Unitarization of infinite-range forces: graviton-graviton scattering
Abstract A method to unitarize the scattering amplitude produced by infinite-range forces is developed and applied to Born terms. In order to apply S-matrix techniques, based on unitarity and analyticity, we first derive an S-matrix free of infrared divergences. This is achieved by removing a diverg...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-08-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP08(2022)266 |
| _version_ | 1828356387908878336 |
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| author | D. Blas J. Martín Camalich J. A. Oller |
| author_facet | D. Blas J. Martín Camalich J. A. Oller |
| author_sort | D. Blas |
| collection | DOAJ |
| description | Abstract A method to unitarize the scattering amplitude produced by infinite-range forces is developed and applied to Born terms. In order to apply S-matrix techniques, based on unitarity and analyticity, we first derive an S-matrix free of infrared divergences. This is achieved by removing a divergent phase factor due to the interactions mediated by the massless particles in the crossed channels, a procedure that is related to previous formalisms to treat infrared divergences. We apply this method in detail by unitarizing the Born terms for graviton-graviton scattering in pure gravity and we find a scalar graviton-graviton resonance with vacuum quantum numbers (J PC = 0++) that we call the graviball. Remarkably, this resonance is located below the Planck mass but deep in the complex s-plane (with s the usual Mandelstam variable), so that its effects along the physical real s axis peak for values significantly lower than this scale. This implies that the corrections to the leading-order amplitude in the gravitational effective field theory are larger than expected from naive dimensional analysis for s around and above the peak position. We argue that the position and width of the graviball are reduced when including extra light fields in the theory. This could lead to phenomenological consequences in scenarios of quantum gravity with a large number of such fields or, in general, with a low-energy ultraviolet completion. We also apply this formalism to two non-relativistic potentials with exact known solutions for the scattering amplitudes: Coulomb scattering and an energy-dependent potential obtained from the Coulomb one with a zero at threshold. This latter case shares the same J = 0 partial-wave projected Born term as the graviton-graviton case, except for a global factor. We find that the relevant resonance structure of these examples is reproduced by our methods, which represents a strong indication of their robustness. |
| first_indexed | 2024-04-14T02:58:26Z |
| format | Article |
| id | doaj.art-b236f34327a0491580dac9fc07f666a8 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-04-14T02:58:26Z |
| publishDate | 2022-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-b236f34327a0491580dac9fc07f666a82022-12-22T02:16:01ZengSpringerOpenJournal of High Energy Physics1029-84792022-08-012022816810.1007/JHEP08(2022)266Unitarization of infinite-range forces: graviton-graviton scatteringD. Blas0J. Martín Camalich1J. A. Oller2Theoretical Particle Physics and Cosmology Group, Department of Physics, King’s College LondonInstituto de Astrofísica de Canarias, C/ Vía LácteaDepartamento de Física. Universidad de MurciaAbstract A method to unitarize the scattering amplitude produced by infinite-range forces is developed and applied to Born terms. In order to apply S-matrix techniques, based on unitarity and analyticity, we first derive an S-matrix free of infrared divergences. This is achieved by removing a divergent phase factor due to the interactions mediated by the massless particles in the crossed channels, a procedure that is related to previous formalisms to treat infrared divergences. We apply this method in detail by unitarizing the Born terms for graviton-graviton scattering in pure gravity and we find a scalar graviton-graviton resonance with vacuum quantum numbers (J PC = 0++) that we call the graviball. Remarkably, this resonance is located below the Planck mass but deep in the complex s-plane (with s the usual Mandelstam variable), so that its effects along the physical real s axis peak for values significantly lower than this scale. This implies that the corrections to the leading-order amplitude in the gravitational effective field theory are larger than expected from naive dimensional analysis for s around and above the peak position. We argue that the position and width of the graviball are reduced when including extra light fields in the theory. This could lead to phenomenological consequences in scenarios of quantum gravity with a large number of such fields or, in general, with a low-energy ultraviolet completion. We also apply this formalism to two non-relativistic potentials with exact known solutions for the scattering amplitudes: Coulomb scattering and an energy-dependent potential obtained from the Coulomb one with a zero at threshold. This latter case shares the same J = 0 partial-wave projected Born term as the graviton-graviton case, except for a global factor. We find that the relevant resonance structure of these examples is reproduced by our methods, which represents a strong indication of their robustness.https://doi.org/10.1007/JHEP08(2022)266Effective Field TheoriesModels of Quantum GravityNonperturbative EffectsScattering Amplitudes |
| spellingShingle | D. Blas J. Martín Camalich J. A. Oller Unitarization of infinite-range forces: graviton-graviton scattering Journal of High Energy Physics Effective Field Theories Models of Quantum Gravity Nonperturbative Effects Scattering Amplitudes |
| title | Unitarization of infinite-range forces: graviton-graviton scattering |
| title_full | Unitarization of infinite-range forces: graviton-graviton scattering |
| title_fullStr | Unitarization of infinite-range forces: graviton-graviton scattering |
| title_full_unstemmed | Unitarization of infinite-range forces: graviton-graviton scattering |
| title_short | Unitarization of infinite-range forces: graviton-graviton scattering |
| title_sort | unitarization of infinite range forces graviton graviton scattering |
| topic | Effective Field Theories Models of Quantum Gravity Nonperturbative Effects Scattering Amplitudes |
| url | https://doi.org/10.1007/JHEP08(2022)266 |
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