  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. Based on the requirement for a
well-behaved unitarized effective-field theory of gravity, we can exclude
values $\ln a\lesssim 0.5$, and obtain hints that larger ones $\ln a\gtrsim
1.7$ are disfavored too. Briefly, we discuss the $D$-wave scattering that is
weaker than the $S-$wave scattering, repulsive and non-resonant for $\ln
a\approx 1$.
