Unitarity and Dilaton effective theory

TL;DR

This paper investigates the unitarity of dilaton scattering amplitudes within an effective theory, revealing unitarity violation at high energies and proposing that including a spin-2 state can restore unitarity, with implications for conformal dynamics.

Contribution

It demonstrates that adding a spin-2 state near the cutoff improves unitarity in dilaton effective theory, linking mass ratios to near conformal scaling.

Findings

One-loop dilaton scattering amplitude violates unitarity near cutoff.

Including a spin-2 state restores unitarity.

Mass ratio relates to Miransky-BKT scaling of conformal dynamics.

Abstract

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.