  From the low-energy effective theory of dilatons, consistent with the scale
anomaly, we calculate the $2\to2$ scattering amplitudes of dilatons. We find
that the one-loop amplitude violates the unitarity bound as the scattering
energy approaches the cutoff of the effective theory, $\sqrt{s}=\sqrt{4\pi}
f_D$. We then show that the inclusion of the next-to-lightest state, namely the
spin-2 state, of mass around the cutoff improves the unitarity. The unitarity
argument suggests that the mass ratio of the dilaton and the spin-2 state is
proportional to the square of the Miransky-BKT scaling of the near conformal
dynamics.
