  In this work, we prove global well-posedness and scattering for systems of
quadratic nonlinear Schr\"odinger equations in the critical three-dimensional
case, for small, localized data. For the terms corresponding to the
nonlinearity $u\bar{u}$, we need to do an $\epsilon$ regularization of this
part of the nonlinearity.
  In order to tackle quadratic space-time resonances, after performing a
Littlewood-Paley decomposition, we use integration by parts in the Duhamel
term, to take advantage of the oscillations when space-time resonances are
absent.
