I. Core Identity & Value

• Symbol: \( m_n \)
• Mass Value: \( 1.67492749804(95) \times 10^{-27} \text{kg} \) (2018 CODATA)
• Mass Energy: \( 939.56542052(54) \text{MeV}/c^2 \)
• Mass Difference:
  \[ \Delta m = m_n – m_p = 1.29333236(45) \text{MeV}/c^2 \]
• Composition: One up quark + two down quarks + gluons + quark-antiquark pairs
• Lifetime: 879.4(6) seconds (free neutron decay)

II. Historical Discovery

Chadwick’s Experiment: Bombarded beryllium with α-particles, detecting neutral radiation that ejected protons from paraffin wax.

III. Theoretical Significance

1. Quantum Chromodynamics (QCD)

• Mass decomposition:
  \[ m_n c^2 = \sum_{\text{quarks}} m_q + E_{\text{gluons}} + E_{\text{kinetic}} + E_{\text{EM}} \]
• Electromagnetic contribution: ≈ -0.13 MeV (vs proton’s +0.63 MeV)

2. The Mass Difference Mystery

• Origin of proton-neutron mass difference:
  \[ \Delta m = (m_d – m_u) + \delta_{\text{EM}} + \delta_{\text{QCD}} \]
• Current estimate: ≈ 70% from quark mass difference, 30% EM effects

3. Weak Interaction Physics

• Neutron β-decay: \( n \rightarrow p + e^- + \bar{\nu}_e \)
• Decay rate depends on \( m_n – m_p \) and CKM matrix element \( V_{ud} \)

IV. Precision Measurement Techniques

V. Role in Fundamental Physics

1. Standard Model Tests

• Neutron decay asymmetry measures CKM unitarity:
  \[ |V_{ud}|^2 + |V_{us}|^2 + |V_{ub}|^2 = 1 – \text{deviation} \]
• Current deviation: 0.041(9) suggests new physics

2. Neutron Electric Dipole Moment

• Current limit: |d_n| < 1.8 × 10⁻²⁶ e·cm
• Tests CP-violation beyond Standard Model

3. Quark Flavor Dynamics

• Mass difference sensitive to d-quark vs u-quark mass difference
• Lattice QCD calculations: m_d – m_u ≈ 2.5 MeV/c²

VI. Cosmic Significance

1. Big Bang Nucleosynthesis

• Freeze-out ratio at T ≈ 0.7 MeV:
  \[ \frac{n_n}{n_p} = e^{-\Delta m c^2 / k_B T} \approx \frac{1}{6} \]
• Determines primordial helium abundance: Y_p ≈ 24%

2. Stellar Evolution

• s-process nucleosynthesis (slow neutron capture)
• Neutron star formation:
  \[ R_{\text{NS}} \approx 10 \text{km} \quad ; \quad \rho \approx 4 \times 10^{17} \text{kg/m}^3 \]

3. Anthropic Constraints

• If Δm > 1.5 MeV: No neutrons survive Big Bang → no elements beyond hydrogen
• If Δm < 0.7 MeV: All hydrogen converts to helium → no water, no life
• Life-permitting range: 0.8-1.4 MeV/c²

VII. Unsolved Mysteries

1. Lifetime Discrepancy

• Bottle method: 879.4(6) s
• Beam method: 887.7(17) s
• 8-second difference (4σ) suggests unknown decay paths

2. Quark-Gluon Composition

• Precise gluonic contribution to mass still uncertain
• Role of strange quark content?

3. Gravitational Interaction

• Does gravity affect antimatter differently? (AEgIS experiment)
• Quantum gravity signatures in neutron interferometry

“The neutron is nature’s alchemist – transforming elements in stellar furnaces while walking the quantum tightrope between stability and decay.”

– Inspired by Arthur Eddington

References

1. Chadwick, J. (1932). “Possible Existence of a Neutron” (Nature)
2. Reines, F., Cowan, C.L. (1956). “Detection of the Free Neutrino” (Phys. Rev.)
3. Pattie, R.W., et al. (2018). “Neutron Lifetime Measurement” (Science)
4. Schneider, G., et al. (2021). “High-Precision Neutron Mass” (Nature Physics)
5. Workman, R.L., et al. (2022). “Review of Particle Physics” (Particle Data Group)
6. Cyburt, R.H., et al. (2016). “Big Bang Nucleosynthesis” (Rev. Mod. Phys.)