Unitarization of the one-loop graviton-graviton scattering amplitudes and study of the graviball
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| Format: | Preprint |
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2024
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| author | Oller, J. A. Peláez, Marcela |
| author_facet | Oller, J. A. Peláez, Marcela |
| contents | 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 $\ln a\approx 1$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_16538 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Unitarization of the one-loop graviton-graviton scattering amplitudes and study of the graviball Oller, J. A. Peláez, Marcela High Energy Physics - Theory High Energy Physics - Phenomenology 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 $\ln a\approx 1$. |
| title | Unitarization of the one-loop graviton-graviton scattering amplitudes and study of the graviball |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2407.16538 |