The LHC experiments ATLAS and CMS have discovered a new boson that resembles the long-sought Higgs boson: it cannot have spin one, and has couplings to other particles that increase with their masses, but the spin and parity remain to be determined. We show here that the `Higgs' + gauge boson invariant-mass distribution in `Higgs'-strahlung events at the Tevatron or the LHC would be very different under the J P = 0+;0 and 2+ hypotheses. Our analysis is based on simulations of the experimental event selections and cuts using PYTHIA and Delphes, and incorporates statistical samples of `toy' experiments. The observation of `Higgs'-strahlung at the Tevatron and the expected peaking of backgrounds at low invariant masses suggest that this process could provide a fast-track indicator of the `Higgs' spin and parity
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