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Scattering from an external field in quantum chromodynamics at high energies: from foundations to interdisciplinary connections
by Athanasia-Konstantina Angelopoulou, Anh Dung Le, Stéphane Munier
Submission summary
| Authors (as registered SciPost users): | Stéphane Munier |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2311.14796v2 (pdf) |
| Date submitted: | 2024-10-15 14:30 |
| Submitted by: | Munier, Stéphane |
| Submitted to: | SciPost Physics Lecture Notes |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We review the factorization of the $S$-matrix elements in the context of particle scattering off an external field, which can serve as a model for the field of a large nucleus. The factorization takes the form of a convolution of light cone wave functions describing the physical incoming and outgoing states in terms of bare partons, and products of Wilson lines. The latter represent the interaction between the bare partons and the external field. Specializing to elastic scattering amplitudes of onia at very high energies, we introduce the color dipole model, which formulates the calculation of the modulus-squared of the wave functions in quantum chromodynamics with the help of a branching random walk, and the scattering amplitudes as observables on this classical stochastic process. Methods developed for general branching processes produce analytical formulas for the asymptotics of such observables, and thus enable one to derive exact large-rapidity expressions for onium-nucleus cross sections, from which electron-nucleus cross sections may be inferred.
Current status:
Reports on this Submission
Report
I am happy to recommend publication of this set of notes in this format after some not very extesive changes have been made. I find the presentation suitable for honours or masters students and certainly a well presented source for material otherwise not easily accessible.
Requested changes
1) In the introduction of eikonal scattering (the paragraph above Eq.(33)) the authors state that the "the external potential is unaffected, technically..."
This is true, technically, but that does not explain what is going physicswise. The physics point of the matter is that the projectile is moving fast against the field. We do not boost the whole system -- rather we accelerate the probe relative to the target. One meets boost very differently as a student, as a means to discuss inertial frames, but that is precisely not what is going on here and a good fraction of your readers will likely be confused, my own students have been often encough. I would urge the authors to add a paragraph to clarify the issue.
2) Before and in Eq. (81) fundamental and defining appear as synomymous, without you linking them. Your intended audience likely needs either one of the two be used exlusively or the fact that they are synonymous spelled out.
3) I personally find the exposition of branching random walks sufficintly clear and the notation in Eq. (236) self explanatory. However: Why $2\mu+r \le 1$ is imposed should be explained. Likewise the notation used in Eq. (240) with the zeroes below the "location bucket graphs" fail to be fully self explanatory and does need explanations.
Recommendation
Ask for minor revision
Strengths
The paper is a valuable review of relation of high energy QCD evolution equations to statistical physics. It present the material in great detail.
Weaknesses
I do not see weeknesses of the paper
Report
The paper is a very valuable write up of lecture on relation of QCD at high energy to statistical physics. While the paper is focused on theory the equations that it discusses are of phenomenological interest. In particular tt discusses BFKL and BK equations and their relation to the FKKP equation. In particular I appreciate very much rederivation of the BK equation.
Before the paper can be published I have few minor points to be addressed.
1 Below formula (54) the Authors describe the inverse derivative. Their discuss in words the meaning of this operator. I suggest to write explicitly the formula i.e. as integral operator acting on test function
2 While the equation equation is not closed there exist closed equation equivalent to the Balitsky hierarchy i.e. JIMWLK equation. I suggest that the Authors mention it here
3 After the equation (245) the Authors discuss the quantity q_n(t+\Delta t). The transition from the "Random walk" section is not clear. Furthermore the authors arrive at eqn 247 and 249. As the lecture notes are on QCD and statistical physics it would be good to mention that the eq (249) appeared in the context of Mueller model A. H. Mueller, “Unitarity and the bfkl pomeron,” Nuclear Physics B 437 no. 1, (1995) and eq (247) in Lublinsky, Levin Nucl.Phys.A 730 (2004) 191-211
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)