The Standard Model of Particle Physics

Our observations point to fundamental forces governing the interactions of everything in the universe. To promote these observations to theory, we need a mathematical framework in which both matter and interactions are given a complete description. Not only is the theory meant to describe, but it also predicts new phenomena and poses sharp questions at which our colliders can be pointed.

Such a framework, or model, was assembled more than half a century ago. In this article, we present the history of the Standard Model of particle physics, explain its content and successes, and lament over its limitations and shortcomings.

Assembling the Puzzle

Science mostly proceeds gradually, and only retrospectively does it seem like progress was rapid. The Standard Model is an example of an exception to that rule. Over the course of twenty years, physicists from across the globe assembled the puzzle that uncovered the interactions of all observable matter.

The story begins with Tomonaga, Schwinger, and Feynman. These three theoretical physicists shared the 1965 Nobel Prize "for fundamental work in quantum electrodynamics." Quantum electrodynamics is the theory that incorporates the weirdness of the quantum world into the description of electromagnetism.

In high school, we are taught that the electric force follows the same profile as the gravitational one. This is Coulomb's law. However, one might expect that at smaller distances, quantum effects become relevant and modify this behavior. Indeed, this is what happens in quantum electrodynamics. The main concept that we will need from this theory is matter that interacts electromagnetically and carries an electric charge. Electromagnetism is a large part of the Standard Model, except it proved to be the simplest.

One theoretical question one might pose at this point is: what if there existed a force, not unlike electromagnetism, whose "charged" objects carried more complicated notions of charge? What if the charged objects had a vector or a matrix of charges instead of just a single number as in electromagnetism? The answer to this question, and much more, was given by Yang and Mills in 1954. They provided a theory that is true, typically referred to as the Yang-Mills gauge theory.

The importance of Yang-Mills theory cannot be understated in the Standard Model or more generally in modern physics. The three fundamental forces (excluding gravity): electromagnetism describing charged objects, and light, weak interactions explaining radiation and decay, and strong interactions gluing subatomic particles together, are each described by their own version of Yang-Mills theory. The difference is the type of charges that can arise.

Quite rapidly after this discovery, experimental evidence pointed to what sorts of charges nature really has allotted for its matter. Each of the three fundamental forces was given its own mathematical description, and arguing based on observation and aesthetics, physicists were able to predict and subsequently discover new particles like the tau lepton and quarks.

The Structure of the Model

The structure of the Standard Model was explained briefly in our article about the fifth force. Here, instead of focusing on the interactions which were reviewed in the previous section, we show the matter content of the theory.

The particles are mainly distinguished based on whether or not they are fermions or bosons. The difference lies in how these particles align themselves in the presence of a magnetic field. Then, one divides these based on whether or not they mediate one of the three interactions. For example, the photon mediates electric exchange between two electrons when they repel each other. The photon is the force carrier but the electron only participates in the interaction. We say that the electron is charged under the electromagnetic interaction. Particles are further distinguished by the types of interactions in which they participate. The electron does not participate in the strong interaction, so it is called a lepton. Particles that do are called hadrons.

Successes and Limitations

The Standard Model has been a great source of realized predictions and mystifying confusions. The major successes of the model have been predicting the existence of:

1. The W and Z bosons, which are the analogues of the photon for the weak force.
2. The gluons (there are eight), which are the analogues of the photon for the strong force and serve to glue quarks together to give rise to protons and neutrons.
3. A large agreement with the predicted value of magnetic properties of electrons and experiment.
4. The Higgs boson, which was the final link in the puzzle of the Standard Model. This boson gives rise to mass for all particles that interact with it.

The Model is not without its faults, and we list several in the following:

1. While the masses of the W, Z, and gluon bosons were predicted correctly, the mass of the Higgs boson, which was observed in 2012, was not. Theory says that the mass of the Higgs should be much larger than it actually is, which puts the entire model at risk because of the profound importance of the boson.
2. It is not valid at all energy scales. One can show that the theory develops certain pathologies and estimates the scale at which they begin. While this scale is quite large, it nevertheless means that the Model is incomplete.
3. Another hint towards its incompleteness is the fact that it cannot account for dark matter, which is the most prominent type of matter making up our entire universe. For a theory purporting to describe all types of matter and their interactions, the Model seems to be missing quite a lot.

There are many ideas in the literature on how to subsume the Standard Model into a bigger theory. These include, but are not limited to, Grand Unified Theories where the Model is embedded into a larger one that contains more exotic matter and forces, appending an additional force that solves the dark matter problem and positing new sorts of symmetries that neutralize the heavy mass of the Higgs and more. Without experimental evidence, it is difficult to rule out or favor certain directions, but the search for a more fundamental theory still continues.