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This article explains quarks and the Higgs boson, shows how the Higgs field gives quarks mass, and lists what measurements and open problems matter today.
1. The Standard Model in one page
The Standard Model is a quantum field theory for known particles and forces except gravity.
| Category | Fields | Role |
|---|---|---|
| Gauge bosons | Gluon g, Photon γ, W±, Z0 | Force carriers for strong, electromagnetic, and weak forces. |
| Fermions | Quarks and leptons in three generations. | Constituents of matter. |
| Scalar | Higgs H | Spontaneous symmetry breaking and mass generation. |
2. Quark flavors, charges, and typical masses
Quarks are spin-1/2 fermions that carry color charge and electric charge.
| Flavor | Symbol | Electric charge | Current mass (≈, MeV/GeV) | Notes |
|---|---|---|---|---|
| Up | u | +2/3 e | ≈ 2.2 MeV | Light quark. |
| Down | d | −1/3 e | ≈ 4.7 MeV | Light quark. |
| Strange | s | −1/3 e | ≈ 96 MeV | Light but heavier than u, d. |
| Charm | c | +2/3 e | ≈ 1.28 GeV | Heavy quark. |
| Bottom | b | −1/3 e | ≈ 4.18 GeV | Heavy quark. |
| Top | t | +2/3 e | ≈ 172.7 GeV | Heaviest quark. |
Caution: Numerical quark masses depend on renormalization scheme and energy scale. Treat values above as order-of-magnitude references.
Quarks are never isolated due to color confinement. Quarks form hadrons. Baryons have three quarks. Mesons have a quark and an antiquark.
3. Most of a proton’s mass is not quark rest mass
A proton’s mass is about 938 MeV. The sum of its valence quark rest masses is only a few MeV. The remainder comes from gluon fields and kinetic energy inside quantum chromodynamics, or QCD.
4. The Higgs field and electroweak symmetry breaking
The electroweak symmetry SU(2)L×U(1)Y breaks to U(1)EM when the Higgs field acquires a vacuum expectation value v.
# Key numbers and relations
v ≈ 246 GeV.
m_W = g v / 2.
m_Z = sqrt(g^2 + g'^2) v / 2.
H(x) is the quantum excitation: the Higgs boson with m_H ≈ 125 GeV.
5. How quarks get mass: Yukawa couplings
Fermion masses arise from Yukawa interactions with the Higgs field. After symmetry breaking, each fermion’s mass is proportional to its Yukawa coupling.
# Lagrangian sketch
L_Yukawa ⊃ - y_u * Q̄_L ϕ̃ u_R - y_d * Q̄_L ϕ d_R + h.c.
# After ϕ → (0, (v + h)/√2)
m_f = y_f * v / √2.
# Example
Given v = 246 GeV:
y_t ≈ √2 * m_t / v ≈ 1.0. | Fermion | Mass (≈) | Yukawa yf (≈) |
|---|---|---|
| Top quark t | 172.7 GeV | ≈ 0.99 |
| Bottom quark b | 4.18 GeV | ≈ 0.024 |
| Charm quark c | 1.28 GeV | ≈ 0.007 |
| Strange quark s | 96 MeV | ≈ 0.00055 |
| Down quark d | 4.7 MeV | ≈ 0.000027 |
| Up quark u | 2.2 MeV | ≈ 0.000013 |
Caution: The Higgs sets quark rest masses. It does not account for binding energy inside hadrons.
6. Measuring Higgs–quark interactions at colliders
Experiments access quark–Higgs couplings through specific production and decay channels.
| Channel | What it probes | Comment |
|---|---|---|
| tt̄H production | Direct top Yukawa yt. | Large coupling makes this channel central. |
| H → bb̄ | Bottom Yukawa yb. | Largest branching ratio but challenging due to QCD background. |
| VH with H → bb̄ (V = W/Z) | yb with cleaner triggers. | Leptonic V decays aid background rejection. |
| gg → H (gluon fusion) | Top loop dominance. | Sensitive to heavy colored new particles. |
| H → γγ | Loop process with top and W contributions. | Precision tests for deviations. |
| H + jet with flavor tagging | Light-quark couplings. | Currently low sensitivity. Improving with statistics and ML tagging. |
7. Flavor mixing and the CKM matrix
Weak interactions couple quark flavor eigenstates through the CKM matrix. Magnitudes below are representative.
| d | s | b | |
|---|---|---|---|
| u | 0.974 | 0.225 | 0.0037 |
| c | 0.225 | 0.973 | 0.041 |
| t | 0.0087 | 0.040 | 0.999 |
Caution: CKM elements carry phases and uncertainties. Values above are approximate magnitudes for orientation.
8. Common misconceptions to avoid
- “The Higgs gives the proton its mass.” Incorrect. Proton mass is dominated by QCD energy, not quark rest masses.
- “Higgs discovery explains dark matter.” Incorrect. The Higgs is part of the Standard Model. Dark matter remains unexplained.
- “Quarks are seen directly.” Incorrect. Detectors infer quarks from jets and hadrons due to confinement.
9. Worked examples
9.1 Compute a Yukawa coupling from a known mass
# Input
m_b = 4.18 # GeV
v = 246.0 # GeV
# Relation
# m_f = y_f * v / √2 ⇒ y_f = √2 * m_f / v
import math
y_b = math.sqrt(2.0) * m_b / v
print(round(y_b, 3)) # ≈ 0.024 9.2 Estimate the top Yukawa
# Input
m_t = 172.7 # GeV
v = 246.0 # GeV
y_t = math.sqrt(2.0) * m_t / v
print(round(y_t, 2)) # ≈ 0.99 9.3 From Yukawa to mass
# Given y_s ≈ 5.5e-4 and v = 246 GeV
m_s = y_s * v / math.sqrt(2.0)
print(round(m_s*1e3, 0), "MeV") # ≈ 96 MeV
10. Experimental milestones
- 1995. Discovery of the top quark at the Tevatron.
- 2012. Discovery of a Higgs boson with mass ≈ 125 GeV at the LHC.
- 2018–2024. Observation and refinement of tt̄H production and H → bb̄.
- Run-2 and Run-3. Global fits favor Standard Model-like couplings within current errors.
11. What remains unknown
- Flavor puzzle. The Standard Model does not predict Yukawa values. It inputs them.
- Naturalness. Why is mH stable against large quantum corrections.
- CP violation. CKM phase is insufficient to explain the baryon asymmetry.
- Light-quark Yukawas. Direct measurements remain statistically limited.
- Is the Higgs elementary. Composite Higgs models remain viable within bounds.
12. Quick glossary
- Yukawa coupling. Dimensionless parameter linking a fermion to the Higgs field.
- Vacuum expectation value (VEV). Constant background value of a field in its lowest energy state.
- Confinement. Property of QCD that prevents isolation of color-charged states.
- Parton distribution functions (PDFs). Probability densities for partons inside protons.
- Branching ratio. Fraction of decays that follow a given channel.
FAQ
Does the Higgs boson directly bind quarks.
No. The strong force via gluons binds quarks. The Higgs sets quark rest masses through Yukawa couplings.
Why is the top quark central to Higgs physics.
Its large Yukawa dominates gluon fusion loops and allows direct yt extraction in tt̄H production.
Why are light-quark masses hard to measure.
Confinement and hadronic effects mask direct sensitivity. Lattice QCD and global fits infer values with scheme dependence.
Is most everyday mass from the Higgs.
No. Most of the mass of atoms is from QCD binding in nucleons. Electron mass is from the Higgs, but electrons contribute little to atomic mass.