You can get information about the spin of the particles by looking at the angular distribution of the reaction products. If the particle is spin-0, this should be isotropic, and that is what’s being seen; in fact, I’ve heard that a spin-2 particle is excluded at 90% confidence, but I’m not willing to bet the house on that figure.
Matt Strassler does a pretty good job of explaining why the “two higgs” hype from Sci. Am. is pretty clueless and irresponsible.
“Sterile” here means “does not interact via the strong, weak, or electromagnetic forces”. Imagining such a particle isn’t too crazy, as you’ve got (1) quarks that experience all three of strong, weak, and EM forces, (2) electrons and their heavier cousins that experience two of the forces [weak and EM], and (3) neutrinos that experience only one of the forces [weak]. Why not have (4) a “sterile” particle that experiences none of them?
The motivation for introducing such particles isn’t the above naive extrapolation, though. Some of the ways sterile particles touch on current research:
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Sterile particles would still interact gravitationally and could be relevant in understanding dark matter.
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You might have heard of “neutrino oscillations”, the phenomenon by which neutrinos of one type can change into another type as they travel. If there is a type of neutrino out there that is sterile, it may be possible to detect its presence via changes it induces in how neutrinos oscillate. In fact, a pile of unexplained data has accumulated over the past 15 years or so that could be explained by introducing sterile neutrinos. (As an aside: the particular variety of sterile neutrino you would need for this happens not to help with the dark matter issue in any clean way.)
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An open question is why neutrinos are so much less massive than everything else. An attractive explanation involves a different type of sterile particle that has an extremely high mass and has a certain quantum mechanical mixing with the “everyday” neutrinos that results in their physical masses being inversely proportional to the (very high) mass of this hypothesized sterile particle. This new particle would need a mass close to the Planck mass (actually a hair less), which one could argue is as natural a choice as anything. This heavy particle (or particles) could also provide a source of matter/antimatter asymmetry in the early universe, something sorely needed to explain why everything created at the time of the Big Bang didn’t just annihilate away again.
He isn’t saying that it doesn’t matter in a general way. He’s just saying that the particular sort of graviton he’s referring to could be massless or merely very nearly massless and it wouldn’t affect whether it would show up as a “heavy” particle at the LHC. Outside of that context, though, if that graviton weren’t massless but were in fact only very nearly massless, it would matter a great deal.
There’s no measurement you can perform to tell that something’s mass is truly exactly zero. All you can ever do is say “If it has a mass, it’s below this threshold”, and then work on improving your experiment to push that threshold down further. For photons, say, this threshold is very, very low, and so we usually assume that photons are massless. For gravitons, the threshold is far lower even than it is for photons, so it’s even more reasonable to assume that gravitons are massless. We can’t be sure of either, but no experiment has ever produced significant evidence that photons or gravitons are massive, hence, for purposes of current technology, they’re “close enough to massless as makes no difference”.