# Can we infer from weak isospin symmetry the existence of sub-quark particles?

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).

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?

• "... 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? Oct 25, 2020 at 16:20
• Well, by the same token one can say that a unit of a strong charge is precisely a unit of strong isospin charge. Oct 26, 2020 at 22:38
• 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). Oct 26, 2020 at 22:45
• 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. Oct 27, 2020 at 13:53
• 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). Oct 27, 2020 at 13:54