Weak interaction

The weak interaction or weak force is the fundamental interaction that governs the decay of elementary particles and, by extension, the decay of atoms.

The modern theory of weak force is electroweak theory (EWT), which describes the weak force in conjunction with electromagnetism. In fact, at sufficiently high energies ($\sim 246\text{ GeV}$, the electroweak scale), the two fundamental forces unify into a singular electroweak interaction. The weak interaction is an exchange interaction mediated by the W boson or the Z boson, two of the four known gauge bosons.

The weak interaction has a tiny range of only approximately $10^{-18}\text{ m}$, considerably less than even the effective radius of a proton. It is therefore relegated to subatomic interactions.

Coupling constant#

Starting from the characteristic time of beta decay, $\tau\sim10^{2}$ s, we can experimentally determine the effective Fermi coupling constant $G_{F}$:

Starting from this, we define the Fermi units of energy and length:

where $E_{F}$ is the electroweak scale (also called Fermi scale). The Fermi length $\lambda_{F}$ tells us that the effective range of weak interaction is just below $10^{-18}\text{ m}$. We take the conventional weak coupling constant $\alpha_{W}$ as

Taking the rest energy of a proton $m_{p}\sim1$ GeV, we want to find the coupling constant at this scale. This is complicated quantum field theory math; I'll just report the result:

which shows that the weak interaction is, indeed, weak on the nuclear scale.