of the electron.
A negative muon can decay through the weak interaction:
μ⁻ → e⁻ + ν̄ₑ + νμ
The products are:
- electron
- electron antineutrino
- muon neutrino
Checking Muon Decay
Consider:
μ⁻ → e⁻ + ν̄ₑ + νμ
Charge
Before:
−1
After:
−1 + 0 + 0 = −1
Charge is conserved.
Baryon Number
All particles involved are leptons.
Therefore:
B = 0 before and after
Total Lepton Number
Before:
Muon:
L = +1
After:
Electron:
+1
Electron antineutrino:
−1
Muon neutrino:
+1
Total:
+1 − 1 + 1 = +1
Lepton number is conserved.
Tau Decay
The tau is even heavier than the muon and is also unstable.
It can decay through several different pathways.
One possible decay is:
τ⁻ → e⁻ + ν̄ₑ + ντ
Another is:
τ⁻ → μ⁻ + ν̄μ + ντ
The tau can also decay into combinations involving hadrons.
This illustrates an important feature of particle physics:
One unstable particle can have several possible decay channels.
What Is a Decay Channel?
A decay channel is one possible set of products that can result from the decay of a particle.
For example, the tau particle has several decay channels.
A particular decay does not produce all possible channels simultaneously. Each individual tau follows one allowed pathway.
Different channels occur with different probabilities.
The probability of a particular decay channel is described by its branching fraction or branching ratio.
Pion Decay
Pions are particles called mesons.
A charged pion can decay through the weak interaction.
For example:
π⁺ → μ⁺ + νμ
The positive pion has charge:
+1
The antimuon has charge:
+1
The neutrino has charge:
0
Therefore:
+1 = +1 + 0
Charge is conserved.
What Is a Pion Made Of?
The positive pion is a meson with valence quark structure:
π⁺ = u d̄
Because it contains a quark and an antiquark:
B = +⅓ − ⅓ = 0
Therefore, the pion has baryon number:
B = 0
The decay products also have total baryon number zero.
Particle-Antiparticle Annihilation
Annihilation is not technically the spontaneous decay of a single particle, but it is an important particle transformation.
For example:
e⁻ + e⁺ → γ + γ
An electron and positron annihilate and produce photons.
Charge
Before:
−1 + 1 = 0
After:
0
Lepton number
Before:
+1 − 1 = 0
After:
0
Baryon number
0 before and after
The reaction conserves all three.
The energy and momentum of the electron and positron are transferred to the photons.
Decay and Mass-Energy
Particle decay is closely connected to mass-energy equivalence.
A parent particle can decay into products whose combined rest mass is lower than the rest mass of the parent, with the remaining energy appearing as kinetic energy or other forms of energy.
The available energy is related to:
Q = (minitial − mfinal)c²
For a spontaneous decay:
Q > 0
must be satisfied.
In other words, the decay must be energetically possible.
Example: Why Can't an Electron Decay into a Neutron?
Imagine the proposed reaction:
e⁻ → n + νₑ
Check the charge:
Before:
−1
After:
0
Charge is not conserved.
It therefore cannot occur.
It also violates baryon number:
Before:
B = 0
After:
B = +1
So the reaction fails multiple conservation laws.
Example: A Reaction That Passes Some Tests but Still Fails
Consider:
p → n + e⁺ + νₑ
Charge is conserved.
Baryon number is conserved.
Lepton number is conserved.
However, a free proton cannot spontaneously undergo this decay.
Why?
Because the neutron and positron together have more rest mass than the proton.
There is not enough initial energy.
In suitable nuclei, however, the overall nuclear energy difference can allow beta-plus decay.
This demonstrates an important principle:
Conservation of charge, baryon number, and lepton number is necessary, but not sufficient.
Energy and momentum must also be conserved.
Nuclear Decay vs Particle Decay
The terms nuclear decay and particle decay are related but not identical.
Nuclear Decay
Nuclear decay involves an unstable atomic nucleus.
Examples include:
- alpha decay
- beta decay
- gamma decay
Particle Decay
Particle decay involves an unstable subatomic particle transforming into other particles.
Examples include:
- neutron decay
- muon decay
- tau decay
- pion decay
Comparing Nuclear and Particle Decay
| Feature | Nuclear Decay | Particle Decay |
|---|---|---|
| Initial object | Atomic nucleus | Subatomic particle |
| Example | ¹⁴C → ¹⁴N + β⁻ | μ⁻ → e⁻ + ν̄ₑ + νμ |
| Can change particle identity? | Yes | Yes |
| Conservation laws apply? | Yes | Yes |
| Energy conserved? | Yes | Yes |
| May involve weak interaction? | Yes | Yes |
| May emit photons? | Yes | Yes |
The same fundamental physics underlies both types of processes.
Nuclear Beta Decay
Consider carbon-14:
¹⁴₆C → ¹⁴₇N + e⁻ + ν̄ₑ
At the nuclear level, carbon-14 changes into nitrogen-14.
Inside the nucleus, one neutron has effectively changed into a proton:
n → p + e⁻ + ν̄ₑ
At the quark level, one down quark changes into an up quark:
d → u + W⁻
followed by:
W⁻ → e⁻ + ν̄ₑ
So the same event can be described at several different scales:
nuclear level → nucleon level → quark level
Alpha Decay Is Different
In alpha decay, a heavy nucleus emits an alpha particle:
⁴₂He
For example:
²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He
The alpha particle itself contains:
2 protons + 2 neutrons
Unlike beta decay, alpha decay does not involve a neutron changing into a proton or vice versa.
Instead, a preformed or dynamically formed cluster of nucleons escapes from the nucleus through quantum tunnelling.
Gamma Decay
A nucleus can also exist in an excited energy state.
It can move to a lower-energy state by emitting a photon:
Nucleus → Nucleus + γ*
The asterisk indicates an excited nucleus.
During gamma decay:
proton number does not change
neutron number does not change
mass number does not change
Only the nuclear energy state changes.
This is similar in principle to an excited atom emitting a photon, although nuclear gamma-ray energies are typically much greater than ordinary atomic photon energies.
Particle Lifetimes
Different unstable particles survive for very different amounts of time.
Some particles decay extremely quickly.
Others survive much longer.
The average time before a particle decays is related to its mean lifetime.
For a large collection of identical unstable particles, the number remaining decreases approximately exponentially with time.
This is similar to radioactive decay of unstable nuclei.
However, it is impossible to predict exactly when one particular unstable particle will decay.
Quantum mechanics predicts the probability of decay.
Decay Products and Missing Particles
Conservation laws can help identify an unknown product.
Suppose:
μ⁻ → e⁻ + ν̄ₑ + X
What is X?
The muon begins with:
Q = −1
B = 0
L = +1
The electron and electron antineutrino give:
Charge:
−1 + 0 = −1
Lepton number:
+1 − 1 = 0
Therefore X must have:
Q = 0
B = 0
L = +1
For the known muon decay, the required particle is:
νμ
Therefore:
μ⁻ → e⁻ + ν̄ₑ + νμ
A Reliable Method for Analyzing Particle Decays
When given a decay equation, use this process.
Step 1: Identify the parent particle
Look at the particle on the left side of the arrow.
Step 2: Identify the products
List every particle on the right.
Step 3: Check electric charge
Qbefore = Qafter
Step 4: Check baryon number
Bbefore = Bafter
Step 5: Check lepton number
Lbefore = Lafter
Step 6: Consider mass-energy
The products must be energetically accessible from the initial state.
Step 7: Remember momentum
Momentum must also be conserved.
If one of these required conditions fails, the proposed decay cannot occur as written.
Common Decays to Recognize
| Process | Simplified Equation |
|---|---|
| Free neutron beta decay | n → p + e⁻ + ν̄ₑ |
| Muon decay | μ⁻ → e⁻ + ν̄ₑ + νμ |
| Positive pion decay | π⁺ → μ⁺ + νμ |
| Nuclear beta-minus decay | ᴬZX → ᴬZ+1Y + e⁻ + ν̄ₑ |
| Nuclear beta-plus decay | ᴬZX → ᴬZ−1Y + e⁺ + νₑ |
| Alpha decay | ᴬZX → ᴬ⁻⁴Z−2Y + ⁴₂He |
| Gamma decay | X* → X + γ |
You do not necessarily need to memorize every possible particle decay. More importantly, you should be able to interpret the equation and test whether the relevant quantities are conserved.
Did You Know?
Many particles discovered in particle accelerators exist for such short times that they cannot be observed directly travelling through a detector.
Instead, physicists identify them from their decay products.
If a short-lived particle produces several detectable particles, physicists can measure the products' energies and momenta and reconstruct the properties of the original particle.
In this sense, particle physicists often discover particles by examining what they leave behind.
Connecting the Ideas
Particle decay connects many of the concepts studied so far:
Unstable particle
↓
Possible lower-energy state
↓
Particle transformation
↓
Decay products produced
↓
Charge, baryon number and lepton number checked
↓
Energy and momentum conserved
↓
Allowed decay
At an even deeper level, many particle decays can be explained through the fundamental interactions and transformations of quarks and leptons.
Key Terms
Particle decay – The spontaneous transformation of an unstable particle into other particles.
Parent particle – The original unstable particle before decay.
Decay product – A particle produced during a decay.
Decay channel – One possible set of products from the decay of a particle.
Branching fraction – The fraction or probability of decays that follow a particular decay channel.
Nuclear decay – A spontaneous transformation involving an unstable atomic nucleus.
Beta decay – A weak-interaction process involving changes between protons and neutrons.
Gamma decay – The release of excess nuclear energy through emission of a gamma-ray photon.
Conservation law – A rule requiring a physical quantity to remain balanced during an interaction.
Lifetime – A measure of how long an unstable particle typically exists before decaying.
Key Takeaways
- Particle decay occurs when an unstable particle spontaneously transforms into other particles.
- The original particle is the parent, while the resulting particles are the decay products.
- Particle decay equations show the parent on the left and the products on the right.
- Particle decays must obey conservation of electric charge, energy, momentum, angular momentum, and applicable particle quantum numbers.
- Baryon and lepton numbers provide useful tests for many introductory particle reactions.
- A free neutron can decay through n → p + e⁻ + ν̄ₑ.
- Muons, taus, pions, and many other particles are unstable and undergo characteristic decay processes.
- The weak interaction is responsible for many particle transformations.
- Nuclear decay involves an unstable nucleus, while particle decay involves an unstable subatomic particle.
- Nuclear beta decay can be understood at the nuclear, nucleon, and quark levels.
- Conservation laws can be used to identify missing particles in decay equations.
- Passing charge, baryon-number, and lepton-number tests does not by itself guarantee a decay is possible; the decay must also satisfy energy and momentum requirements.
- Studying decay products is one of the main ways physicists identify and investigate short-lived particles.