There are a few ways to visualize the particles in the standard model of particle physics. The one just showing the fundamental particles in a periodic table might be the most common -- however, it ignores interconnections, which is one of the reasons why the Standard Model still lacks an orderly visualization.
How we can accomplish a better visualization has puzzled scientists for years, and back in 2005, particle physicist Chris Quigg from the Fermi National Accelerator Laboratory in Illinois came up with the "double simplex" representation to help familiarize people with the known particles of nature.
In 2020, Quanta Magazine adopted Quigg's scheme and made further modifications to achieve what they call "a new map of all the particles and forces."
Before we dive into the "double simplex" representation, however, let's look at the periodic table of standard model particles to get a better grasp of particle physics:
In this format, matter particles called fermions, and force carriers called bosons are separated into two major columns. Fermions are further divided into two sub-groups called quarks and leptons, and bosons are divided into sub-groups called vector and scalar bosons. Fermions are also divided into three generation columns based on their masses.
Particle groups explained:
We need to explore what each of these groups means and how they differ before we talk about how they could be arranged into a table. Let’s start with fermions. An important feature of fermions is called “spin”, and it is either left-handed or right-handed. Handedness is important when grouping because it affects how certain particles interact with each other, and because, somewhat weirdly, there is no right-handed neutrino!
The first sub-group in fermions is quarks. First generation of quarks called up and down quarks make up the atomic nuclei, and they are, like all quarks, charged. The up quark has +2/3 and the down quark has -1/3 of the total charge a proton possesses. These quarks can either be left or right-handed. While the left-handed top and bottom quarks can transform into each other by emitting or absorbing a W boson, right-handed quarks do not transform into each other!
Quarks also have a feature called a “color charge”. This has nothing to do with regular color; it’s just a measure of how they interact with the strong force. Quarks of different colors bind to each other by emitting or absorbing gluons, the carrier particle of the strong force. The gluons also have color charge, this means gluons interact with themselves in addition to quarks.
The second group in fermions is leptons. There are two types: electrons and neutrinos. Just like left-handed up and down quarks, left-handed electrons and neutrinos can transform into one another via the weak force. As we said before, a right-handed neutrino is yet to be discovered. In contrary to quarks, leptons do not have color charge, therefore don’t feel the strong force. Also, just like in bosons, none of the right-handed leptons transform into one another via the weak charged interaction.
Now, let’s switch our discussion to bosons, which are the force carriers of all known forces (except gravity). We have already talked about all the ways strong and weak charged interactions can happen. What we have missed so far are the electromagnetic interaction, weak neutral interaction, and the Higgs mechanism.
Maybe the most familiar of all these forces is the electromagnetic force, and the rule of thumb is simple: If a particle has charge, it feels the electromagnetic force. The interaction is carried by the photon, and it does not cause a transformation of particles, only a force.
The weak neutral interaction, carried by the Z^0 boson, in contrary to the weak charged interaction, does not cause a transformation of particles; it only causes a change in momentum or energy, in other words, it only exerts a force. The weak neutral and electromagnetic interactions closely resemble each other, and this is not surprising due to the fact they once were a single force called the electroweak force. The separation of these forces happened when the universe cooled, synchronous with the appearance of a field called the Higgs field, excitations on which correspond to the Higgs boson.
This field is said to give particles mass. A simpled-down explanation of this process goes like this: When a particle (with mass) is moving through space, it constantly interacts with the Higgs field via the Higgs boson. These interactions correspond to changes in momentum and handedness in the particle, making the particle feel as if it were moving through a filled medium. These slow down the particle, and that resistance to motion is what is perceived as mass.
Now, the final piece of the puzzle is fermion generations. We have already talked about the first generations of both quarks and leptons. The second and third generations are just the heavier cousins of those particles. The charm and top quarks are heavier cousins of the up quark, and the strange and bottom quarks are the heavier cousins of the down quark. The same analogy is true for muon and tau, and their neutrino counterparts. Muon and tau particles are heavier cousins of the electrons, and muon neutrinos and tau neutrinos are the particles you get when a left-handed muon or tau transforms via the weak (charged) interaction.
It should be noted that there is a difference between leptons and quarks in the way in which they transform via the weak interaction: Quarks can transform between generations while leptons haven't been observed to do that.
Chris Quigg's map
Finally, we can talk about the map devised by Chris Quigg. The map is divided into right and left-handed fermions, bosons which carry the interactions shown as lines, triangular areas between different colors of quarks (these areas represent the gluons and the gluon interactions between the gluons), and the Higgs boson sitting in the middle giving particles mass.
The weak charged interactions (W boson) which transform fermions to each other are shown with orange straight lines. Notice that these lines as well as neutrinos are not seen on the right-hand side.
The weak neutral interactions (Z^0 boson) are shown with orange wavy lines. The electromagnetic interactions (photon) are shown with white wavy lines. Higgs interactions (Higgs boson) are shown in yellow dotted lines. And the strong interactions (gluons) are shown in the shaded triangular areas.
While the classic periodic table of elementary particles offers a simple and concise visualization, this map devised by Quigg shows the intricate relations and interactions between different particles, as well as the importance of handedness in greater detail, making it an excellent visual learning tool.