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Renormalizable Extension of the Abelian Higgs-Kibble Model with a Dim.6 Derivative Operator
by Daniele Binosi, Andrea Quadri
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Submission summary
| Authors (as registered SciPost users): | Andrea Quadri |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2212.02453v1 (pdf) |
| Date submitted: | 2022-12-06 07:45 |
| Submitted by: | Quadri, Andrea |
| Submitted to: | SciPost Physics Proceedings |
| Proceedings issue: | 34th International Colloquium on Group Theoretical Methods in Physics (GROUP2022) |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We present a new approach to the consistent subtraction of a non power-counting renormalizable extension of the Abelian Higgs-Kibble (HK) model supplemented by a dim.6 derivative-dependent operator controlled by the parameter $z$. A field-theoretic representation of the physical Higgs scalar by a gauge-invariant variable is used in order to formulate the theory by exploiting a novel differential equation, controlling the dependence of the quantized theory on $z$. These results pave the way to the consistent subtraction by a finite number of physical parameters of some non-power-counting renormalizable models possibly of direct relevance to the study of the Higgs potential at the LHC.
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Reports on this Submission
Report #1 by Anonymous (Referee 1) on 2023-2-21 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2212.02453v1, delivered 2023-02-21, doi: 10.21468/SciPost.Report.6772
Report
The paper arXiv:2212.02453 discusses the renormalisation of a U(1) gauge theory, broken spontaneously by a charged scalar field, in the presence of a dimension-six, derivative operator. The manuscript corresponds to a talk presented in a conference, while more details on the same subject were published in a previous paper by the same Authors, arXiv:2206.00894, appeared in PRD.
The Authors argue that the model can be renormalised in a predictive way (by a finite number of physical parameters), thanks to (i) a formalism based on a choice of gauge-invariant field coordinates, and (ii) a specific, unique choice of the deformation (i.e. one particular dimension-six operator). It is then shown that all 1-PI correlators (involving all possible insertions of the deformation) can be renormalised in one shot by a finite set of renormalisation conditions.
While the computation appears to be careful and illustrates some non-trivial recursive relations among the correlators, I find the physical interpretation of the result somewhat misleading. Firstly, the Authors claim in the Introduction that effective theories are not predictive. However, it is well-known that effective theories remain predictive at low energies, as a finite number of operators of dimension less or equal than D exists, and thus a finite number of counterterms is sufficient to subtract all UV divergences up to dimension D.
Secondly, in an effective theory, if one fixes the values of the Wilson coefficients up to dimension D (by measurements), it is possible to make (finite) predictions for as many observables as desired. When the Authors assume a single dimension-6 operator, this is equivalent to assume that all others are measured to be zero (including those of higher dimensions). Under such strong assumption, it is not surprising that all correlators can be predicted as a function of that single Wilson coefficient. Of course, additional measurements may disagree with the assumption that all other operators were vanishing.
Therefore, there seems to be nothing special in the derivative operator selected by the Authors. The heavy formalism elaborated by the Authors is suitable to explicitly renormalise all amplitudes involving that particular operator. But the analogous result for any set of operators holds, and it could be proved with the standard renormalisation formalism for effective field theories. Thus, I suggest the Authors to reconsider and to specify the scope of their analysis before publication.