October 22, 2020
Ashley Mackenzie for Quanta Magazine
[Editor’s note: The full, interactive map is available below.]
All of nature springs from a handful of components — the fundamental particles — that interact with one another in only a few different ways. In the 1970s, physicists developed a set of equations describing these particles and interactions. Together, the equations formed a succinct theory now known as the Standard Model of particle physics.
The Standard Model is missing a few puzzle pieces (conspicuously absent are the putative particles that make up dark matter, those that convey the force of gravity, and an explanation for the mass of neutrinos), but it provides an extremely accurate picture of almost all other observed phenomena.
Yet for a framework that encapsulates our best understanding of nature’s fundamental order, the Standard Model still lacks a coherent visualization. Most attempts are too simple, or they ignore important interconnections or are jumbled and overwhelming.
Consider the most common visualization, which shows a periodic table of particles:
This approach doesn’t offer insight into the relationships between the particles. The force-carrying particles (namely the photon, which conveys the electromagnetic force; the W and Z bosons, which convey the weak force; and the gluons, which convey the strong force) are put on the same footing as the matter particles those forces act between — quarks, electrons and their kin. Furthermore, key properties like “color” are left out.
Another representation was developed for the 2013 film Particle Fever:
While this visualization properly emphasizes the centrality of the Higgs boson — the linchpin of the Standard Model, for reasons explained below — the Higgs is placed next to the photon and gluon, even though in reality the Higgs doesn’t affect those particles. And the quadrants of the circle are misleading — implying, for instance, that the photon only couples to the particles it touches, which isn’t the case.
A New Approach
Chris Quigg, a particle physicist at the Fermi National Accelerator Laboratory in Illinois, has been thinking about how to visualize the Standard Model for decades, hoping that a more powerful visual representation would help familiarize people with the known particles of nature and prompt them to think about how these particles might fit into a larger, more complete theoretical framework. Quigg’s visual representation shows more of the Standard Model’s underlying order and structure. He calls his scheme the “double simplex” representation, because the left-handed and right-handed particles of nature each form a simplex — a generalization of a triangle. We have adopted Quigg’s scheme and made further modifications.
Let’s build up the double simplex from scratch.
Quarks at the Bottom
Matter particles come in two main varieties, leptons and quarks. (Note that, for every kind of matter particle in nature, there is also an antimatter particle, which has the same mass but is opposite in every other way. As other Standard Model visualizations have done, we elide antimatter, which would form a separate, inverted double simplex.)
Let’s start with quarks, and in particular the two types of quarks that make up the protons and neutrons inside atomic nuclei. These are the up quark, which possesses two-thirds of a unit of electric charge, and the down quark, with an electric charge of −1/3.
Up and down quarks can be either “left-handed” or “right-handed” depending on whether they are spinning clockwise or counterclockwise with respect to their direction of motion.
Weak Change
Left-handed up and down quarks can transform into each other, via an interaction called the weak force. This happens when the quarks exchange a particle called a W boson — one of the carriers of the weak force, with an electric charge of either +1 or −1. These weak interactions are represented by the orange line:
Strangely, there are no right-handed W bosons in nature. This means right-handed up and down quarks cannot emit or absorb W bosons, so they don’t transform into each other.
Strong Colors
Quarks also possess a kind of charge called color. A quark can have either red, green or blue color charge. A quark’s color makes it sensitive to the strong force.
The strong force binds quarks of different colors together into composite particles such as protons and neutrons, which are “colorless,” with no net color charge.
Quarks transform from one color to another by absorbing or emitting particles called gluons, the carriers of the strong force. These interactions form the sides of a triangle. Because gluons possess color charge themselves, they constantly interact with one another as well as with quarks. The interactions between gluons fill the triangle in.
More Matter
Now let’s turn to the leptons, the other kind of matter particles. Leptons come in two types: electrons, which have an electric charge of −1, and neutrinos, which are electrically neutral.
As with left-handed up and down quarks, left-handed electrons and neutrinos can transform into each other via the weak interaction. However, right-handed neutrinos have not been seen in nature.
Note that leptons do not possess color charge and do not interact via the strong force; this is the main feature that distinguishes them from quarks.
The Simplex Skeleton
Putting together what we’ve done so far, we’ve got the left-handed particles on the left, while right-handed particles are shown on the right. They form the basic skeleton of Quigg’s double simplex.
Three Generations
Now, a complication: For unknown reasons, three progressively heavier but otherwise identical versions of each type of matter particle exist. For instance, along with the up and down quark, there’s the charm and strange quark and, heavier still, the top and bottom quark. The same is true of the leptons: Along with the electron and electron neutrino, there are the muon and muon neutrino and the tau and tau neutrino. (Note that the neutrinos have small but unknown masses.)
All these particles live at the corners of the double simplex. Note that a small amount of weak interaction happens between left-handed quarks in different generations, so that an up quark could occasionally spit out a W+ boson and become a strange quark, for example. Leptons in different generations have not been seen interacting in this manner.
Forces and Charge
What other ways do particles interact with one another? We mentioned already that many matter particles have electric charge — all, in fact, except neutrinos. What it means to have electric charge is that these particles are sensitive to the electromagnetic force. They interact with one another by exchanging photons, the carriers of the electromagnetic force. We represent electromagnetic interactions as wavy lines connecting charged particles with each other. Note that these interactions do not transform particles into one another; in this case, particles just feel a push or a pull.
The weak force is a little more complicated than we let on earlier. Aside from the W+ and W– bosons — the electrically charged carriers of the weak force — there is also a neutral carrier of the weak force, called the Z0 boson. Particles can absorb or emit Z0 bosons without changing identities. As with electromagnetic interactions, these “weak neutral interactions” merely cause loss or gain of energy and momentum. Weak neutral interactions are represented here by orange wavy lines.
It’s no coincidence that the weak neutral interactions closely resemble the electromagnetic interactions. The weak and electromagnetic forces both descend from a single force that existed in the first moments of the universe, called the electroweak interaction.
As the universe cooled, an event known as electroweak symmetry breaking split the forces in two. This event was marked by the sudden appearance of a field extending throughout space, known as the Higgs field, which is associated with a particle called the Higgs boson — the final piece of our puzzle.
Enter the Higgs
The Higgs boson is the linchpin of the Standard Model and the key to why the double simplex arrangement makes sense. When the Higgs field arose in the early universe, it joined left- and right-handed particles to each other, imbuing the particles at the same time with the property we call mass. (Note that the neutrino has mass, but its origin remains mysterious, since it derives from some mechanism other than the Higgs.)
Here’s a cartoon version of how this generation of mass works. As a particle such as an electron moves through space, it constantly interacts with Higgs bosons — excitations of the Higgs field. When a left-handed electron bumps into a Higgs boson, the electron might ricochet off it in a new direction and become right-handed, then bump into another Higgs and become left-handed again, and so on. These interactions slow down the electron, and that’s what we mean by “mass.”
In general, the more a particle interacts with the Higgs boson, the more mass it has. Furthermore, the frequent interactions with Higgs bosons make those massive particles quantum mixtures of left- and right-handed.
And with that, we have the Standard Model of particle physics:
Model by Olena Shmahalo/Quanta Magazine
The original version of this article stated that left-handed leptons in different generations occasionally interact via the weak force. In fact, though such interactions have been hypothesized, they have not been observed.
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