Renormalization group and effective potential in classically conformal theories

For a classically conformal model of QCD coupled via quarks to a colorless scalar field we present an exact solution of the RG improved effective (Coleman-Weinberg) potential at one loop. This closed form expression allows us to discuss the range of validity of the effective potential as well as the issue of `large logarithms' in a way different from previous such analyses. Remarkably, in all examples considered, convexity of the effective potential is restored by the RG improvement, or otherwise the potential becomes unstable. In the former case, symmetry breaking becomes unavoidable due to the appearance of an infrared barrier, which hints at a so far unsuspected link between $\Lambda_{QCD}$ and the scale of electroweak symmetry breaking