  We consider the cubic-quintic nonlinear Schr\"odinger equation in two space
dimensions. For this model, X. Cheng established scattering for $H^1$ data with
mass strictly below that of the ground state for the cubic NLS. Subsequently,
R. Carles and C. Sparber utilized the pseudoconformal energy estimate to obtain
scattering at the sharp threshold for data belonging to a weighted Sobolev
space. In this work, we remove the weighted assumption and establish scattering
at the threshold for radial data in $H^1$.
