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The chart below from Wikipedia lists the weak isospins of all elementary particles.

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It states that right-handed matter particles and left-handed anti-matter particles have a weak isospin of 0.

  1. Is right-handed matter particles and left-handed anti-matter particles having weak isospin 0 the reason they do not interact with the weak force?

  2. Are the two statements equivalent?

    • right-handed matter particles and left-handed anti-matter particles having weak isospin 0
    • right-handed matter particles and left-handed anti-matter particles do not interact with the weak force

  3. Are the weak isospin values an experimental determination or theoretical? Did we measure right-handed matter particles and left-handed anti-matter particles and see that they have weak isospin 0 or did we see that they do not interact with the weak force and assigned them a weak isopsin of 0?

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  1. Yes

  2. Yes.

  3. An experimental determination, evolving hand-in-hand with a sequence of theoretical developments. The final organization in this language, the SM, was theoretical, as it fit all pieces of experimental data "to a T". Specifically, it was known since 1956 (V-A theory/experiments) that parity was violated in weak interactions in a "maximal" way, i.e. in a way that ignored right-handed matter particles and left-handed anti-matter particles: only the other two cases interacted weakly through the charged current.

  • After some theoretical ferment, in 1967, the gauge electroweak theory (SM) was proposed, postulating a neutral current, which did involve right-handed matter particles and left-handed anti-matter particles, as well, albeit in a subtle way that respected its underlying indifference to weak isospin (long story, dubbed EW mixing). So, it accommodated an experimental fact. Finally, in 1973, this neutral current was observed experimentally, thereby confirming the SM proposed theory.

So, you see, theory and experiment evolved hand-in-hand, trading tips, and any narrative classifying a fact as strictly part of one or the other, is bound to misrepresent reality here...

In the intervening half century, a plethora of measurements and experiments have all "measured" weak isospins and hypercharges, indirectly, and have confirmed all aspects of the SM.

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  • $\begingroup$ Thank you. Let me clarify the last point - I am not asking whether we experimentally can determine whether left handed matter particles and right handed anti matter particles are the only ones that can interact with the weak force. I am asking the actual value of the weak isospin (-1/2 for left handed electron, 0 for right handed electron) - is there an experiment that spits out these specific values for these particles or are these values theoretical representations? $\endgroup$
    – NonPartisanObservor
    Mar 16 at 21:59
  • $\begingroup$ We agreed in 2) no interaction means weak isosinglet, so that's as good as 0. The 1/2 is gotten from the eigenvalues of $I_z$ in isodoublets, i.e. multiplets under the weak charge current interaction, verified in hundreds of experiments, which contain only two members, (ν,e), (u,d), ... There is no other consistent way to describe weak isospin. Hundreds of experiments "spit out" these values because there is no other successful accounting for them. $\endgroup$
    – Cosmas Zachos
    Mar 16 at 22:05
  • $\begingroup$ Thanks. That answers my question. I was caught in the chicken and the egg loop - about which came first. Whether right handed matter particles have weak isospin zero because they don’t interact with the weak force or do right handed matter particles not interact with the weak force because their weak isospin is zero. But your answer clarifies my concern. $\endgroup$
    – NonPartisanObservor
    Mar 16 at 23:42

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