We know quarks and leptons (including electrons and neutrinos), which make up what is classically known as matter, are all fermions with spin-1/2. The common idea that "matter takes up space" actually comes from the Pauli exclusion principle acting on these particles to prevent the fermions that make up matter from being in the same quantum state. It is also this pressure which prevents stars collapsing inwardly, and which, when it finally gives way under immense gravitational pressure in a dying massive star, triggers inward collapse and the dramatic explosion into a supernova.
Furthermore, elementary particles which are thought of as carrying forces are all bosons with spin-1. They include the photon which carries the electromagnetic force, the gluon (strong force), and the W and Z bosons (weak force).
But elementary fermions with other spins (3/2, 5/2 etc.) are not known to exist, until now and elementary bosons with other spins (0, 2, 3 etc.) were not historically known to exist, although they have received considerable theoretical treatment and are well established within their respective mainstream theories. In particular theoreticians have proposed the graviton (predicted to exist by some quantum gravity theories) with spin 2, and the Higgs boson (explaining electroweak symmetry breaking) with spin 0.
As I understand, a boson particle has been detected at a mass of ~125 GeV/c^2 that has been confirmed to be a Higgs boson - its zero spin property has been 'tentatively confirmed'.
http://home.web.cern.ch/about/updates/2013/03/new-results-indicate-new-particle-higgs-boson
"Whether or not it is a Higgs boson is demonstrated by how it interacts with other particles, and its quantum properties. For example, a Higgs boson is postulated to have no spin, and in the Standard Model its parity – a measure of how its mirror image behaves – should be positive. CMS and ATLAS have compared a number of options for the spin-parity of this particle, and these all prefer no spin and positive parity. This, coupled with the measured interactions of the new particle with other particles, strongly indicates that it is a Higgs boson."
"To determine if this is the Standard Model Higgs boson, the collaborations have, for example, to measure precisely the rate at which the boson decays into other particles and compare the results to the predictions. The detection of the boson is a very rare event – it takes around 1 trillion (1012) proton-proton collisions for each observed event. To characterize all of the decay modes will require much more data from the LHC."
Interesting question - I hope that someone can explain the physical meaning of zero spin!
There is some research going on gravitino dark matter. Gravitino is the superpartner of graviton. it is a spin 3/2 particle. So it does not follow dirac equation. it follows Rarita Schwinger equation.. Various model is there that predicts gravitino is a good candidate of dark matter
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