We address the question of whether there are 4D Lorentz invariant unitary quantum field theories with scale invariance but not conformal invariance. An important loophole in the existing arguments is that trace of the energy-momentum tensor T could be a generalized free field. We rule out this possibility. This is achieved by using the structure of four-dimensional anomalies. In addition, we emphasize that short distance physics is not the same as large momentum physics and explain the relation to the problem of scale vs conformal invariance.