The Sun has been shining for about four and a half billion years, and it will keep going for roughly five billion more. That leisurely, planet-friendly pace is not an accident of how much fuel it holds — it is set by the weak interaction. Deep in the solar core the very first step of fusion, turning two protons into a deuteron, requires one proton to convert into a neutron: p \to n + e^+ + \nu_e. That conversion is a weak process, and it is so slow that an average proton in the core waits billions of years for its turn. If the weak force were as brisk as the electromagnetic or strong forces, the Sun would have flashed its whole fuel supply in an eye-blink and life would never have had time to appear.

This one page is about that force: what carries it, why it looks so feeble, and the two things that make it utterly unlike gravity, electromagnetism or the strong force. The weak interaction is the only force that changes one kind of particle into another — it turns a down quark into an up quark, a muon into an electron — and it is the only force that tells left from right, coupling to left-handed particles while ignoring right-handed ones. The single idea to carry away: the weak force is the flavour-changing, parity-violating interaction carried by the heavy W and Z bosons — and above about 100\ \text{GeV} it is revealed to be the same force as electromagnetism.

The messengers: heavy W and Z bosons

Every force in the Standard Model is carried by an exchanged particle. Electromagnetism sends the massless photon; the strong force sends massless gluons. The weak force is different: its carriers are enormously heavy. There are three of them, discovered at CERN in 1983 with exactly the masses the theory had predicted:

That heaviness is the whole story of why the force is "weak" and short-ranged. A virtual carrier of mass M can only be borrowed for a time set by the uncertainty principle, \Delta t \sim \hbar/(Mc^2), and in that time even light travels at most a distance

Put in the numbers with the handy constant \hbar c = 197\ \text{MeV·fm} and M_W c^2 = 80.4\ \text{GeV} = 80\,400\ \text{MeV}:

That is about a thousandth of the radius of a proton. The photon, being massless, gives r \to \infty — electromagnetism reaches across the universe. The weak force reaches barely across a fraction of a nucleon, which is why two particles must practically overlap before it can act.

The charged current: a vertex that changes flavour

Here is the single most distinctive thing the weak force does. When a particle emits or absorbs a W^\pm, its identity changes. A down quark becomes an up quark; an electron becomes an electron neutrino. No other interaction can do this — the photon, the gluon and the graviton all leave a particle's type untouched. Charge must still balance at the vertex, and the W is exactly the accountant that carries away the difference.

The textbook example is nuclear beta decay. A free neutron (quark content udd) is unstable and, after about 15 minutes on average, turns into a proton (uud):

Zoom in and only one quark actually does anything: a single down quark converts to an up quark, emitting a virtual W^- which immediately decays into the electron and antineutrino:

Let's check the books at the vertex. The down quark has charge -\tfrac{1}{3} and the up quark +\tfrac{2}{3}, so the quark's charge rose by +\tfrac{2}{3} - (-\tfrac{1}{3}) = +1. To keep charge conserved the emitted boson must carry the opposite, -1 — and indeed it is a W^-. That W^- then splits into an electron (-1) and an antineutrino (0), so -1 in equals -1 out. Every charge balances; what has changed is flavour.

The diagram below builds the process one line at a time — watch the incoming down quark turn into an up quark, throw off a W^-, and the W^- split into the two leptons we detect.

The same picture, with different particles at the vertices, powers almost everything the weak force touches: muon decay (\mu^- \to e^- + \bar{\nu}_e + \nu_\mu), the fusion that lights the Sun, and the decays of every heavy quark.

The neutral current: the Z that changes nothing but energy

The W^\pm is charged, so it must change the charge — and therefore the flavour — of whatever emits it. The Z^0 is different: it is electrically neutral, so at a Z vertex a particle emits the boson and stays exactly what it was. A neutrino comes in, exchanges a Z, and leaves as the same neutrino, merely nudged in energy and direction:

This is the weak neutral current. It sounds unremarkable, but its existence was a triumph: the electroweak theory predicted a neutral weak boson before anyone had seen one, and in 1973 the Gargamelle bubble chamber at CERN spotted neutrinos scattering off electrons with no charged particles produced — the fingerprint of a Z at work. Finding the neutral current was the first hard evidence that the weak force and electromagnetism are two faces of one thing. A useful way to keep the two vertices straight:

• Charged current (W^\pm): charge changes by \pm 1, flavour changes, an electron and a neutrino swap roles.
• Neutral current (Z^0): charge and flavour are unchanged; the particle survives, having exchanged only energy and momentum.

Parity violation: the force that tells left from right

For a long time physicists took it for granted that the laws of nature cannot tell a process from its mirror image — that parity P (reflecting all coordinates, \vec{x}\to-\vec{x}) is a perfect symmetry. Gravity, electromagnetism and the strong force all respect it. Then in 1956 Lee and Yang noticed that nobody had ever tested it for the weak force, and Chien-Shiung Wu set out to check.

In the Wu experiment, cobalt-60 nuclei were lined up by a magnetic field at a fraction of a degree above absolute zero, and the electrons from their beta decay were counted. If parity held, equal numbers should fly out along the spin and against it. Instead the electrons came out preferentially in one direction — the decay knew its own handedness. Parity is not merely bent by the weak force; it is violated maximally.

The deep reason is that the weak W couples only to the left-handed component of matter particles (and the right-handed component of antiparticles). "Handedness" here is chirality; for a fast particle it is nearly the same as helicity — whether its spin points along its motion (right-handed) or against it (left-handed). The most striking consequence is in the neutrinos:

No other force in nature makes this distinction. The weak interaction is, quite literally, the reason the universe is not left–right symmetric.

Electroweak unification: one force wearing two masks

Here is the payoff. At everyday energies electromagnetism (long-range, parity-respecting) and the weak force (ultra-short-range, parity-violating) look like total opposites. Yet in the 1960s Glashow, Salam and Weinberg showed they are a single "electroweak" force, and the difference we see is an illusion of low energy.

The unified theory starts with four massless force-carriers of one symmetric family. What we actually detect — the photon \gamma and the Z^0 — are two mixtures of the underlying neutral fields, blended by a single number, the Weinberg (weak mixing) angle \theta_W:

The same angle fixes the boson masses. The theory predicts the tidy relation

and plugging in M_W = 80.4 and M_Z = 91.2\ \text{GeV} gives \cos\theta_W \approx 0.881, i.e. \theta_W \approx 28^\circ — a value measured a dozen different ways that all agree. That a single mixing angle simultaneously sets the boson masses, the strength of the neutral current and the electron's electric charge is one of the great confirmations in physics.

Why, then, does the symmetry hide at low energy? Because the W and Z acquired their huge masses from the Higgs field, while the photon stayed massless. That mass difference is what splits one force into two faces. Push the collision energy above the boson mass scale, roughly \sqrt{s} \gtrsim 100\ \text{GeV}, and the mass becomes a negligible part of the story: the weak force stops being weak, its reach and strength climb to match electromagnetism's, and the two merge back into one. The symmetry was there all along; only at low energy is it hidden.

Worked examples

Example 1 — the range of the weak force. Estimate the reach of a force carried by the Z^0 (M_Z c^2 = 91.2\ \text{GeV}) from r \sim \hbar c/(Mc^2), using \hbar c = 197\ \text{MeV·fm}. Convert the mass to MeV: 91.2\ \text{GeV} = 91\,200\ \text{MeV}, so

A shade shorter than the W's reach, because the Z is a touch heavier. Either way, the two particles must be within a few attometres to interact at all.

Example 2 — why weak processes are slow. The strength of a low-energy weak process is governed by Fermi's constant. In a Feynman diagram the exchanged W contributes a factor g^2/(q^2 - M_W^2 c^4). At the tiny momentum transfer of beta decay (q \ll M_W c) the q^2 is negligible and this collapses to a constant:

A decay rate goes as the amplitude squared, so it scales like G_F^2 \propto (g^2/M_W^2)^2 \propto 1/M_W^4. The rate is throttled by four powers of the enormous W mass in the denominator — that, and nothing about a small coupling, is why beta decay takes minutes while a strong-force reaction takes 10^{-23}\ \text{s}.

Example 3 — the Weinberg angle from the masses. Using \cos\theta_W = M_W/M_Z with M_W = 80.4\ \text{GeV} and M_Z = 91.2\ \text{GeV}:

The measured value \sin^2\theta_W \approx 0.231 is beautifully close — the small gap is a real, calculable quantum correction, not an error. One angle ties the two masses together.