Unitarization of the one-loop graviton-graviton scattering amplitudes and study of the graviball

TL;DR

This paper develops a formalism for unitarizing one-loop graviton scattering amplitudes, confirming the graviball resonance and analyzing the effects of a parameter on the theory's spectrum and unitarity.

Contribution

It introduces a method to unitarize one-loop graviton scattering amplitudes, confirming the graviball resonance across different unitarization techniques.

Findings

Confirmation of the graviball resonance in S-wave amplitudes.

Identification of the optimal range for the parameter a for effective field theory.

Analysis of D-wave scattering showing weaker, non-resonant behavior.

Abstract

From the graviton-graviton scattering amplitudes calculated perturbatively in quantum gravity to the one-loop order, we develop further a formalism that allows one to calculate infrared-finite partial-wave amplitudes fulfilling perturbative unitarity. As a result of this process a parameter dubbed $\ln a$ emerges that separate between infrared and typical external momenta. The resulting partial-wave amplitudes are next unitarized by employing the Inverse Amplitude Method and the algebraic-$N/D$ method. Then, the graviball resonance, with a similar pole position, is confirmed in the $S$-wave partial-wave amplitude for all unitarization methods, also with respect to the unitarization of only the leading-order amplitude. Although the spectrum of the theory is independent of the specific value of $\ln a$, the requirement for a well-behaved unitarized effective field theory of gravity identifies the optimal range of $\ln a$ for our next-to-leading-order calculations as $0.5 \lesssim \ln a \lesssim 1.7$. Briefly, we discuss the $D$-wave scattering that is weaker than the $S-$wave scattering, repulsive and non-resonant for $\ln a\approx 1$.