The Weak Force and Beta Decay: How Neutrons Turn Into Protons

The weak force, or weak interaction, is one of the four fundamental forces. It is the only one that can change the identity of a particle, and its best-known job is beta decay, where a neutron becomes a proton. Our character Decay Dancer is that change caught in motion. This post goes deeper than our explainer Beta Decay Unveiled into the force itself.

What does the weak force do?

The Nobel committee’s 1979 press release describes the typical process: a neutron, with zero charge, turns into a positively charged proton, giving off a negatively charged electron and a neutral particle, the neutrino (NobelPrize.org, 1979 press release^[1]). Written as a reaction, with the antineutrino that modern notation uses:

n → p + e⁻ + ν̄_e

A free neutron does this on average after 878.4 ± 0.5 s, the Particle Data Group’s 2024 average, whose error bar has been scaled up by a factor of 1.8 because individual measurements disagree more than expected (PDG 2024, neutron^[2]). Inside some proton-rich nuclei the reverse happens: a proton turns into a neutron and emits a positron and an electron neutrino. This is beta-plus decay. It needs the energy supplied by the nucleus, so a free proton does not decay this way.

The same force matters for life on Earth. The first reaction in the chain that powers the Sun, turning hydrogen into heavy hydrogen (deuterium), is caused by the weak force, and without it solar energy production would not be possible (NobelPrize.org, 1979 press release^[1]).

Who carries the weak force?

Forces between particles are carried by other particles. For the weak force these are the electrically charged W bosons and the neutral Z boson. CERN explains that by emitting a charged W, the weak force can change a particle’s charge by changing the flavour of its quarks (CERN, “The Z boson”^[3]). Our W-ZED tee is that carrier.

The history runs over half a century. Enrico Fermi put forward the first theory of the weak force, published in 1934 as “Versuch einer Theorie der β-Strahlen” (Fermi, 1934^[4]). In the 1960s Sheldon Glashow, Abdus Salam and Steven Weinberg proposed that the weak and electromagnetic forces are two faces of a single electroweak force. They shared the 1979 Nobel Prize, with the citation noting their prediction of the weak neutral current (NobelPrize.org, Physics 1979^[5]). The Gargamelle bubble chamber at CERN found the first convincing evidence for that neutral current in 1973, and the W and Z themselves were discovered at CERN’s Super Proton Synchrotron in 1983 (CERN^[3]). Carlo Rubbia and Simon van der Meer received the 1984 prize for the project that found “the field particles W and Z, communicators of weak interaction” (NobelPrize.org, Physics 1984^[6]).

Why is the weak force so weak?

CERN puts it plainly: the weak force is essentially as strong as the electromagnetic force, but it appears weak because its influence is limited by the large mass of the W and Z bosons. Their mass limits its range to about 10⁻¹⁸ metres (CERN^[3]). A simple estimate of that range uses the W mass:

R ≈ ħc / (M_Wc²)

Worked example

The W mass-energy is M_Wc² = 80.3692 GeV = 80 369.2 MeV (PDG 2024, gauge bosons^[7]), and ħc = 197.326 980 4 MeV fm (NIST, ħc^[8]). So R ≈ 197.327 / 80 369.2 ≈ 0.002 46 fm, which is 2.46 × 10⁻¹⁸ m. That matches CERN’s figure, and CERN adds that the force vanishes altogether beyond the radius of a single proton. For comparison, the Z mass is 91.1880 GeV.

Measuring the strength with a muon

The weak force’s strength at low energies is summed up by the Fermi constant, G_F. The Particle Data Group’s electroweak review gives G_F = 1.1663788(6) × 10⁻⁵ GeV⁻², derived from the muon lifetime formula (Erler & Freitas, PDG 2024^[9]). The muon is a heavier cousin of the electron that decays only through the weak force. Leaving out small corrections that the PDG includes, its decay rate Γ_μ in natural units (energies in GeV, c = 1) is

Γ_μ ≈ G_F² m_μ⁵ / (192π³)

With m_μ = 0.105 658 375 5 GeV (PDG 2024, leptons^[10]): m_μ⁵ ≈ 1.317 × 10⁻⁵ GeV⁵, G_F² ≈ 1.360 × 10⁻¹⁰ GeV⁻⁴, and 192π³ ≈ 5953. That gives Γ_μ ≈ 3.009 × 10⁻¹⁹ GeV. The lifetime is τ = ħ/Γ_μ; with ħ = ħc/c ≈ 6.582 × 10⁻²⁵ GeV s (using c = 299 792 458 m/s, NIST, c^[11]), τ ≈ 2.187 × 10⁻⁶ s. The measured muon mean life is 2.196 981 1 × 10⁻⁶ s. The leading-order estimate is less than 0.5% short, and the PDG’s full formula closes the gap.

Weak force characters

Our Decay Dancer tee shows beta-minus decay and the W-ZED tee its carrier boson; for more designs, browse our Forces collection. For the strong force that the weak force works against inside nuclei, read What Holds the Nucleus Together?.

Quick FAQ

Is the weak force really weak?

At the distances where it acts, it is about as strong as electromagnetism. It looks weak at larger distances because the heavy W and Z limit its reach.

What are the W and Z bosons?

The particles that carry the weak force: two electrically charged W bosons and one neutral Z, discovered at CERN in 1983.

Why does the weak force matter for the Sun?

The first step of the Sun’s fusion chain, making deuterium from hydrogen, needs the weak force.

References

1. NobelPrize.org, Press release: The 1979 Nobel Prize in Physics. https://www.nobelprize.org/prizes/physics/1979/press-release/
2. S. Navas et al. (Particle Data Group) (2024), Review of Particle Physics: neutron listing (mean life). https://pdg.lbl.gov/2024/listings/rpp2024-list-n.pdf
3. CERN, “The Z boson”. https://home.cern/science/physics/z-boson
4. E. Fermi (1934), “Versuch einer Theorie der β-Strahlen. I,” Zeitschrift für Physik 88, 161–177 (DOI 10.1007/BF01351864; metadata verified via Crossref). https://doi.org/10.1007/BF01351864
5. NobelPrize.org, “The Nobel Prize in Physics 1979” (S. L. Glashow, A. Salam & S. Weinberg). https://www.nobelprize.org/prizes/physics/1979/summary/
6. NobelPrize.org, “The Nobel Prize in Physics 1984” (C. Rubbia & S. van der Meer). https://www.nobelprize.org/prizes/physics/1984/summary/
7. S. Navas et al. (Particle Data Group) (2024), Review of Particle Physics: Gauge and Higgs bosons summary table. https://pdg.lbl.gov/2024/tables/rpp2024-sum-gauge-higgs-bosons.pdf
8. NIST CODATA 2022 recommended values: reduced Planck constant times c in MeV fm. https://physics.nist.gov/cgi-bin/cuu/Value?hbcmevf
9. J. Erler & A. Freitas, “Electroweak Model and Constraints on New Physics,” in S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024). https://pdg.lbl.gov/2024/reviews/rpp2024-rev-standard-model.pdf
10. S. Navas et al. (Particle Data Group) (2024), Review of Particle Physics: Leptons summary table. https://pdg.lbl.gov/2024/tables/rpp2024-sum-leptons.pdf
11. NIST CODATA 2022 recommended values: speed of light in vacuum (exact). https://physics.nist.gov/cgi-bin/cuu/Value?c

Written by Pixelated Physics. Every factual claim is linked to the source we checked; points that are still debated are labelled open.