Quarks
Fundamental constituents of hadrons
Introduction to Quarks
Quarks are elementary fermions that interact through the strong force described by quantum chromodynamics (QCD). They combine to form hadrons such as baryons and mesons.
General Properties
| Property | Description |
|---|---|
| Spin | \( \frac{1}{2} \) |
| Statistics | Fermi–Dirac |
| Color Charge | Red, Green, Blue |
| Isolation | Not observed freely (confinement) |
Properties of Quarks
| Flavor | Symbol | Charge | Mass (approx.) | Charm (C) | Colour | Beauty (B′) | Strangeness (S) | Baryon Number (B) |
|---|---|---|---|---|---|---|---|---|
| Up | u | +2/3 | 2.2 MeV | 0 | Red / Green / Blue | 0 | 0 | +1/3 |
| Down | d | −1/3 | 4.7 MeV | 0 | Red / Green / Blue | 0 | 0 | +1/3 |
| Strange | s | −1/3 | 96 MeV | 0 | Red / Green / Blue | 0 | −1 | +1/3 |
| Charm | c | +2/3 | 1.27 GeV | +1 | Red / Green / Blue | 0 | 0 | +1/3 |
| Bottom | b | −1/3 | 4.18 GeV | 0 | Red / Green / Blue | −1 | 0 | +1/3 |
| Top | t | +2/3 | 173 GeV | 0 | Red / Green / Blue | 0 | 0 | +1/3 |
Color Confinement
The force between quarks increases with separation distance. This leads to color confinement, preventing free quarks.
\[
V(r) \approx kr
\]
Quark Composition of Various Particles
All hadrons are made of quarks. There are two main categories:
- Baryons → Made of 3 quarks (qqq)
- Mesons → Made of 1 quark + 1 antiquark (q q̄)
1️⃣ Baryons (Three Quark States)
| Particle | Symbol | Quark Composition | Charge |
|---|---|---|---|
| Proton | p | u u d | +1 |
| Neutron | n | u d d | 0 |
| Lambda | Λ⁰ | u d s | 0 |
| Sigma Plus | Σ⁺ | u u s | +1 |
| Sigma Zero | Σ⁰ | u d s | 0 |
| Sigma Minus | Σ⁻ | d d s | −1 |
| Xi Zero | Ξ⁰ | u s s | 0 |
| Xi Minus | Ξ⁻ | d s s | −1 |
| Omega Minus | Ω⁻ | s s s | −1 |
2️⃣ Mesons (Quark–Antiquark States)
| Particle | Symbol | Quark Composition | Charge |
|---|---|---|---|
| Positive Pion | π⁺ | u d̄ | +1 |
| Negative Pion | π⁻ | d ū | −1 |
| Neutral Pion | π⁰ | (u ū − d d̄)/√2 | 0 |
| Positive Kaon | K⁺ | u s̄ | +1 |
| Negative Kaon | K⁻ | s ū | −1 |
| Neutral Kaon | K⁰ | d s̄ | 0 |
| Anti-Kaon | K̄⁰ | s d̄ | 0 |
3️⃣ Heavy Quark Hadrons
| Particle | Quark Composition | Type |
|---|---|---|
| J/ψ | c c̄ | Charmonium (Meson) |
| Υ | b b̄ | Bottomonium (Meson) |
| Lambda_c | u d c | Charmed Baryon |
| Lambda_b | u d b | Bottom Baryon |
Important Points
- All baryons have baryon number = +1
- All mesons have baryon number = 0
- Quark charges: u, c, t → +2/3 ; d, s, b → −1/3
- Antiquarks have opposite charge and quantum numbers