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Efficient on-shell matching
by Mikael Chala, Javier L. Miras, José Santiago, Fuensanta Vilches
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Submission summary
| Authors (as registered SciPost users): | Mikael Chala |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202411_00055v1 (pdf) |
| Date submitted: | 2024-11-27 22:46 |
| 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
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In this article, the authors present an efficient algorithm for the on-shell matching of effective field theories (EFTs). While the off-shell matching has been automated in recent years, no efficient method for on-shell matching has been previously available. The central advantage of this approach, which is presented by the authors, is that it allows to perform the matching directly in a minimal basis of the EFT, and no operators that are redundant due to field redefinitions have to be considered, contrary to the off-shell approach. This offers the potential to significantly simplify various EFT calculations, as the authors show in several examples.
The paper is very pedagogical and all details are clearly presented. I only have a few minor comments as suggestions to the authors:
1) While the treatment of evanescent operators is excellently described in section 2.1, the introduction could give the impression that the issues of evanescent operators are circumvented by performing the matching on-shell. However, these issues are resolved by computing also the relevant parts of the soft region in the EFT and full theory. To my understanding, this could equally well be done in an off-shell matching calculation to remove the evanescent structures. I would thus suggest, to add some clarification in the introduction, stating that the removal of evanescent operators is due to computing the soft region and not due to matching on-shell.
2) In the conclusions, it is written "No redundant or evanescent operators have to be included in the calculation". I would suggest to exchange the word "calculation" with, e.g., "basis". In the intermediate steps of the calculation, i.e., when taking the difference of the soft regions of EFT and full theory, evanescent structures are present, even though their explicit form is never visible. While it is unavoidable to have these evanescent operators in the calculation, the advantage of the algorithm presented in this work is that their form never has to be specified and their physical effects are automatically computed.
3) In the context of the matching conditions in Eqs. (65-74), it might be useful to indicate for completness that the matching scale is chosen as the mass of the heavy Higgs $(\mu_\text{match}=M)$.
4) In appendix A, the authors mention the algorithm used for generating the rational on-shell kinematics. I belief it would be valuable to add the corresponding references [54,55] also in the main part of the paper, where appropriate, and not only in the appendix.
5) When listing the higher-dimensional EFT operator bases for SMEFT/LEFT in the introduction, the authors should consider also adding the following citation Li et al. [2005.00008] for the $d=8$ SMEFT basis.
6) In the second to last line on page 22 there is presumably a typo in the variable name $\texttt{perturbatuveOrder}$.
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