Smooth conformal deformations of the generalized free field theories in arbitrary dimensions can be studied by exploiting the singula rity structure of the conformal blocks dictated by the null states. It is straightforward to derive in this way\, to the first non-trivial order in the epsilon expansion\, using just CFT data\, the anomalous dimensions and OPE coefficients of infinite classes of local operators in single-scala r and O(N)-invariant theories. We do not use Lagrangians nor equations of motion. In the cases where other computational methods apply\, the results agree

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