Renormalization of the energy--momentum tensor in phi4 theory

The problem of the improvement term of the energy-momentum tensor theta/sub μν/ in phi4 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 theta/sub μν/. This theta/sub μν/ has a soft trace at a fixed point. It coincides with the theta/sub μν/ 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 theta/sub μν/ is finite only up to the three-loop level, and not beyond, even if it is correctly dimensionally regularized