Universal features of $ 2\to N$ scattering in QCD and gravity from shockwave collisions
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866913216572948480 |
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| author | Raj, Himanshu Venugopalan, Raju |
| author_facet | Raj, Himanshu Venugopalan, Raju |
| contents | A remarkable double copy relation of Einstein gravity to QCD in Regge asymptotics is $Γ^{μν}= \frac12C^μC^ν- \frac12N^μN^ν$, where $Γ^{μν}$ is the gravitational Lipatov vertex in the $2\to 3$ graviton scattering amplitude, $C^μ$ its Yang-Mills counterpart, and $N^μ$ the QED bremssstrahlung vertex. In QCD, the Lipatov vertex is a fundamental building block of the BFKL equation describing $2\to N$ scattering of gluons at high energies. Likewise, the gravitational Lipatov vertex is a key ingredient in a 2-D effective field theory framework describing trans-Planckian $2\to N$ graviton scattering. We construct a quantitative correspondence between a semi-classical Yang-Mills framework for radiation in gluon shockwave collisions and its counterpart in general relativity. In particular, we demonstrate the Lipatov double copy in a dilute-dilute approximation corresponding to $R_{S,L}$, $R_{S,H}$ $ \ll b$, with $R_{S,L}$, $R_{S,H}$ the respective emergent Schwarzchild radii generated in shockwave collisions and $b$ is the impact parameter. We outline extensions of the correspondence developed here to the dilute-dense computation of gravitational wave radiation in close vicinity of one of the black holes, the construction of graviton propagators in the shockwave background, and a renormalization group approach to compute $2\rightarrow N$ amplitudes that incorporates graviton reggeization and coherent graviton multiple scattering. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_03463 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Universal features of $ 2\to N$ scattering in QCD and gravity from shockwave collisions Raj, Himanshu Venugopalan, Raju High Energy Physics - Theory General Relativity and Quantum Cosmology High Energy Physics - Phenomenology Nuclear Theory A remarkable double copy relation of Einstein gravity to QCD in Regge asymptotics is $Γ^{μν}= \frac12C^μC^ν- \frac12N^μN^ν$, where $Γ^{μν}$ is the gravitational Lipatov vertex in the $2\to 3$ graviton scattering amplitude, $C^μ$ its Yang-Mills counterpart, and $N^μ$ the QED bremssstrahlung vertex. In QCD, the Lipatov vertex is a fundamental building block of the BFKL equation describing $2\to N$ scattering of gluons at high energies. Likewise, the gravitational Lipatov vertex is a key ingredient in a 2-D effective field theory framework describing trans-Planckian $2\to N$ graviton scattering. We construct a quantitative correspondence between a semi-classical Yang-Mills framework for radiation in gluon shockwave collisions and its counterpart in general relativity. In particular, we demonstrate the Lipatov double copy in a dilute-dilute approximation corresponding to $R_{S,L}$, $R_{S,H}$ $ \ll b$, with $R_{S,L}$, $R_{S,H}$ the respective emergent Schwarzchild radii generated in shockwave collisions and $b$ is the impact parameter. We outline extensions of the correspondence developed here to the dilute-dense computation of gravitational wave radiation in close vicinity of one of the black holes, the construction of graviton propagators in the shockwave background, and a renormalization group approach to compute $2\rightarrow N$ amplitudes that incorporates graviton reggeization and coherent graviton multiple scattering. |
| title | Universal features of $ 2\to N$ scattering in QCD and gravity from shockwave collisions |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology High Energy Physics - Phenomenology Nuclear Theory |
| url | https://arxiv.org/abs/2311.03463 |