A Beginner Physics Guide to Baryon Particles

Introduction
At the beginning of the 20th century, it was thought that all matter consisted of only three particles: the electron, the neutron, and the proton.  The major outstanding question was how the neutrons held the positively charged protons together within the atomic nucleus.
In the search to answer that question, however, it was found that the proton and neutron were not elementary particles at all, but each was composed of three elementary quarks.  Furthermore, a menagerie of additional elementary and composite particles was discovered.  The centerpiece is the set of eighteen baryons: particles, like the proton and neutron, composed of three lightweight quarks.  This Insight provides an introduction to these baryons, whose discovery and classification constitute perhaps the first great achievement of what is now known as the standard model of particle physics.
In particular, it is shown why there are precisely eighteen such particles and why they divide into two...

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A very nice article and I enjoyed reading it a lot.
I'd just have one minor comment: I would not write sentences like

The purpose of this Insight was to explain, as simply as possible, the existence of precisely eighteen baryons,...

without any further comment on heavy flavors. I could imagine that a statement like this might be a bit confusing for somebody who does not know particle physics very well and later stumbles over a list of baryons.
I mean, I know what you did there, and why you considered only the three light quarks that lead to the SU(3)_flavor of the eightfoldway, but I would just suggest to add one small comment or footnote at the very end about the existence of heavy flavors and additional baryonic states that come with them.

Great Insights article!

Maybe somebody might wonder why there are only "18 baryons" as you state at the end of the article, but the particle data booklet lists a plethora of baryons (also within the light baryons of course). The answer is of course that all these are excited states of the ones listed in your article and that lattice QCD even seems to find more such states than listed (particularly in those with strangeness).

And that is a proton in a nutshell! It’s a particular superposition of (antisymmetric) quark flavor and (antisymmetric) spin 1/2 states, which combine to produce a completely symmetric overall state called the proton.

@PeroK Can you elaborate on this? What does it mean for the proton to actually be a superposition of other states? I'm reminded of my chemistry class where we talked about a particular bonding arrangement to be a combination of three bonds. One would expect this molecule to have a 1/3 chance of being in each one of these bonds, and that it would be forced to be in one bond at a time. But that wasn't the case. Instead it was, in some respect, in all three bonds at the same time. I suppose the proton is something like that?

Drakkith said:

@PeroK Can you elaborate on this? What does it mean for the proton to actually be a superposition of other states? I'm reminded of my chemistry class where we talked about a particular bonding arrangement to be a combination of three bonds. One would expect this molecule to have a 1/3 chance of being in each one of these bonds, and that it would be forced to be in one bond at a time. But that wasn't the case. Instead it was, in some respect, in all three bonds at the same time. I suppose the proton is something like that?

Yes, that's the general idea. Superposition is fundamental to QM. Suppose you have two particles that each can be in one of two states. Let's call these states ##\psi_a## and ##\psi_b##. Classically, if the two particles were bound together, then there would be four definite, distinct possibilities:
$$\psi_a \psi_a, \ \psi_a \psi_b, \ \psi_b \psi_a, \ \psi_b\psi_b$$
You could always look into the system and see definitely what state each of the two particles is in.

In QM, however, in addition you can have any linear combination of these basis states. The system could, for example, be in the state:
$$\frac 1 {\sqrt 2} (\psi_a \psi_b + \psi_b \psi_a)$$
If we look at this system the particles are always in different states but there is an equal probability that the first particle will be found in state ##\psi_a## and the second in state ##\psi_b## and vice versa. The critical thing is that it's not that we didn't know which particle was in which state, the particles are simply not in definite one-particle states until you measure them. This is fundamental to QM.

The interesting thing, which we saw in my article, is that the concept of superpositions creates a much richer physics (and chemistry!). If we were limited to the four definite basis states, then there would be nothing like the variety we see in elementary particle physics and chemistry.

I spun off several posts which weren't related to the article.

If you have questions about quantum physics in general, or about certain topics, feel free to create a new thread. Thank you.

For people who are interested in the history surrounding this (and more), there's a nice writeup on a not very technical level in the beginning of Griffiths' "Introduction to Elementary Particles".

The baryons in the decuplet are even less stable than those in the octet, again explaining that their fleeting existence is only confirmed by specialized experiments to create them for a few instants before they decay.

Source https://www.physicsforums.com/insights/a-beginners-guide-to-baryons/

The problem with this is that:
1) why then is the decuplet even relevant and how does it form a "set of 18 particles"?
2) there actually is one, but precisely one, important decuplet member which is actually more stable than one of the octet. Which is why there is a set of 8 particles but they are not octet!
Observation: why is this thread in "Quantum physics", not "Particle physics"?

There is also a large number of resonances outside the set of 18.
Looking at just the flavourless baryons, the spectrum starts:
N(940) 1/2⁺****
Δ(1232) 3/2⁺****
N(1440) 1/2⁺****
N(1520) 3/2^-****
N(1535) 1/2^-****
Δ(1600) 3/2⁺****
Δ(1620) 1/2^-****
N(1650) 1/2^-****
N(1675) 5/2^-****
N(1680) 5/2⁺****
Δ(1700) 3/2^-****
N(1700) 3/2^-***
N(1710) 1/2⁺****
N(1720) 3/2⁺****

All except N(940) decay strongly. Δ(1232) is about 120 MeV wide.
Just what makes Δ(1232) a set with N(940), rather than just one of the many excited states?

There are several modes a bound system of three fermions could be excited. They might undergo radial oscillations, or orbital movement. One possible excitation mode is spin alignment. 3 spin 1/2 fermions might combine to have spins aligned to total 3/2 spin, or one with opposite spin with total 1/2. Turns out that for quarks that are not all the same flavour, the 3/2 state is highly excited.
It is supposed that N(940) and Δ(1232) have no internal excitations other than the spin alignment of Δ(1232). Are the internal excitation modes of all the other low-lying well-known resonances, from N(1440) to N(1720), known?