The photon plus missing energy signature is a primary handle on two important
classes of theories. Theories with large extra dimensions predict the
production of photons in association with Kaluza-Klein excitations of the
graviton. In supersymmetric theories with superlight gravitinos, photons can be
produced in association with gravitino pairs. The signatures for these two
theories are compared, and it is found that they can be distinguished by
studying the photon energy distributions and scaling of the cross section with
center-of-mass energy. Both these methods fail, however, if there are six extra
dimensions. In that case, additional phenomena predicted by the theories would
be required to narrow down the underlying causes of the photon plus missing
energy signal. We also study the ability of these measurements to determine the
number of extra dimensions.Comment: 4 pages, 2 figures. Contributed to APS / DPF / DPB Summer Study on
the Future of Particle Physics (Snowmass 2001), Snowmass, Colorado, 30 Jun -
21 Jul 200