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Is there any explanation/theorem which justifies that most fundamental particles have spin half or spin one?

Apriori, studying representations of symmetry groups and their connection with spin of fundamental particles, one wouldn't expect that nature give overwhelming preference to spin half or spin one particles being in abundance but AFAIK that's what is observed. Is there any explanation for this observation or is it an open question? Is this anyhow connected to the matter-antimatter asymmetry problem?

Edit : In nature, most of the fundamental particles we find, by abundance, are spin half, spin one (gauge bosons) at most and we typically don't find other spin particles like spin three-half or spin two, by abundance.

Qmechanic
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self.grassmanian
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1 Answers1

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Just to flesh out all the comments above (eg. to this answer and the Weinberg-Witten, Coleman-Mandula and Haag-Lopuszanski-Sohnius theorems) in a heuristic summary (which ignores infinite towers as appear e.g. in string theory):

  • Spins higher than 2 cannot appear.
  • A spin-2 particle can only be the graviton, and there is one of those.
  • A spin-3/2 particle can only be the gravitino, and there are as many of those as there are SUSY generators. In the standard model, there are none; the only plausible way to accomodate the (chiral) standard model in a SUSY theory has one.
  • A spin-1 particle needs to be a gauge boson, and you can have as many of them as you have gauge group generators. In the standard model, there are twelve (photon, $W^\pm$, $Z$, eight gluons), but there is no (generally agreed-upon) deep reason why there couldn't be more, e.g in grand unified theories.
  • Spin-1/2 particles are unrestricted, but only the chiral ones are massless (the non-chiral ones will (* waves hands *) want to be very massive and hence unobservable). These will come in some representation of the gauge group, and the chiral ones have to fulfill anomaly cancellation requirements, but there is no obvious constraint on the overall number. In the SM; there are three generations, but there is no deep reason why there are not two or four generations.
  • Spin-0 particles are unrestricted, but will want to be very massive and hence unobservable -- this is essentially the hierarchy problem for the Higgs boson.

Note that in theories beyond the standard model, there may be stronger constraints, e.g. for supersymmetric theories in six dimensions, but these are speculative.

Toffomat
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  • Very nice summary. However, I think, it still doesn't fully answer my question. Your summary does explain why particles with spin>2 etc are not observed but it still fails to explain (in my view) why would there be more types (quarks and leptons : total 12) of particles having spin half (chiral) than spin one (gauge bosons : 4) as one goes about in the group theory perspective. Perhaps I should ask why are there less gauge group generators for gauge bosons? – self.grassmanian Dec 01 '21 at 14:03
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    @self.grassmanian There simply may be no fundamental reason. – Toffomat Dec 01 '21 at 16:33
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    @self.grassmanian Seems to me you are ignoring that any theory of physics has to fit the observations and be predictive , and tested of validity for those predictions. The spin portrait described above maps with mathematical theories the observations and does not predict differently. if (when?) observations reveal a contradiction to the theoretical models summarized above, I am sure new ones will be found. The ultimate answer to your question is that the standard model (data bank) and the existence of gravity are taken in the answer as axiomatic. – anna v Dec 02 '21 at 04:30