Measuring the Spin of Invisible Massive Graviton Excitations at Future Linear Colliders

We consider the production process e−e+→Gγ of invisible gravitons (G) at future linear colliders. We discuss whether the angular distribution of the photon (γ) can be used to measure the spin of the invisible graviton, or of any other invisible objects produced. We propose a method based on the Fourier expansion of the transverse energy squared moment distribution of the photon. We provide justification for this method, and confirm, especially for the case of two extra dimensions, that the method is valid within a realistic setup, which includes the simulation of the Standard Model background, beamstrahlung, bremsstrahlung, calorimeter resolution and calorimeter coverage. When the number of extra dimensions is increased, the angular distribution does not provide sufficient information to extract the spin, but this method still offers a useful parameterization of the single photon cross section using which the nature of the missing object can be studied.