Softly broken conformal symmetry and the stability of the electroweak scale

We point out a novel possible mechanism by which the electroweak hierarchy problem can be avoided in the (effective) quantum field theory. Assuming the existence of a UV complete underlying fundamental theory and treating the cutoff scale $\Lambda$ of the effective field theory as a real physical scale we argue that the hierarchy problem would be solved if the coefficient in front of quadratic divergences vanished for some choice of $\Lambda$, and if the effective theory mass parameters fixed at $\Lambda$ by the fundamental theory were hierarchically smaller than $\Lambda$ itself. While this mechanism most probably cannot work in the Standard Model if the scale $\Lambda$ is to be close to the Planck scale, we show that it can work in a minimal extension (Conformal Standard Model) proposed recently for a different implementation of soft conformal symmetry breaking.