Updated: Dec 26, 2019
One of the continual efforts of physics is that of organizing all the particles, what is often simply referred to as "the particle zoo". For this task, logic and math are the main tools, and the challenge is then organizing all those particles in the most efficient manner. Observed physical qualities are used to group similar particles, and names are given to the group. Over time, many such groups have appeared, such as Bosons, Fermions, Hadrons, Baryons, Mesons, Leptons, Quarks, and So-and-so-ons, just to name some. What then are the patterns within this system, if any?
During my studies I have seen different charts and visual representations attempting to organize all the subatomic particles and variants, many of which are composite subatomics made from each other, and naturally some graphics are better than others. However, 2 things stand out to me when viewing these charts. One, is that there is no overall, simplified "periodic table of the subatomics" reaching widespread standardized acceptance, and two, is that none of the charts seem to show the relation of the groups to the masses of the particles within those groups. At least, not in visuals that I've seen, and not in the manner shown above. So what is the picture above showing exactly?
In the early 20th century, it was observed that at the highest level, all particles seemed to come in one of 2 flavors, either Fermions, with 1/2 integer angular momentum, or Bosons, with whole integer angular momentum. Both types have fundamental particles and composite particles. The composite particles of both types are lumped together under the heading Hadrons, and are separated by whether they have an even or odd number of quarks, which in turn decides if they are a Boson-Hadron or Fermion-Hadron. This is shown in the upper right, and generally splits the particles into 4 groups from left to right; the fundamental Bosons, the composite Bosons (Mesons), the composite Fermions (Baryons), and the fundamental Fermions (Leptons and Quarks).
It is then convenient to organize the particles first by half or whole angular momentum, then by fundamental or composite, and if composite, then by having an even or odd number of constituents. Indeed this is useful, however, at that point, what does it tell about the nature or purpose of those particles? For comparison, consider the periodic table. The table of elements ends up being organized by atomic mass and radius for a given row, and leads to other macro scale physical qualities being observed and organized by column or area within the chart. The 4-group splitting of the subatomics does not on it's own lead to or display such sub structure.
Out of curiosity, I decided to plot all of the subatomics by their mass, to look for patterns in the graph. While doing so, I realized the particles' masses within the 4 groups had ranges. This was not something, I had seen discussed, in and of itself, and figured it useful for finding patterns within the nature of the subatomic particles, and a likely step in attempting to create a chart of subatomics more akin to the periodic table. The bottom part of the picture shows these ranges of masses plotted on a log scale, and the numbers in the upper left show the masses of the particles at group transitions. The colors are associated with the corresponding group underlined in the 4-group split above. Red is fundamental Bosons, Blue is fundamental Fermions, Orange is Mesons, and yellow is Baryons.
So as it turns out, there is an interesting nesting of the 4 particle type groups within each other, according to their masses. Fundamental Bosons can take the entire range of mass, followed by leptons and quarks, then Mesons which can only take a small range, and finally Baryons with the strictest range. In the future, I would like to explore this further, and try to develop a subatomics chart based on this observation. If anyone has seen such a chart or related information, I'd be interested to see it, or if anyone continues this further or wishes to develop the concept, let me know.