Renormalization of the energy-momentum tensor in φ4 theory

The problem of the improvement term of the energy-momentum tensor θμν in φ4 theory is reconsidered. Renormalization-group methods (due to 't Hooft) with dimensional regularization are used. A unique finite improvement coefficient, depending only on the regulator parameter, is shown to renormalize θμν. This θμν has a soft trace at a fixed point. It coincides with the θμν suggested by conformal ideas and by Callan, Coleman, and Jackiw (CCJ), if summation of the perturbation theory divergences is allowed. But order by order, the CCJ θμν is finite only up to the three-loop level, and not beyond, even if it is correctly dimensionally regularized.