Quarks and the Strong Force

The six quarks

Common hadrons

JavaScript — quarks and strong force

// Common hadrons and their compositions
const hadrons = {
  'proton': { content: 'uud', mass_MeV: 938.3, charge: +1 },
  'neutron': { content: 'udd', mass_MeV: 939.6, charge: 0 },
  'pion+': { content: 'ud̄', mass_MeV: 139.6, charge: +1 },
  'pion-': { content: 'dū', mass_MeV: 139.6, charge: -1 },
  'pion0': { content: '(uū − dd̄)/√2', mass_MeV: 135, charge: 0 },
  'kaon+': { content: 'us̄', mass_MeV: 493.7, charge: +1 },
  'lambda': { content: 'uds', mass_MeV: 1115.7, charge: 0 },
  'JPsi': { content: 'cc̄', mass_MeV: 3097, charge: 0 },
  'upsilon': { content: 'bb̄', mass_MeV: 9460, charge: 0 }
};

// Quark masses
const m_u = 2.2;
const m_d = 4.7;

// Proton: 2 up + 1 down
const m_proton_quarks = 2 * m_u + m_d;
console.log(`Proton from quark masses: ${m_proton_quarks} MeV`);
console.log(`Proton actual mass: 938.3 MeV`);
console.log(`From QCD binding: ${(938.3 - m_proton_quarks).toFixed(0)} MeV (~99% of total)`);

// Asymptotic freedom: strong coupling at different scales
function alphaStrong(Q_GeV) {
  // Approximate running of α_s with energy scale Q
  // α_s(M_Z = 91 GeV) ≈ 0.118
  const Lambda_QCD = 0.21;  // GeV (proxy for QCD scale)
  return 12 * Math.PI / (33 * Math.log(Math.pow(Q_GeV/Lambda_QCD, 2)));
  // 33 = 11·3 - 2·6 (33 = 11·N_c - 2·N_f); approximate
}

console.log(`α_s at 1 GeV: ~1 (strong coupling)`);
console.log(`α_s at 100 GeV: ~0.12`);
console.log(`α_s at 1000 GeV (LHC): ~0.09`);
// Asymptotic freedom — weaker at higher Q

// Confinement: linear potential
function quarkPotential_LinearTerm(separation_fm) {
  // V(r) ≈ σ·r where σ ~ 1 GeV/fm (string tension)
  const sigma = 1;  // GeV/fm
  return sigma * separation_fm;
}

console.log(`Energy at 1 fm: ${quarkPotential_LinearTerm(1)} GeV`);
console.log(`Energy at 2 fm: ${quarkPotential_LinearTerm(2)} GeV — enough to make qq̄ pair`);

// Why we see hadrons not free quarks
console.log(`To separate two quarks ~1 fm requires ~1 GeV`);
console.log(`But quark-antiquark pair production from vacuum = ~280 MeV (light pion)`);
console.log(`So instead of separating quarks, vacuum creates pair → hadronization`);

Where this matters

• Particle physics. Standard Model, hadron physics, scattering experiments.
• Nuclear physics. Nucleon-nucleon binding, fission, fusion.
• Cosmology. Quark-gluon plasma in early universe; phase transitions.
• Heavy-ion physics. RHIC, LHC create quark-gluon plasma — recreate early universe conditions.
• Astrophysics. Neutron stars may have quark matter cores; pulsar physics.
• Cosmic rays. High-energy nuclei interact via strong force in atmospheric showers.
• Lattice QCD. Computational physics calculates hadron properties from first principles.

Common mistakes

• Confusing quark color with visible colors. Color charge is named arbitrarily; nothing to do with light. Three values labeled R, G, B.
• Treating quark mass as proton mass source. Proton has 2u + 1d → ~9.1 MeV from quarks. Proton actually 938 MeV. ~99% from QCD binding (gluon energy).
• Believing free quarks can be isolated. Confinement prevents this. Pulling two quarks apart creates new quark-antiquark pair from vacuum — never separated.
• Confusing strong force with strong nuclear force. Same thing. "Strong nuclear" emphasizes nuclei; "strong force" is fundamental between quarks.
• Forgetting asymptotic freedom. Counter-intuitive: stronger at low energy, weaker at high energy. Different from EM.
• Treating hadrons as quark-only. Most of hadron mass is gluon binding energy, not quark rest mass. Plus virtual quark-antiquark "sea" inside.