SciPost Submission Page
Efficient on-shell matching
by Mikael Chala, Javier L. Miras, José Santiago, Fuensanta Vilches
Submission summary
| Authors (as registered SciPost users): | Mikael Chala · Jose Santiago |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202411_00055v2 (pdf) |
| Date submitted: | Jan. 14, 2025, 2:20 p.m. |
| Submitted by: | Chala, Mikael |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
We propose an efficient method to perform on-shell matching calculations in effective field theories. The standard off-shell approach to matching requires the use of a Green's basis that includes redundant and evanescent operators. The reduction of such a basis to a physical one is often highly non-trivial, difficult to automate and error prone. Our proposal is based on a numerical solution of the corresponding on-shell matching equations, which automatically implements in a trivial way the delicate cancellation between the non-local terms in the full theory and those in the effective one. The use of rational on-shell kinematics ensures an exact analytic solution despite the numerical procedure. In this way we only need a physical basis to perform the matching. Our procedure can be used to reduce any Green's basis to an arbitrary physical one, or to translate between physical bases; to renormalize arbitrary effective Lagrangians, directly in terms of a physical basis; and to perform finite matching, including evanescent contributions, as we discuss with explicit examples.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
List of changes
Dear Editor,
We would like to thank the referee for the positive feedback as well as for the concrete suggestions, which we have addressed as follows.
1. The treatment of evanescent operators is indeed identical in both on-shell and off-shell matching, and the standard procedure for computing the evanescent shifts in the on-shell case has been discussed in our current Ref. [41] (Ref. [40] in the previous submission). The difference in our particular case is that, due to our numerical procedure, we have to do the matching in $d=4$ and therefore have to generate the evanescent structures via the soft region expansion in the EFT. The same could be also done in the off-shell matching.
We have added a new footnote in page 3 to account for this.
2. We have followed the referee's recommendation; see page 18.
3. We have added a comment before equation 65.
4. We have added a comment including these references in page 4.
5. We are sorry for having forgotten this reference, which we have now included.
6. We thank the referee for spotting this typo, which is now fixed.
Moreover, we have fixed a typo in Figure 4 and equation 45 ($H^4D^2$ should read $H^4 D^4$).
All modifications in the text are shown in red colour.
Thank you very much.
Best wishes,
The authors.
Current status:
Reports on this Submission
Report
For this paper, I am not sure what happened in the past. I read the one substancial referee report and the response of the authors, it seems all fine to me.
One additional aspect which I am missing, through, is at least a comment on specific use cases. There are papers where different groups compare analyses in EFT and full UV-frameworks, usually to D6 and D8. What would change for these published analyses with this new approach? Providing this kind of context would very much help the non-expert readers or potential users.
After adding a brief discussion along these lines, I think the paper should be published.
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)
Report
I recommend it for publication in SciPost Physics.
Recommendation
Publish (surpasses expectations and criteria for this Journal; among top 10%)
Author: Mikael Chala on 2025-05-08 [id 5468]
(in reply to Report 3 on 2025-05-06)We would like to thank the referee for his/her comments on our manuscript (incidentally, we don't understand either what the problem with the previous reports was). Regarding the referee's request, our method is completely equivalent to the one previously used based on off-shell matching in terms of the results obtained with them. They are just two different ways of computing the same thing. The difference is that our method can be much more convenient than the traditional one in certain circumstances. For instance, the full reduction of the SMEFT Green's basis to the physical one at mass dimension 8 has not been completed yet, despite the fact that the two bases have been known for five years. The reason is that the reduction is extremely challenging and some of the available partial results could only be completed using our new on-shell matching method.