{
  "id": "2412.10560",
  "version": "v1",
  "published": "2024-12-13T21:05:51.000Z",
  "updated": "2024-12-13T21:05:51.000Z",
  "title": "Born-Oppenheimer Renormalization group for High Energy Scattering: the Modified BFKL, or where did it all go?",
  "authors": [
    "Haowu Duan",
    "Alex Kovner",
    "Michael Lublinsky"
  ],
  "comment": "25 pages, 8 figures",
  "categories": [
    "hep-ph",
    "hep-th",
    "nucl-th"
  ],
  "abstract": "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 $\\eta$ becomes quite weak with $Q^2_s\\sim e^{a\\bar\\alpha_s\\eta}$ 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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-12-13T21:05:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "high energy scattering",
      "modified bfkl",
      "born-oppenheimer renormalization group generating evolution",
      "bfkl value",
      "canonical lo bfkl result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}