8.10.1.3. Weak Interaction

Table of Contents

What makes the weak interaction special

The weak interaction is one of the four fundamental interactions in nature. It is responsible for processes in which one type of particle can change into another type. This is its most distinctive feature. Unlike gravity and electromagnetism, which mainly pull, push, or attract, the weak interaction can change particle identity, especially among quarks and leptons.

A familiar example is beta decay in nuclei. In beta minus decay, a neutron can turn into a proton while emitting an electron and an antineutrino. In beta plus decay, a proton can turn into a neutron while emitting a positron and a neutrino. These processes are possible because of the weak interaction.

The weak interaction acts over an extremely short range, much smaller than the size of an atom. It is much weaker than the strong interaction and electromagnetism in most everyday situations, which is why its effects are not directly obvious in daily life. Even so, it is essential in radioactivity, in the energy production of stars, and in neutrino interactions.

Particles involved in the weak interaction

The weak interaction is carried by heavy exchange particles called the $W^+$ boson, the $W^-$ boson, and the $Z^0$ boson. These are called weak gauge bosons. Because they are very massive, the weak force has a very short range.

There are two main kinds of weak processes. In charged current interactions, a $W^+$ or $W^-$ boson is exchanged. In neutral current interactions, a $Z^0$ boson is exchanged.

Charged current interactions are especially important because they allow changes in particle type. For example, a down quark can become an up quark by emitting a $W^-$ boson, or an up quark can become a down quark by emitting a $W^+$ boson. Since protons and neutrons are made of quarks, this explains how one can transform into the other.

Neutral current interactions do not change electric charge. They often appear in neutrino scattering, where a neutrino interacts through the exchange of a $Z^0$ boson.

The weak interaction is unique because it can change one flavor of particle into another.
Its force carriers are $W^+$, $W^-$, and $Z^0$.
Its range is very short because these bosons are massive.

Weak interaction and beta decay

A neutron is made of quarks with composition $udd$, and a proton has composition $uud$. In beta minus decay, one of the neutron's down quarks changes into an up quark. This changes the neutron into a proton.

At the quark level, the process is

$$
d \to u + W^-
$$

Then the $W^-$ boson quickly decays into an electron and an electron antineutrino,

$$
W^- \to e^- + \bar{\nu}_e
$$

Putting these steps together gives the familiar beta minus decay:

$$
n \to p + e^- + \bar{\nu}_e
$$

Similarly, in beta plus decay, an up quark changes into a down quark:

$$
u \to d + W^+
$$

and then

$$
W^+ \to e^+ + \nu_e
$$

This leads to

$$
p \to n + e^+ + \nu_e
$$

These transformations are central examples of the weak interaction.

Rendering scientific sketch…

Beta minus decay at the quark level

Leptons and neutrinos in weak processes

The weak interaction acts on leptons as well as quarks. In fact, neutrinos interact only through the weak interaction and gravity. Because the weak interaction is so weak and short ranged, neutrinos can pass through large amounts of matter with little chance of interaction.

This makes neutrinos difficult to detect. A neutrino may travel through Earth and still not interact. When it does interact, it is usually through a weak process involving a $W$ or $Z$ boson.

For example, a neutrino can interact with a neutron and produce a proton and an electron:

$$
\nu_e + n \to p + e^-
$$

This is a charged current weak interaction. A neutrino can also scatter from another particle through $Z^0$ exchange without changing its type.

Range and strength of the weak interaction

The weak interaction is short ranged because its mediators are heavy. In simple terms, heavier exchange particles make the force fade away very quickly with distance. The range is about

$$
10^{-18}\ \text{m}
$$

which is far smaller than atomic size.

The weak interaction is stronger than gravity at the particle level, but weaker than electromagnetism and much weaker than the strong interaction in most nuclear and particle processes.

The following table gives a rough comparison.

Interaction	Relative strength, rough	Range	Typical carrier
Strong	1	Short, about $10^{-15}\,\text{m}$	Gluons
Electromagnetic	$10^{-2}$	Infinite	Photon
Weak	$10^{-5}$	About $10^{-18}\,\text{m}$	$W^\pm$, $Z^0$
Gravitational	$10^{-39}$	Infinite	Graviton, hypothetical

These numbers are approximate and mainly help show the large differences between interactions.

A very short range does not mean the interaction is unimportant.
The weak interaction controls many radioactive decays and plays a central role in stellar energy production and neutrino physics.

Flavor change

An important idea in the weak interaction is flavor change. Flavor is the label that distinguishes types of quarks and leptons, such as up, down, electron, and neutrino types.

The weak interaction can change quark flavor. For introductory physics, the most important example is

$$
d \leftrightarrow u
$$

This is what allows neutrons and protons to convert into each other in beta decay.

The weak interaction also connects leptons in pairs, such as an electron with an electron neutrino. In weak decays, these particles often appear together.

Parity and the weak interaction

The weak interaction has a remarkable property, it violates parity symmetry. Parity is the idea that the laws of physics should work the same way in a mirror image. Many physical laws do respect this symmetry, but the weak interaction does not always do so.

This was a major discovery in twentieth century physics. It showed that nature distinguishes between left and right in weak processes. For beginners, the most important point is simply that the weak interaction behaves differently from the other familiar forces in this respect.

Weak interaction in the Sun

The Sun shines because nuclear reactions in its core release energy. Some of the key steps in these reactions require the weak interaction. In the proton-proton chain, one proton must effectively turn into a neutron so that deuterium can form. This conversion happens through the weak interaction.

A simplified reaction is

$$
p + p \to d + e^+ + \nu_e
$$

Without the weak interaction, this essential step would not occur, and stars like the Sun would behave very differently.

Summary view

The weak interaction is the force responsible for certain kinds of radioactive decay, for neutrino interactions, and for processes in stars. Its carriers are the massive bosons $W^+$, $W^-$, and $Z^0$. Because they are heavy, the weak interaction acts only over a tiny distance. Its most distinctive feature is that it can change particle flavor, allowing transformations such as neutron to proton and proton to neutron.

Key facts about the weak interaction:
$$
n \to p + e^- + \bar{\nu}_e
$$
$$
p \to n + e^+ + \nu_e
$$
Charged current weak interactions use $W^\pm$ bosons.
Neutral current weak interactions use the $Z^0$ boson.
The weak interaction can change particle type and violates parity symmetry.

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