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It has been always said that $W$ an $Z$ bosons are bosons and not fermions but is there any experimental trial that prove that? Has anyone put two of them in the same quantum state or studies have shown they obey Bose-Einstein statistics rather than Fermi-Dirac’s ?
It is really strange to me that such a short living particle been studied so.

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The spin of a decaying particle dictates in part the angular distribution that you would see from its decay products, due to conservation of angular momentum. We can use this to experimentally determine the spin of the W and Z bosons.

In particular, we can use the fact that the angular decay spectra of the W and Z are not isotropic (i.e. they're asymmetric) to eliminate the possibility of them being spin-0 particles (as the only property of a spin-0 particle that can enter into the amplitude at tree-level is its mass, by Lorentz invariance, this means that their decays must be isotropic in the decaying particle's rest frame). The particular way in which their decay spectra are asymmetric helps to rule out other spins; quantifying this process, there are eight spin observables which have been measured at colliders like the LHC (more details in section 5 of this paper: https://arxiv.org/abs/1701.03115). Their spin has been measured to be 1; therefore, they are bosons.

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  • $\begingroup$ I think you arxiv link is incorrect--it was about relativistic ideal gases. $\endgroup$ – JEB Mar 30 '18 at 2:42
  • $\begingroup$ Oops; I apparently got two arxiv links mixed up. Should be fixed now. $\endgroup$ – probably_someone Mar 30 '18 at 2:44

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