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From the EFT to the UV: the complete SMEFT one-loop dictionary
by Guilherme Guedes, Pablo Olgoso Ruiz
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Submission summary
| Authors (as registered SciPost users): | Pablo Olgoso |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202509_00042v1 (pdf) |
| Code repository: | https://gitlab.com/jsantiago_ugr/sold/ |
| Date submitted: | Sept. 24, 2025, 4:32 p.m. |
| Submitted by: | Pablo Olgoso |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Computational, Phenomenological |
Abstract
Effective field theories (EFTs) provide an excellent framework for the search of heavy physics beyond the Standard Model, using the so-called bottom-up and top-down approaches. However, the vastness of possible UV scenarios makes the complete connection between the two approaches a difficult challenge at the loop-level. UV/IR dictionaries fill precisely this gap, efficiently connecting the EFT with the UV. In this work we present the complete one-loop dictionary for the Standard Model EFT at dimension six for completions with an arbitrary number of heavy fermions and scalars. Our results (as well as several new functionalities) are added to the previously partial package {\tt SOLD}, introduced in [1]. In this new form, {\tt SOLD} is prepared to serve as an important guiding tool for systematic and complete phenomenological studies. To illustrate this, we use the package to explore possible explanations for the tension on the measurement of $\mathcal{B}(B\rightarrow K \overline{\nu}\nu)$.
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- 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
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In this work, the authors present an updated version of the code SOLD, which provides a dictionary between the SMEFT and all possible multi-particle SM extensions at one-loop level, containing only heavy scalars and fermions. In particular, the tool allows to determine the quantum numbers (or constraints on their combination) for all particles that are required in all n-particle one-loop models that generate this operator. In addition, the code also allows to determine the one-loop matching conditions onto the full SMEFT for any of the models thus obtained. This dictionary can certainly be useful for the model building community, as it allows to get a better overview of the BSM model landscape required for specific IR scenarios. The article is well written and mostly clear. However, I have several (mostly minor) questions: 1) Global symmetries can significantly modify the IR description of a theory. How would one treat such global symmetries in SOLD? 2) I suppose that SOLD is fully specific to the Warsaw basis. Is that the case, or is it possible to include also other bases? 3) Since the matching of the generic UV Lagrangian onto SMEFT is precomputed in SOLD, I am wondering to which order in the number of BSM fields this is done? Or in other words, how many BSM fields are possible to include when running the code? 4) It is not quite clear to me in which cases one needs to use MatchMakerEFT in order to obtain the full one-loop matching of a given model, or when this can be done with SOLD. A clarification for this would be good. 5) It would be useful to state the $\gamma_5$ scheme employed in the computation, given that subsequent calculations in the EFT are required to be performed in the same scheme. 6) The authors state that UV theories with a tree-level mass mixing are not supported. What is the specific reason behind that? As long as the mixing parameter is an IR scale, the matching should be still possible. 7) In Mathematica input In[4] it seems like there are some curly brackets missing. 8) Regarding figure 2: Why is the operator $O_{lequ}^{(3)}$ missing in the table, which is generated by the $S_1$? Also, assuming that the operators $O_{lambdau}$ and $O_{lambdad}$ represent the SMEFT up- and down-quark Yukawas, I would assume that the $S_1$ generates an up-Yukawa correction at one loop and not a down-Yukawa correction, contrary to what figure 2 claims.
While the example of $B \to K \nu \nu$ used in Sec. 4 to showcase the workings of SOLD might be not entirely ideal, due to the large NP effect that is required to satisfy the central value, making a one-loop explanation less compelling, I still think the example nicely highlights all benefits of using a dictionary like SOLD. However, the description is partially difficult to follow: 9) The code presented in Mathematica input In[15,20,23,24] is extremely difficult to read and a non-expert in Mathematica syntax will likely not be able to understand this. In my opinion it would be better to either move this code to an appendix or maybe better to create an example notebook as ancillary material, where one can directly evaluate the example. That way, the main part of the article could still be understood without substantial experience with Mathematica. 10) It appears that for inputs In[25] and In[26] the output is missing. 11) It might be good to add the BSM masses to the list of parameters in Eq. (4.13). I recommend a minor revision for this article and believe that once these minor issues and questions have been addressed, it will be suitable for publication in SciPost Physics.
Recommendation
Ask for minor revision
Report #1 by Jaco ter Hoeve (Referee 2) on 2025-10-27 (Invited Report)
Strengths
- Presents the first tool that allows translating the space of Wilson coefficients to the space of UV models, rather than the other way around.
- Phenomenologically relevant: the authors demonstrate explicitly how SOLD helps efficiently map out certain classes of UV models that induce a certain pattern of known EFT coefficients in the IR. This makes it a useful tool for the wider community.
- The SOLD package is easy to install, user friendly and well documented and presented.
Weaknesses
- A few syntax errors and warnings are raised by Mathematica when running SOLD (see report and requested changes).
- The phenomenological section that uses smelli and flavio could be made clearer by adding a couple of supporting plots.
Report
Requested changes
- Unfortunately, I am not able to reproduce Figure 2 of the main manuscript. I am on Mathematica v14.3. I type ListOperators[{Sa -> {3, 1, -1/3}}, True] , which then gives me Figure 2 except for green ticks at tree level for operators OmuH2, Olambdad, Olambdae and Old. Everything else agrees. See attached file for more details (point 1)
- I have tried whether SOLD "closes": can I go back and forth between the SMEFT and the UV? For instance, ListModelsWarsaw[alphaOuG[i, j]] gives, among many other models, model {-3, 1, 1/3}, but when I do ListOperators[{Sa-> -3, 1, 1/3}] I do not retrieve OuG. Please check whether this is correct. ListOperators also gives me PreDrecrement errors, please see the attached file for more details (point 2).
- Please remind the reader of the notation Sa and Fa. I suspect these stand for Scalar and Fermion. It is also a bit unclear to me why all EFT operators are written with alpha in front, e.g. alphaOlq1. Why not just Olq1? Why this choice specifically?
- Just below Eq. 3.1, page 9: In[4] contains a typo: the replacement for Sa misses surrounding curly braces. Please correct.
- I spotted a minor grammatical mistake on page 9: this numbers distinguishes -> these numbers distinguish.
- Page 16, first paragraph: it says "pick models that include S3~(3, 3, -1/3)", but a bit later on underneath In[15] it says "selecting those that do not include S3 ~(3, 3, -1/3)". This seems contradictory, maybe a typo?
- Page 17, last paragraph: notation S3 + Q5 ~ (3, 2, -5/6). You probably mean just Q5 ~ (3, 2, -5/6), but it reads like the representation belongs to S3 and Q5 combined. Writing S3 + Q5 with Q5 ~ (3, 2, -5/6) should fix this.
- The part on page 17 that introduces Flavio and smelli could do with some plots to illustrate the tension with existing measurements. That way the arguments become easier to follow for the reader.
- What syntax should be used to list operators generated by a model defined in terms of a product of representations?
- Ref. 46 from the SMEFiT collaboration has been superseded by https://inspirehep.net/literature/2779255 and https://inspirehep.net/literature/2895783. Please update.
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)
Let us start by thanking the referee for the detailed and insightful comments. Furthermore we are very grateful for some bugs that were identified as a result of this report and which have been solved.
We address the questions below. 1. Indeed, in SOLD's version v1 the ListOperators function was considering the contributions of the UV Standard Model couplings as a tree-level contribution. This was changed in the latest version of the code (v2.0.0). We will update the figure correspondingly in the manuscript. We thank the referee for pointing out this inconsistency. 2. We believe the problem arises from an incorrect input for the representation. For conjugated representations, one should write its Dynkin indices (in this case, {0,1} instead of -3). We have emphasized this in the manuscript in the definition of the Match2Green function in section 2.5. Regarding the PreDecrement errors, we detected a small bug in the ListOperators function that we will fix in an updated version of the code. We thank the referee for pointing out this bug. 3. The notation procedure for the coefficient and extension options in {\tt SOLD} function has been added in section 2.5, in the Match2Green function. 4. We corrected this typo and thank the referee for pointing it out. 5. We corrected this typo and thank the referee for pointing it out. 6. We corrected this typo and thank the referee for pointing it out. 7. We corrected this typo and thank the referee for pointing it out. 8. We would like to keep the focus of the section on the functionalities of SOLD, and use the tension and measurements as an exercise to show the power of the dictionary. However, we agree that more information could be useful and as such we write a sentence in section 4 --with appropriate references with more detailed information -- such that the reader can immediately be aware of the challenge between explaining the $B\rightarrow K \nu\bar\nu$ measurement and current bounds. 9. Symmetry groups other than the Standard Model one are not supported in SOLD. To study a model with a larger gauge group that breaks into the SM gauge group, the user should introduce the quantum numbers of the new fields under the SM group after the symmetry breaking. 10. This has been updated.
Improvements on the text have been left with blue color to be easier for the referee to see. We hope we have addressed the referee's comments to their satisfaction and that with these changes, the revised manuscript will be published.
Strengths
Weaknesses
Report
Requested changes
It is not obvious that this program can be easily applied to compute the same beyond dimension six. Thus, the article's title is misleading. I suggest mentioning dimension-six in the title of the manuscript, e.g., “From the EFT to the UV: the complete dimension-six SMEFT one-loop dictionary”.
I have a few queries regarding the manuscript that I failed to note:
It is not clear whether this program can handle an arbitrary number of non-degenerate scalars and fermions.
Can this program be used to integrate out the scalar and fermions together?
How does this program take care of loops that consist of the light-heavy mixed propagators? How do they separate the local and non-local contributions?
Does this program address the emergence of dimension-six CP-violating operators?
Apart from these basic queries, I have a few generic comments:
- This manuscript seriously lacks proper referencing. They must cite all the efforts made so far to build the EFT program. I am naming a few here (if they are not cited already):
https://inspirehep.net/literature/1683160 https://inspirehep.net/literature/1389176 https://inspirehep.net/literature/1591722 https://inspirehep.net/literature/1631353 https://inspirehep.net/literature/1667740 https://inspirehep.net/literature/1332938 https://inspirehep.net/literature/1442364 https://inspirehep.net/literature/219220 https://inspirehep.net/literature/219217 https://inspirehep.net/literature/1374234 https://inspirehep.net/literature/1418809 https://inspirehep.net/literature/1474691 https://inspirehep.net/literature/1444897 https://inspirehep.net/literature/1835607 https://inspirehep.net/literature/1854479 https://inspirehep.net/literature/1852352
The title of the manuscript suggests that the EFT guides the choice of UV models. But I fail to have one. The authors must include a discussion of how EFT guides the choice of possible UV theories to justify the title of the manuscript, “From the EFT to the UV:….” In this context, the authors must add a discussion that relies on the following references:
https://inspirehep.net/literature/1852818 https://inspirehep.net/literature/2075735 https://inspirehep.net/literature/1898320 https://inspirehep.net/literature/2064830 https://inspirehep.net/literature/2127403
- Assignment of quantum numbers/representations for product groups in the function “ListModelsWarsawTree[alphaOlq1[i,j,k,l]]” is misleading when the group is SU(3) \otimes SU(2), then the prepresentation is depicted as (3 \otimes 1). Since the representations belong to different groups, the tensor product of two representations is not well-defined. That should be written as (3, 1), where the ordering of representations follows the same order as the group is defined. This should be consistent throughout the manuscript for other functions as well.
Recommendation
Ask for major revision
We thank the referee for the feedback and questions/comments. We agree with the referee that the dictionary applies only to dimension-six SMEFT and so we have updated the title to reflect that. Let us address the other questions posed by the referee:
- The program can indeed handle an arbitrary number of (degenerate or non-degenerate in mass) scalars and fermions, as mentioned in the abstract and the text. Of course, the execution time of the routines increases with the number of particles included.
- Yes, the program can handle the integration of scalars and fermion at the same time. For example in Section 4.2, when we consider two-field extensions, the fact that both fermions and scalars can be integrated at the same time is seen explicitly.
- Matching is done using the expansion by regions technique. As detailed in Refs. [1] and [8] (appropriately cited in the text), light massive propagators are expanded out to extract the hard region of the loop integrals, which are then local and thus can be absorbed by SMEFT coefficients.
- All dimension-six operators are treated within SOLD, regardless of their CP-nature. Whether or not they can indeed be generated will then depend on the UV theory the user considers. Because we start with the most general renormalizable theory in Eq. (2.1), we include cases where the UV has couplings which are CP-even and couplings which are CP-odd.
Regarding the general comments of the referee:
- We included some of the references provided by the referee.
- In the introduction, we attempt to clarify the questions SOLD addresses: "What are all models that can generate a specific operator (or a set of operators)? What are the low-energy consequences, through the matching conditions onto the SMEFT, of a specific UV model?" The first question addresses the "From the EFT to the UV" part as SOLD carves the UV space responsible for EFT patterns. The second questions addresses the "and back" part as SOLD also gives all the EFT consequences of a particular UV scenario. Schematically, this can also be understood in Figure 3. Within the rest of the paper we exemplify how this interplay plays out in SOLD: we dedicated sections 3 and 4 to show how the code is envisaged to translate a low energy deviation from the SM to specific UV models, subsequently analyzed by projecting them into the full SMEFT and providing a phenomenological study. In particular we address a real tension in current experimental data. With all this being said, we believe the title of the manuscript is sufficiently justified in the text.
- Some of the citations suggested by the referee are already cited in our draft. Nevertheless, we will add some of the remaining ones suggested by the referee.
- We added a sentence after Eq. (3.1) to clarify this notation.
We again thank the referee for the time dedicated. We hope that all questions raised have been satisfactorily answered and that our paper is now suitable for publication in SciPost.
Author: Pablo Olgoso on 2026-01-14 [id 6227]
(in reply to Report 3 on 2025-11-08)Let us thank the referee for carefully reading our draft and for their feedback, questions and comments raised. In the following, let us address the referee's questions:
Improvements on the text have been left with blue color to be easier for the referee to see. We once again thank the referee for their questions and feedback and hope we have addressed them satisfactorily.