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In a conformal field theory with weakly broken higher spin symmetry, the leading order anomalous dimensions of the broken currents can be efficiently determined from the structure of the classical non-conservation equations. We apply this method to the explicit example of O(N) invariant scalar field theories in various dimensions, including the large N critical O(N) model in general d, the Wilson-Fisher fixed point in d=4-ϵ, cubic scalar models in d=6-ϵ and the nonlinear sigma model in d=2+ϵ.doi:10.1007/jhep11(2016)068 fatcat:ppm3si6cozfoloh7ekfwzzlkuy