Born-Oppenheimer Renormalization group for High Energy Scattering: the Modified BFKL, or where did it all go?
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917878267117568 |
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| author | Duan, Haowu Kovner, Alex Lublinsky, Michael |
| author_facet | Duan, Haowu Kovner, Alex Lublinsky, Michael |
| contents | We continue exploring the Born-Oppenheimer renormalization group generating evolution in frequency of physical observables. In this paper we study the evolution of the total cross section for dilute-dilute scattering retaining only eikonal emissions. We derive and analyze the analog of the BFKL equation in this framework. The frequency evolution has a very strong effect on the solutions of the BO-BFKL equation, slowing down the evolution of the scattering amplitude in a spectacular fashion: the intercept of the Pomeron is decreased by about a factor of three relative to the canonical LO BFKL result. The anomalous dimension is also modified significantly - from the BFKL value of one it goes down to the negative value of $\approx-0.2$. Introducing saturation boundary as a proxy for the full saturation dynamics, we find that the dependence of the saturation momentum on rapidity $η$ becomes quite weak with $Q^2_s\sim e^{a\barα_sη}$ with $a\approx 0.784$ as opposed to the BFKL value $a=4.88$. Our results underscore the necessity to take into account the DGLAP effects in the high energy evolution. This is left for future work. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_10560 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Born-Oppenheimer Renormalization group for High Energy Scattering: the Modified BFKL, or where did it all go? Duan, Haowu Kovner, Alex Lublinsky, Michael High Energy Physics - Phenomenology High Energy Physics - Theory Nuclear Theory We continue exploring the Born-Oppenheimer renormalization group generating evolution in frequency of physical observables. In this paper we study the evolution of the total cross section for dilute-dilute scattering retaining only eikonal emissions. We derive and analyze the analog of the BFKL equation in this framework. The frequency evolution has a very strong effect on the solutions of the BO-BFKL equation, slowing down the evolution of the scattering amplitude in a spectacular fashion: the intercept of the Pomeron is decreased by about a factor of three relative to the canonical LO BFKL result. The anomalous dimension is also modified significantly - from the BFKL value of one it goes down to the negative value of $\approx-0.2$. Introducing saturation boundary as a proxy for the full saturation dynamics, we find that the dependence of the saturation momentum on rapidity $η$ becomes quite weak with $Q^2_s\sim e^{a\barα_sη}$ with $a\approx 0.784$ as opposed to the BFKL value $a=4.88$. Our results underscore the necessity to take into account the DGLAP effects in the high energy evolution. This is left for future work. |
| title | Born-Oppenheimer Renormalization group for High Energy Scattering: the Modified BFKL, or where did it all go? |
| topic | High Energy Physics - Phenomenology High Energy Physics - Theory Nuclear Theory |
| url | https://arxiv.org/abs/2412.10560 |