Disperon QED

Report about arXiv:2512.10709v1

Disperon QED

by Yizhou Fang, Sophie Kollatzsch, Marco Rocco, Adrian Signer, Yannick Ulrich and Max Zoller

The calculation of precise predictions for scattering processes is often limited when strong interaction effects come into play. There are several examples where such effects can be located inside form factors for which input from data is available. Using a dispersion relation for this input allows one to separate the problem into standard loop integrals with an additional massive propagator and an integration over a dispersion parameter which can be performed numerically.

The idea is well-known and has been used in a number of applications already. The authors now present a framework which allows one to systematically apply the method and they present several important technical improvements. One can expect that the results described in the manuscript pave the way for more complicated future applications. It therefore definitely deserves consideration for publication.

The foundation of the method is described in section 2 and some appendices. It is shown, in section 3, how the standard well-established loop technology, combined with Monte Carlo techniques can be used. One important improvement concerns numerical stability of the dispersion integral for which the authors rely on ideas from effective theory and the method of regions (section 4). Another extension of the method serves to tame the problem of threshold singularities by constructing counter terms in section 5. Several numerical results are shown. Some of them serve to validate the approach by comparing exact with effective theory calculations (section 4.3), some more results are a first study of the cross section for pion pair production in electron positron annihilation (section 6). It is very helpful that input data, plots and analysis pipelines are separately made public on the webpage of the McMule team.

Some parts of the paper are very technical and require a good knowledge of previous literature. The manuscript is nevertheless very well written and comprehensible. As far as I can see, the list of references is appropriate and complete. I have only two points where additional information and clarification might be helpful:

1. For the calculation presented in section 4.3 the authors introduce a cut-off s_cut to separate two regions of the dispersion integral where two different approaches are used. They say that a value for s_cut has to be chosen 'such that the final result is independent of it'. I believe that this cannot be strictly made true since below and above the cut-off different approximations are used. I rather believe that the independence on the cut-off can be obtained within a certain error. If my understanding is correct, the authors should use a more careful wording. In addition, there is only one specific example for which a value of s_cut is given. It would be really helpful if the authors could provide some additional hints on how s_cut should be chosen in other cases.

2. For validation of their framework the authors show some ratios of different calculations in figures 2 and 3. While the message is clear, it seems unlikely that someone else could reproduce these plots since the authors don't state explicitly from which quantity or observable these reatios are obtained. What is the 'exact' quantity underlying these calculations?

I will support publication of the submitted article after clarification of my questions as described above.

Ask for minor revision

1. The paper details a new technique to deal with dispersive integrals in one-loop calculations in QED, dubbed as "Disperon QED".

2. The authors combine standard one-loop calculations with an EFT approach to stabilise and speed-up the numerical evaluation of dispersive integrals.

3. The framework the authors introduce is general and can be sistematically applied to more complex processe than the ones discussed in the present paper. They stress the generality of the approach thoroughly.

4. The authors provide succint and clear appendixes which are very helpful to understand the technical details skipped in the main text.

5. The links to external repositories are informative and complete the presentation of the results.

6. The bibliography is broad and comprehensive.

1. no major general weaknesses, I only suggest an integration in the presentation of the plots.

1. I spotted a typo: in the first paragraph of section 4, the sentence "For very large vales of [...]" should read "For very large values of [...]".

2. In appendix B, after eq. (70) "In other words" is repeated twice in the same sentence, I suggest a rephrasing to avoid the repetition.

3. Figures 2, 3a and 3b show the difference of the integrands of eq. (20) for (pd) and two (dd) situations, calculated in different ways and relative to the exact Mathematica result. It might help the reader to show also the squared absolute value, or separately the real and imaginary parts, of the integrands themselves. I think this would help to better appreciate the goodness of the approximations.

4. At the end of section 4.3, the authors mention their approach is much faster than the "brute-force" calculation with OpenLoops in double precision. If this assertion could be made more quantitative (perhaps in the cases shown in figures 2, 3a and 3b), I think it would be beneficial, since speed-up is one of the motivations of the approach presented in this paper.

Ask for minor revision