In the old theory of the strong force, where the strong force was thought to be conveyed by massive mesons (pions), as one can read here:

The discovery of the neutron in 1932 revealed that atomic nuclei were made of protons and neutrons, held together by an attractive force. By 1935 the nuclear force was conceived to be transmitted by particles called mesons. This theoretical development included a description of the Yukawa potential, an early example of a nuclear potential. Pions, fulfilling the prediction, were discovered experimentally in 1947. By the 1970s, the quark model had been developed, by which the mesons and nucleons were viewed as composed of quarks and gluons. By this new model, the nuclear force, resulting from the exchange of mesons between neighboring nucleons, is a residual effect of the strong force.

Protons and neutrons were considered the same particle after isospin was introduced. As isospin was mathematically described as spin (though their interpretaions were completely different) the proton had an isospin projection on the $I_z$ axis of $I_z=1/2$ while the neutron's isospin projection is $I_z=-1/2$.
The name "isospin" is more properly described as "isobaric spin" as it derived from the Greek word for "heavy" (βαρύς, barýs) and protons and neutrons (to which isospin was applied) have almost the same mass. For most hadrons except neutrons and protons, the difference in mass is not almost zero (see this list) and the symmetry is broken more severely.
In the same Wikipedia article on isospin one can read:

Before the concept of quarks was introduced, particles that are affected equally by the strong force but had different charges (e.g. protons and neutrons) were considered different states of the same particle, but having isospin values related to the number of charge states.

And also

A close examination of isospin symmetry ultimately led directly to the discovery and understanding of quarks and to the development of Yang-Mills theory.

This led to the formula $I_z=\frac 1 2 (n_u - n_d)$, which indeed gives $I_z=1/2$ for the proton and $I_z=-1/2$ for the neutron. The em. force is considered to break the symmetry between the two particles slightly (in my point of view saying that two partcles are the same but different in charge and a bit different in mass already suggests that they are made up of other particles).

The this article on the weak isospin one can read:

In particle physics, weak isospin is a quantum number relating to the weak interaction, and parallels the idea of isospin under the strong interaction. Weak isospin is usually given the symbol $T$ or $I$ with the third component written as $T_z$, $T_3$, $I_z$, or $I_3$. It can be understood as the eigenvalue of a charge operator (see here).

The weak isospin conservation law relates to the conservation of $T_3$; all weak interactions must conserve $T_3$. It is also conserved by the electromagnetic and strong interactions. However, one of the interactions is with the Higgs field. Since the Higgs field vacuum expectation value is nonzero, particles interact with this field all the time even in vacuum. This changes their weak isospin (and weak hypercharge). Only a specific combination of them, $Q=T_3 +\frac 1 2 Y_w$ (electric charge), is conserved. $T_3$ is more important than T and often the term "weak isospin" refers to the "3rd component of weak isospin".

Now, the theoretical unification (sometimes wrongly compared to the unification of the electric and magnetic force) seems quite contrived to me (for example, I can't seem to figure out out what exactly a unit of weak charge is).
So isn't it possible that, just as in the case of the old strong force, after a close examination of the isospin symmetry ultimately led directly to the discovery and understanding of quarks and to the development of Yang-Mills theory, a close examination of the weak isospin symmetry can lead to an alleged existence of sub-quark particles and an associated sub-quark Lagrangean, while the weak force is a residue force, just as the old strong force turned out to be a residue force?

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    $\begingroup$ "... seems quite contrived to me (for example, I can't seem to figure out out what exactly a unit of weak charge is)." is thoroughoingly baffling, perhaps deserving its own question. A unit of weak charge is precisely a unit of weak isospin charge, no? $\endgroup$ Oct 25, 2020 at 16:20
  • $\begingroup$ Well, by the same token one can say that a unit of a strong charge is precisely a unit of strong isospin charge. $\endgroup$ Oct 26, 2020 at 22:38
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    $\begingroup$ No: this is the heart of my answer. Weak isospin is the gauged group in the weak interactions (partially), but strong isospin is not gauged in the strong interactions--which gauge color SU(3), which is the strong charge. Strong isospin commutes with the strong interactions (~ is ignored/respected by them). $\endgroup$ Oct 26, 2020 at 22:45
  • $\begingroup$ Why couldn't some type of Higgs mechanism (SSB and a Lagrangian invariant under non-local phase (gauge) transformations) be developed in the case of the old nuclear force, giving mass to the pions? Of course, quarks were not yet discovered yet, which would eventually catch up with that theory (maybe this theory could survive when low energies were considered). It's very true that modern SM is an impressive mathematical structure. $\endgroup$ Oct 27, 2020 at 13:53
  • $\begingroup$ But what if new sub-quarks, like the two in the rishon model which makes the Higgs boson a particle that isn't necessary to provide mass (which isn't to say it doesn't exist) are found? Would the SM be still valid? At small energies compared to the energies of finding them (if they are found)? I think this is very well possible, in the same way, quarks were found in protons). This theory is more satisfactory (at least, to me), as all three forces are conveyed by massless particles (the photon, the gluon, and the hyper gluon). $\endgroup$ Oct 27, 2020 at 13:54

1 Answer 1

  • The invention of quarks, ultimately turning to a discovery, certainly was not motivated by strong isospin and could not plausibly have been made without extending isospin to flavor SU(3); and even then... it turned out to be a breathtaking fluke--it would have been much harder had flavor SU(4) been around at the time! Ignorance of charm allowed people to focus on triality, a feature of color group SU(3) reps, completely coincidental to the flavor SU(3) being thereby organized. This bizarre history is more appropriate for the History of Science SE. The critical handle here is that the approximate strong isospin symmetry SU(2) did not really "lead" to quarks, any more than motivating Lie Group theory applications to flavor physics. My claim is that strong isospin provided a training ground and educational device in best discerning and appreciating weak isospin.

  • Weak isospin is also an approximate SU(2), see, e.g., this question, this time its lowest energy conservation laws spontaneously broken through coupling to the Higgs, especially in the Yukawa couplings/fermion mass terms. That is, the non-vanishing quark and lepton mass terms (Higgs-field induced) siphon off weak isospin into the vacuum, converting the left chiral component to the null WI right-handed components of fermions. The neutral Higgs stealing 1/2 a unit of WI to sink into the vacuum or -1/2 for its conjugate. (At the primitive level, one could muse about such breakings as small "explicit WI violations".) However, historically, it was a closer examination of weak isospin and its chiral structure in the 4-Fermi interaction that ushered in the SM. It motivated the heavy intermediate vector bosons, and the Higgs field which makes that possible, new particles to be sure, but not constituents. The resulting SM fit everything almost perfect together. It seems you are after a different option, but I cannot see any hint in the group structure of the SM pointing to further constituents.

You might, of course, be welcome to speculate on further particles and structures, but SU(2) s of any type don't appear to have led or lead anyone there...

  • $\begingroup$ I think the rishon model does a good job of ordering the small zoo of elementary particles. This means of course that the "truly basic" Lagrangean has to be found, incorporating the two rishons and three long-range forces (the em force, the color force, and the hyper color force, ignoring gravity) of which the weak interaction is a residue force as is the case for the old fashioned strong force. $\endgroup$ Oct 26, 2020 at 22:44

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