On the Weak Nuclear Force and the distinction between the W and the Z Bosons.

Published in

The Quantastic Journal

11 min readJun 29, 2024

The Weak Nuclear Force is one of the 4 Fundamental Forces and is primarily responsible for inducing certain forms of Nuclear Decay, which helps maintain the balance between the Strong Nuclear Force, and the Electromagnetic Forces in the nucleus, which results in the breakdown of the atom. It’s one of the more mysterious forces since it doesn’t interact via a simple “push and pull”, typical of most other forces, but rather through other, more complex interactions essential in the context of the atom and maintaining its stability.

In this article, we’ll explore the role of this Fundamental Force, the physical characteristics of the corresponding bosons, and their differences in mediating the Weak Nuclear Force.

The W & Z Bosons

The W and Z bosons are vector gauge bosons, characterized by a Spin of 1, and they act as the mediators of the Weak Nuclear Force.

The W boson is the only electrically charged boson, with an electric charge of ±1. There are two types of W bosons: W+ bosons, with a +1 electric charge, and W– bosons, with a -1 charge, with these particles being “one another’s antiparticles” (Medium). An interaction between both types of W boson would result in annihilation, converting their masses into energy, in the form of photons, all while conserving charge and energy (mass being converted to energy works due to Einstein’s Mass-Energy Equivalence). By contrast, the Z boson is electrically neutral, yet has a higher rest energy, meaning a higher mass.

The Role of the Weak Nuclear Force & Radioactive Decay

One of the roles of the Weak Nuclear Force is in inducing radioactive decay, with there being 4 primary forms of Radioactive Decay, alongside some other more exotic manners of radioactive decay being variations of these Fundamental Decays.

Alpha Decay results from an excess of nucleons within the nucleus, which causes instability in the nucleus and results in excess protons and neutrons being ejected, in the form of Alpha Particles, which have the structure of Helium nuclei, with 2 protons and 2 neutrons. This form of radiation has the lowest penetrating power but is also the most ionizing due to its higher electric charge of +2.

Beta Decay involves the changing of nucleons, and results in the ejection of a charged particle. This involves a Nucleon emitting a W boson, causing it to change its Quark flavors, with the W boson decaying soon after.

Figure 1. A Feynman Diagram representing Beta Plus Decay.

Beta Plus decay causes a proton to decay into a neutron via the emission of a W+ boson, which then decays into a positron and neutrino.

Figure 2. A Feynman Diagram for Beta Minus Decay.

Beta Minus decay, the more common of the two forms of Beta decay, causes neutrons to decay into protons via the emission of W- bosons, which decay into electrons and antineutrinos.

Within Beta decay, there are two other forms of possible decay, which can take place:

Proton Emission decay occurs when there’s an excess of protons, with the nuclide being in an excited state, resulting in the emission of a Proton, which will also cause the atom to change element.
Neutron Emission decay occurs in nuclides (specific nuclei) where there’s an excess of neutrons, or a lack of protons, which causes the emission of nucleons.

Gamma decay is the nuclei’s “de-excitation of from an excited state to a lower energy state, preceded by some decay or reaction” (Ohio State University)

Figure 3. A Feynman Diagram for Electron-Capture.

Electron Capture decay occurs when a nucleus has too many protons, which can affect the balance between the Strong Nuclear Force in the nucleus, and the Electrostatic Force of Attraction between the nucleus and electrons. To balance this out, electrons are taken from orbitals, which results in the formation of a neutron and the emission of a neutrino. By changing the number of protons, “electron capture transforms the Nuclide into a new element” (ARPANSA). Though similar to Beta-Plus decay, the key difference is that Beta-Plus decay is spontaneous, and doesn’t involve the absorption of electrons.

It’s essential to know that Weak Interaction isn’t responsible for all of these forms of Nuclear Decay. Specifically, it doesn’t mediate Alpha or Gamma Decay, with those being a result of imbalanced forces in the nucleus, where the electrostatic repulsion and strong nuclear force are imbalanced. Rather, any form of Nuclear Decay that involves the type, or flavor, of a particle changing is mediated by the Weak Nuclear Force.

The Weak Nuclear Force Beyond Nuclear Decay

Beyond nuclear decay, the Weak Nuclear Force is also responsible for Neutrino Scattering, where neutrinos travelling through space will interact with other particles, which can result in one of two possible interactions:

Neutral Currents, where the particle has its position, or motion changed, without a change in the particle’s identity. The lack of change in the particles’ identity is due to there being no net transfer of electrical charge.
Charged Current Interaction, which involves a transfer of electric charge and weak isospin. Weak Isospin is a Fundamental Quantum number that describes certain properties of particles and, like electric charge, is important in classifying how particles will interact via the Weak Nuclear Force and which Boson is emitted.

This interaction is less likely to occur and can result in the flavor of a Quark changing, where a Quark changes, causing a change in a Hadron. In Beta-Minus Decay, for example, it would involve a change in the neutron from an udd quark configuration to an uud (proton) configuration, with one of the Down Quark changing flavors. Given that this involves a net transfer of electric charge, the W boson likely mediates this interaction.

The Differing Roles of the W and Z Bosons

These two W bosons are the Antiparticles to each other, which mirrors the 2 forms of Beta decay, with Beta Minus decay “that involves the creation and disappearance of the W– boson” (OpenLearn). By extension, the W+ boson must be emitted upon Beta Plus decay, as a Positron being emitted. Generally, for Beta decay, the presence of W bosons enables Quarks to change. This is important, as Quarks act as the Fundamental building block for most particles, known as Hadrons, so the changing of Quarks can result in these subatomic particles changing.
As for the Z boson, it is electrically neutral, and as such is known for not inducing most forms of radioactive decay, as those involve the emission of energy (EPA), and result in changes to quark flavors and/or the ejection of charged particles from the atom. The flavors of a quark include varying properties, such as its topness or bottomness, which can change in radioactive decay. Its interactions with the nuclei of an atom result in the transfer of momentum, spin, and kinetic energy, yet cause no change in other properties, namely baryon/lepton Number, or electric charge. Make no mistake, though, the Z boson is still responsible for specific forms of nuclear decay.

A specific example would be all Neutral-Current Interactions, as those don’t involve any net change in electric charge, but rather a change in their momenta and positions. These Neutral Current Interactions can stem from Neutrino-Scattering, but there’s a caveat.

Even within Neutrino Scattering, there are two possible forms, those being Neutrino-Nucleon Scattering (which can result in either Neutral Currents forming or a Charged-Current Interaction), and Neutrino-Electron Scattering. Neutrino-electron scattering is “where a neutrino scatters off an electron by the exchange of a virtual vector boson” (CERN).

It can’t result in the Charged-Current Interaction, as this would involve a change in its flavor, which should only be possible for Quarks specifically since, to our current understanding, Leptons are unable to change flavors.

From this, it can be inferred that the Z Boson is responsible for all neutrino-electron scattering interactions, but only some neutrino-nucleon scattering.

If the neutrino-nucleon scattering results in a Charged-Current Interaction, then it’s likely that this interaction results from a W boson being emitted, whilst if there’s a Neutral-Current Interaction, then it’s the result of Z bosons.

This ensures a balance is maintained between the Strong Nuclear Force holding the nucleus together and the Electromagnetic Forces within the atom, maintaining the stability of the nucleus. The Weak Nuclear Force is considered the weakest of the 4 Fundamental Forces, primarily due to its limited range. This limited range results from the higher rest energy of the W and Z bosons when compared to other bosons.

The Link between the Weak Nuclear Force and Electromagnetic Force: The Electroweak Force

When the W/Z bosons, and Photons, exceed a specific energy value — known as the Unification Energy—these 2 Fundamental Forces merge into a single interaction, known as the Electroweak Force. This primarily takes place at very high energy values, meaning the bosons have higher individual energy values.

At higher energy levels, it’s this force that mediates nuclear decay, as well as all the electromagnetic interactions that take place between charged particles.

This unification of these Fundamental Forces was first theorized by Sheldon Glasgow, who noted that the Weak Nuclear Force and EM Force were identical in magnitude at a very small distance (1/1000th the diameter of a Proton).

The discovery of the Z boson would help to solidify this theory, as it had suggested the need for 4 total bosons mediating this force, and at the time, there were only 3 Discovered: W+, W–, and the Photon.
The main caveat to this idea was that it required all bosons mediating this force to be massless, yet the 3 bosons mediating the Weak Nuclear Force had a very high rest mass/energy.

Figure 4. A graphical representation of the Higgs Field from CERN, where the Minima, or bottom-most groove, indicate a point of no energy. — Figure 4. A graphical representation of the Higgs Field from **CERN**, where the Minima, or bottom-most groove, indicates a region of no energy.

The solution to this came in 1967–68, when Professor Adbus Salam combined Glasgow’s ideas with that of the Higgs Field (theorized in 1933), and involved the use of an idea known as the Higgs Potential, which suggested that above a value of 160GeV, there would be a value for the Higgs Field, meaning a particle would have mass. Below this value, which the W/Z bosons are (at their lowest energy state, or rest), particles acquire mass.

The reason why the Photon here doesn’t have any mass is because its interactions fundamentally differ from that of other particles with mass. This is because it “doesn’t interact with the Higgs Field” (CERN).
Using the Higgs Field’s graph, we can describe the Photon as freely moving through the groove, or region occupied by the Minima, and since there’s no energy used in moving about the groove, we can say it has no mass (using Einstein’s Energy-Mass Equivalence).
As for the other 3 bosons — those that mediate the Weak Nuclear Force — these oscillate back and forth between the slope on the graph above, with this climbing up of the graph requiring energy. Since these bosons have energy, they must also have mass.

Real-world significance of the Weak Nuclear Force

Figure 5. A diagrammatic representation of Nuclear Fusion from Fusion Energy Base. — Figure 5. A diagrammatic representation of Nuclear Fusion from **Fusion Energy Base.**

Nuclear Fusion is the process of combining two or more nuclei into a single nuclei, with this process releasing vast amounts of energy and being what provides Stars with their energy. For a star to not collapse inwards, there needs to be a balance between the inward-acting Gravitational Forces, and the outward-acting Radioactive Pressure, which is known as Hydrostatic Equilibrium (the balance of forces in main-sequence stars). In the case of the Sun, which is a lower-mass main-sequence star, the primary process in its core for energy production is a proton-proton chain reaction, which requires Deuterium nuclei to be formed from fusing Hydrogen nuclei, as these are then fused to form Helium nuclei. This is only possible through the Weak Nuclear Force, which can “convert a proton (Hydrogen) into a neutron to form Deuterium, which is important for the continuation of Nuclear Fusion” (Wikipedia). Commonly, Deuterium, and Tritium (another isotope, formed similarly to Deuterium, but with 1 more neutron) will fuse to form a Helium nucleus and eject a neutron and an immense amount of energy.

Without Nuclear Fusion, Hydrostatic Equilibrium wouldn’t be maintained, and many stars would reach the end of their life, either collapsing inwards and forming White Dwarfs or, if large enough, forming Black Holes and Supernovae.

Nuclear Fission involves the breakdown of nuclei into 2 smaller daughter nuclei, with the ejection of a few neutrons and photons/energy. For atoms that are particularly neutron-rich or proton-rich, they may have an excessive binding energy (the amount of energy needed to hold the nucleus together). This excessive binding energy means there’s not enough energy to hold the nucleus together, which in turn can cause instability as the forces holding the nucleus together are imbalanced, causing it to break down. To reduce its binding energy, different Nucleons will undergo Beta decay to try and ensure a greater balance of protons and neutrons in the nucleus, resulting in the emission of a W boson.

Note that the Weak Nuclear Force is not the primary force responsible for Nuclear Fission, but rather is a key component in bringing it about.
Its presence in Fission is essential, given the use of Nuclear Fission as a means of producing power in nuclear power stations.

PET (Positron Emission Tomography) is a form of medical imaging that involves the use of positrons. Specifically, it involves the interaction between positrons and electrons, which results in annihilation, and thus the production of high-energy photons, or Gamma Rays. This involves the delivery of an unstable isotope (notably one with a short half-life, such as Fluorine-18) which is then attached “to chemical substances that are naturally used by the particular organ or tissue during its metabolic processes” (Johns Hopkins). This is then administered through an IV into the vein and moves to that respective body part. Whilst present there, positrons will interact with electrons present in organic matter, causing annihilation and the production of gamma rays. Afterward, the person will be placed through a scanner, which detects these gamma rays and they “use the information to create an image map of the organ or tissue being studied” (John Hopkins).

Relating to the Weak Nuclear Force; The positrons are produced through Beta-Plus decay, which involves the emission of a W+ boson, which then decays into a positron and a neutrino.

In general, most real-world applications of the Weak Nuclear Force will most likely be dependent on Beta decay, and its byproducts.