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Towards the renormalisation of the Standard Model effective field theory to dimension eight: Bosonic interactions I
by M. Chala, G. Guedes, M. Ramos, J. Santiago
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Submission summary
| Authors (as registered SciPost users): | Maria Ramos · Jose Santiago |
| Submission information | |
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| Preprint Link: | scipost_202106_00041v1 (pdf) |
| Date submitted: | 2021-06-23 14:50 |
| Submitted by: | Ramos, Maria |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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Abstract
We compute the one-loop renormalisation group running of the bosonic Standard Model effective operators to order $v^4/\Lambda^4$, with $v\sim 246$ GeV being the electroweak scale and $\Lambda$ the unknown new physics threshold. We concentrate on the effects triggered by pairs of the leading dimension-six interactions, namely those that can arise at tree level in weakly-coupled ultraviolet completions of the Standard Model. We highlight some interesting consequences, including the interplay between positivity bounds and the form of the anomalous dimensions; the non renormalisation of the $S$ and $U$ parameters; or the importance of radiative corrections to the Higgs potential for the electroweak phase transition. As a byproduct of this work, we provide a complete Green basis of operators involving only the Higgs and derivatives at dimension-eight, comprising 13 redundant interactions.
Current status:
Reports on this Submission
Report #1 by Anonymous (Referee 1) on 2021-7-5 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202106_00041v1, delivered 2021-07-05, doi: 10.21468/SciPost.Report.3186
Report
In this paper, the contributions of pairs of dimension-6 operators in the SMEFT to the renormalization group evolution of dimension-8 operators are calculated. Some consequences of the results are also briefly explored, including their interplay with positivity bounds and their effects in constraints from experimental data. It is thus relevant to the current developments in the SMEFT, and a first step towards the full calculation of renormalization group running of dimension-8 operators. As such, it meets the criteria for publication in SciPost Physics, and I recommend publication after the following minor points have been addressed:
- Tables 2 and 3 do not show redundant bosonic operators not containing the Higgs, such as (D^mu B_munu)^2. Some justification for this would be welcome.
- In eq. (1): the sign of the negative mass term for the Higgs doublet is reversed.
- The links to arXiv in the references lead to non-existent SciPost pages. This happens in the SciPost version of the paper but not in the arXiv one.
Author: Maria Ramos on 2021-07-06 [id 1548]
(in reply to Report 1 on 2021-07-05)We would like to thank the referee for the positive report.
Our replies to the comments raised by the referee are listed below:
1) We did not build the redundant bosonic operators not involving the Higgs because they are not renormalised by the interactions in Eq. (4). We could have constructed them for completeness, but that is a highly non-trivial task that we will addressed in a forecoming publication. That is the reason why we did not include them in the tables. In order to clarify this point, we will add a comment in this respect in the future version of the manuscript.
2) The sign of the Higgs mass term in the Lagrangian is a convention. Still, we think changing our choice of sign is a good idea in order to match the convention adopted in the papers addressing renormalisation to dimension six [1312.2014, 1310.4838, 1308.2627].
3) We will try to fix the arXiv links in the references in the future version of the manuscript.
Thank you very much.
Best wishes, The authors.