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I'm reading often that a possible reason to explain why the Nobel committee is coping out from making the physics Nobel related to the higgs could be among other things the fact that the spin of the new particle has not yet been definitively determined, it could still be 0 or 2.
This makes me wonder if the spin would (very very surprisingly!) finally be discovered to be 2, this then necessarily would mean that the particle has to be a graviton? Or could there hypothetically be other spin-2 particles? If not, why not and if there indeed exist other possibilities what would they be?
There are theoretical arguments that a massless spin-2 particle has to be a graviton. The basic idea is that massless particles have to couple to conserved currents, and the only available one is the stress-energy tensor, which is the source for gravity. See this answer for more detail.
However, the particle discovered at LHC this year has a mass of 125 GeV, so none of these arguments apply. It would be a great surprise if this particle did not have spin 0. But it is theoretically possible. One can get massive spin 2 particles as bound states, or in theories with infinite towers of higher spin particles.
It depends on your definition of "particle" . In the particle data group listings there exist a number of spin 2 resonances. These ultimately will be built up by quarks.
f_2(1270 MeV) page 9
a_2(1320) page 11
there is a pi_2 (1670) page 16
So the bump called now "the Higgs" could turn out to be one more resonance. Not the graviton as it is envisaged in possible theories of everything, since gravity is long range and it should be massless, I believe.
A massive spin 2 particle must have five modes: helicity
$\pm 2$, $\pm 1$, 0. If a massless spin 2 particle has only helicity
$\pm 2$ modes without other modes and has a dispersion $\omega = c k$, then such a
massless spin 2 particle must be graviton (at least at linear order).
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