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

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 $\ln a\approx 1$.