Fundamental Particles and Interactions
2. Quarks
Learning Outcomes
- I can identify the six types of quarks.
- I can describe the charges of quarks.
- I can explain how quarks combine to form baryons and mesons.
- I can determine the composition of simple hadrons.
- I can explain why quarks are never found in isolation.
- Wave functions and probability density
- Potential wells and quantized energy states
Quarks
Quarks are among the most fundamental known building blocks of matter.
Ordinary matter appears to be made from atoms, and atoms contain:
- electrons
- protons
- neutrons
Electrons are considered elementary particles, but protons and neutrons are not. They contain even smaller particles:
quarks
Quarks are elementary particles, meaning that current experiments have found no smaller internal structure within them.
The Six Quarks
There are six known types of quarks.
Different types of quarks are called:
flavours
The six flavours are:
- up
- down
- charm
- strange
- top
- bottom
They are often represented by the symbols:
| Quark | Symbol |
|---|---|
| Up | u |
| Down | d |
| Charm | c |
| Strange | s |
| Top | t |
| Bottom | b |
These six quarks are elementary particles in the Standard Model.
Three Generations of Quarks
The six quarks are organized into three generations.
| Generation | Quarks |
|---|---|
| First | up, down |
| Second | charm, strange |
| Third | top, bottom |
The first generation contains the quarks found in ordinary stable matter.
Protons and neutrons are constructed mainly from:
up and down quarks
The heavier quarks are usually produced in:
- high-energy particle collisions
- cosmic-ray interactions
- high-energy particle decays
They are unstable and eventually decay into lighter particles.
Up Quark
The up quark is one of the lightest quarks.
Symbol:
u
Electric charge:
+2/3 e
where e represents the magnitude of the elementary electric charge.
Up quarks are important components of both:
- protons
- neutrons
Down Quark
The down quark is another first-generation quark.
Symbol:
d
Electric charge:
−1/3 e
Down quarks also occur in:
- protons
- neutrons
Together, up and down quarks form the basic building blocks of atomic nuclei.
Charm and Strange Quarks
The second generation contains:
charm (c)
and:
strange (s)
Their charges are:
charm:
+2/3 e
strange:
−1/3 e
Particles containing strange or charm quarks can be produced in high-energy interactions but are generally unstable.
Top and Bottom Quarks
The third generation contains:
top (t)
and:
bottom (b)
Their charges are:
top:
+2/3 e
bottom:
−1/3 e
The top quark is exceptionally massive and decays extremely rapidly.
Quark Charges
Quarks have unusual fractional electric charges.
There are two charge groups.
+2/3 e quarks
- up
- charm
- top
−1/3 e quarks
- down
- strange
- bottom
A useful pattern is:
u, c, t → +2/3 e
d, s, b → −1/3 e
Although individual quarks have fractional charges, the familiar hadrons we observe have whole-number electric charges.
Antiquarks
Every quark has a corresponding:
antiquark
An antiquark has:
- the same mass as its corresponding quark
- opposite electric charge
- opposite values of certain other quantum properties
For example:
up quark:
u = +2/3 e
up antiquark:
ū = −2/3 e
Down quark:
d = −1/3 e
down antiquark:
d̄ = +1/3 e
Quarks Form Hadrons
Quarks combine to form composite particles called:
hadrons
The two major groups of hadrons are:
baryons
and:
mesons
Therefore:
hadrons → baryons + mesons
Baryons
A baryon is a hadron made primarily from:
three quarks
Important examples include:
- proton
- neutron
A proton contains:
uud
A neutron contains:
udd
These particles make up atomic nuclei.
The Proton
The proton consists of:
up + up + down
or:
uud
Let's calculate its electric charge.
Up quark:
+2/3 e
Second up quark:
+2/3 e
Down quark:
−1/3 e
Total:
Q = +2/3 e + 2/3 e − 1/3 e
Q = +1 e
Therefore:
proton charge = +e
The familiar +1 charge of the proton results from the combination of fractional quark charges.
The Neutron
The neutron consists of:
up + down + down
or:
udd
Calculate its charge:
up:
+2/3 e
down:
−1/3 e
down:
−1/3 e
Total:
Q = +2/3 e − 1/3 e − 1/3 e
Q = 0
Therefore:
neutron charge = 0
The neutron is neutral even though its individual quarks carry electric charge.
Proton vs Neutron
| Property | Proton | Neutron |
|---|---|---|
| Quark composition | uud | udd |
| Up quarks | 2 | 1 |
| Down quarks | 1 | 2 |
| Electric charge | +1e | 0 |
| Particle type | baryon | baryon |
| Larger family | hadron | hadron |
Changing just one quark flavour changes a neutron into a proton or vice versa.
This is important in processes such as:
beta decay
Beta Decay and Quarks
In beta-minus decay, a neutron changes into a proton.
Initially:
neutron = udd
Afterward:
proton = uud
At the quark level:
d → u
One down quark changes into an up quark through the:
weak interaction
The overall process is:
n → p + e⁻ + ν̄ₑ
This shows that nuclear processes can sometimes be understood by examining what happens to individual quarks.
Other Baryons
Protons and neutrons are not the only baryons.
Other combinations of three quarks produce particles such as:
- lambda particles
- sigma particles
- xi particles
- omega particles
Many of these contain:
- strange quarks
- charm quarks
- bottom quarks
They are generally unstable.
Worked Example: Determine the Charge
Suppose a baryon contains:
uud
Calculate:
Q = +2/3 + 2/3 − 1/3
Q = +1
Therefore, this particle has charge:
+e
This is the proton.
Worked Example: Another Baryon
Suppose a baryon contains:
ddd
Each down quark has charge:
−1/3 e
Therefore:
Q = −1/3 − 1/3 − 1/3
Q = −1 e
So a ddd baryon has charge:
−e
An example is the Δ⁻ particle.
Worked Example: uuu
Suppose a baryon contains:
uuu
Each up quark has:
+2/3 e
Therefore:
Q = +2/3 + 2/3 + 2/3
Q = +2 e
A uuu baryon therefore has electric charge:
+2e
An example is the Δ⁺⁺ particle.
Mesons
The second major group of hadrons is:
mesons
A meson consists primarily of:
one quark + one antiquark
Symbolically:
q q̄
Unlike baryons, mesons do not contain three valence quarks.
Pions
An important family of mesons is the:
pions
Examples include:
- π⁺
- π⁰
- π⁻
A π⁺ can be represented as:
u d̄
Calculate its charge:
u = +2/3 e
d̄ = +1/3 e
Therefore:
Q = +2/3 + 1/3
Q = +1 e
So:
π⁺ charge = +e
Negative Pion
A π⁻ can be represented as:
d ū
Charges:
d = −1/3 e
ū = −2/3 e
Therefore:
Q = −1/3 − 2/3
Q = −1 e
Thus:
π⁻ charge = −e
Neutral Pions
Neutral mesons can also form.
The π⁰ is a quantum combination involving:
uū and dd̄
Each quark-antiquark pair has zero net electric charge.
Therefore:
π⁰ charge = 0
A neutral particle does not necessarily mean that all of its constituents are electrically neutral.
Kaons
Another important group of mesons is:
kaons
Kaons contain a strange quark or strange antiquark together with an up or down quark/antiquark.
For example:
K⁺ = u s̄
Charges:
u = +2/3 e
s̄ = +1/3 e
Total:
+1 e
Kaons played an important historical role in the discovery of:
strangeness
Baryons vs Mesons
| Feature | Baryons | Mesons |
|---|---|---|
| Valence structure | 3 quarks | quark + antiquark |
| Examples | proton, neutron | pion, kaon |
| Composite? | Yes | Yes |
| Hadrons? | Yes | Yes |
| Strong interaction? | Yes | Yes |
Both baryons and mesons are:
hadrons
Valence Quarks
The simple descriptions:
proton = uud
and:
neutron = udd
refer to their:
valence quarks
The real internal structure of a proton or neutron is more complicated.
Inside a proton, for example, there are also:
- gluons
- temporary quark-antiquark pairs
- complex quantum fields
Therefore, uud describes the valence-quark content that determines many of the proton's key quantum properties.
The Strong Interaction
What holds quarks together?
The answer is:
the strong interaction
This is one of the four fundamental interactions of nature.
At the quark level, the strong interaction is described by:
quantum chromodynamics
usually abbreviated:
QCD
The elementary bosons associated with this interaction are:
gluons
Gluons
Gluons bind quarks together inside hadrons.
They continually interact with quarks and with other gluons.
The strong interaction is extremely powerful at the scales found inside hadrons.
This is why quarks cannot simply escape from a proton or neutron.
Colour Charge
Quarks possess a quantum property called:
colour charge
The three labels are commonly called:
- red
- green
- blue
These names do not refer to actual visible colours.
They are simply labels for different forms of the charge involved in the strong interaction.
Antiquarks carry corresponding:
anticolours
Colour-Neutral Hadrons
Observable hadrons are:
colour neutral
For a baryon, the three quarks combine their colour charges to produce an overall colour-neutral state.
A simplified picture is:
red + green + blue → colour neutral
For a meson:
colour + corresponding anticolour → colour neutral
This colour structure is a key feature of QCD.
Why Quarks Are Never Found Alone
Experiments have never observed a free isolated quark.
Instead, quarks appear confined inside:
hadrons
This phenomenon is called:
quark confinement
It results from the unusual behaviour of the strong interaction.
Quark Confinement
For familiar forces such as gravity and electromagnetism, the force generally becomes weaker as objects move farther apart.
The strong interaction between quarks behaves differently.
As quarks are pulled apart, the energy stored in the strong field increases.
Eventually, enough energy is available to produce:
a new quark-antiquark pair
rather than releasing a single isolated quark.
A Useful Analogy
Imagine two quarks connected by something resembling an increasingly stretched elastic band.
As they separate:
stored energy increases
Eventually, instead of producing an isolated quark, enough energy exists to create:
new quark + new antiquark
The original system then becomes two colour-neutral hadrons.
The analogy is imperfect, but it illustrates why simply pulling harder does not release a single quark.
String Breaking
The process can be represented conceptually as:
q — q̄
Pull apart:
q ————— q̄
Energy increases.
Eventually:
energy → new q + q̄
The system rearranges into new hadrons.
This process is sometimes called:
string breaking
or is discussed as part of:
hadronization
Hadronization
In high-energy particle collisions, quarks can be produced with enormous energies.
However, detectors do not normally observe isolated quarks flying away.
Instead, the quarks produce groups of hadrons.
This process is called:
hadronization
Particle detectors often observe these hadrons as:
particle jets
rather than isolated quarks.
Particle Jets
High-energy experiments such as those conducted at particle accelerators can produce energetic quarks.
Because the quarks cannot remain isolated, they generate showers of hadrons.
These appear in detectors as:
jets
Scientists analyze these jets to infer information about the original:
- quarks
- gluons
- particle interactions
Thus we can obtain evidence for quarks even though isolated quarks are not directly observed.
Evidence for Quarks
If quarks cannot be isolated, how do scientists know they exist?
Evidence comes from many experiments.
One particularly important source was:
deep inelastic scattering
High-energy electrons were fired at protons.
The scattering patterns suggested that protons contained smaller, point-like components.
These components were identified with:
quarks
This was conceptually similar to Rutherford's use of scattering to investigate atomic structure.
Quarks and Proton Mass
An interesting result of modern particle physics is that the masses of the three valence quarks account for only a small fraction of the proton's total mass.
Much of the proton's mass-energy comes from:
- quark motion
- gluon fields
- strong-interaction energy
This is an important example of:
E = mc²
The mass of a composite object can include energy stored within its interacting system.
Quark Masses
The six quarks have very different masses.
In general:
up and down → very light
strange → heavier
charm → much heavier
bottom → heavier still
top → extremely massive
The top quark is the most massive known elementary particle.
It decays so rapidly that it does not normally have time to form ordinary hadrons.
Quark Transformations
Quark flavour can change through the:
weak interaction
For example, in beta-minus decay:
down quark → up quark
This changes:
neutron → proton
The strong interaction binds quarks together but does not produce this particular flavour-changing process.
The weak interaction allows quarks to change flavour.
Strong vs Weak Interaction
It is useful to distinguish these roles.
Strong interaction
Primarily:
binds quarks inside hadrons
Associated boson:
gluon
Weak interaction
Can:
change quark flavour
Associated bosons:
W⁺, W⁻, Z
Both are essential for understanding particle behaviour.
Determining Hadron Composition
Quark charges allow us to predict possible hadron charges.
Remember:
u, c, t = +2/3 e
d, s, b = −1/3 e
Antiquarks have the opposite charges.
For a baryon:
add three quark charges
For a meson:
add quark + antiquark charges
Worked Example: uds
Consider a baryon:
uds
Charges:
u = +2/3
d = −1/3
s = −1/3
Total:
Q = +2/3 − 1/3 − 1/3
Q = 0
Therefore the particle is electrically neutral.
A well-known uds baryon is the:
Λ⁰ (lambda) particle
Worked Example: uus
Consider:
uus
Charges:
+2/3 + 2/3 − 1/3
Total:
+1
Therefore:
Q = +e
This quark combination occurs in the:
Σ⁺ particle
Worked Example: u s̄
Consider the meson:
u s̄
Charges:
u = +2/3
s̄ = +1/3
Total:
+1
Therefore:
Q = +e
This is the quark composition of:
K⁺
Worked Example: d s̄
Consider:
d s̄
Charges:
d = −1/3
s̄ = +1/3
Total:
0
Therefore the meson is electrically neutral.
This composition is associated with a neutral kaon state.
Matter Built from Quarks
The hierarchy of ordinary matter can be represented as:
matter
↓
atoms
↓
nucleus + electrons
↓
protons + neutrons
↓
quarks
For ordinary atomic matter:
proton:
uud
neutron:
udd
electron:
elementary lepton
Therefore, most familiar matter ultimately involves:
up quarks + down quarks + electrons
Quarks and the Standard Model
The Standard Model organizes the elementary matter particles into:
quarks
and:
leptons
Quarks:
- experience the strong interaction
- have fractional electric charges
- form hadrons
Leptons:
- do not experience the strong interaction
- include electrons and neutrinos
- are not made from quarks
This distinction is fundamental to particle classification.
Common Mistakes
Mistake: Saying protons and neutrons are elementary particles.
They are composite particles made from quarks.
Mistake: Saying there are only two quarks.
There are six flavours: up, down, charm, strange, top, and bottom.
Mistake: Saying quarks have only +1, 0, or −1 charges.
Quarks have fractional charges of +2/3 e or −1/3 e.
Mistake: Saying the neutron contains neutral quarks.
Its charged quarks combine to produce zero net charge.
Mistake: Saying a proton contains uud because one quark has charge +1.
Its +1 charge comes from adding three fractional quark charges.
Mistake: Saying all hadrons contain three quarks.
Baryons contain three valence quarks; mesons contain a quark and antiquark.
Mistake: Forgetting that antiquark charges are reversed.
For example, d has −1/3 e while d̄ has +1/3 e.
Mistake: Saying colour charge refers to visible colour.
Red, green, and blue are labels for quantum properties.
Mistake: Saying quarks can simply be pulled out of a proton.
Quark confinement prevents isolated quarks from normally being produced.
Mistake: Saying no evidence exists for quarks because isolated quarks cannot be observed.
Scattering experiments, particle jets, hadron properties, and many other measurements provide strong evidence for quarks.
Key Terms
Quark — elementary particle that participates in the strong interaction and combines with other quarks to form hadrons.
Quark flavour — type of quark: up, down, charm, strange, top, or bottom.
Up quark (u) — first-generation quark with charge +2/3 e.
Down quark (d) — first-generation quark with charge −1/3 e.
Antiquark — antimatter counterpart of a quark, with opposite electric charge and other opposite quantum properties.
Hadron — composite particle made from quarks and subject to the strong interaction.
Baryon — hadron containing three valence quarks.
Meson — hadron containing a valence quark and antiquark.
Valence quarks — quarks used to describe the main quantum properties and identity of a hadron.
Gluon — elementary boson associated with the strong interaction between quarks.
Strong interaction — fundamental interaction responsible for binding quarks inside hadrons.
Quantum chromodynamics (QCD) — theory describing the strong interaction between quarks and gluons.
Colour charge — quantum property involved in the strong interaction.
Quark confinement — phenomenon that prevents quarks from normally being observed as isolated particles.
Hadronization — process through which energetic quarks and gluons form colour-neutral hadrons.
Particle jet — narrow collection of particles produced during hadronization of energetic quarks or gluons.
Key Takeaways
- Quarks are elementary particles and fundamental constituents of matter.
- There are six quark flavours: up, down, charm, strange, top, and bottom.
- Quarks occur in three generations.
- Up, charm, and top quarks have charge +2/3 e.
- Down, strange, and bottom quarks have charge −1/3 e.
- Antiquarks have opposite electric charges to their corresponding quarks.
- Quarks combine to form particles called hadrons.
- Hadrons are divided mainly into baryons and mesons.
- Baryons contain three valence quarks.
- Mesons contain a valence quark and antiquark.
- A proton has quark composition uud.
- The proton's quark charges add to +1e.
- A neutron has quark composition udd.
- The neutron's quark charges add to 0.
- The simple uud and udd descriptions refer to valence quarks; the internal structure also contains gluons and quark-antiquark activity.
- Quarks interact through the strong interaction.
- Gluons are associated with the strong interaction between quarks.
- Quarks possess a quantum property called colour charge.
- Observable hadrons are colour neutral.
- Quarks have never been observed as isolated particles because of quark confinement.
- Pulling quarks apart increases the energy in the strong field until new quark-antiquark pairs can be produced.
- High-energy quarks therefore produce hadrons and particle jets rather than appearing as isolated particles.
- Quark flavour can change through the weak interaction, as occurs during beta decay.
- Most ordinary matter is ultimately constructed from up quarks, down quarks, and electrons.
Check Your Understanding
- What is a quark?
- Name the six quark flavours.
- Which quarks belong to the first generation?
- Which three quarks have charge +2/3 e?
- Which three quarks have charge −1/3 e?
- What is an antiquark?
- What is a hadron?
- Explain the difference between a baryon and a meson.
- State the quark composition of a proton.
- Use quark charges to show why the proton has charge +1e.
- State the quark composition of a neutron.
- Use quark charges to show why the neutron has zero electric charge.
- Determine the charge of a baryon with quark composition ddd.
- Determine the charge of a baryon with quark composition uuu.
- A meson contains u and d̄. Calculate its electric charge.
- What role do gluons play inside hadrons?
- What is meant by colour charge?
- Explain what is meant by quark confinement.
- Why does pulling two quarks apart not normally produce isolated quarks?
- Explain how particle jets and scattering experiments provide evidence for quarks even though individual isolated quarks have never been observed.