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Renormalization group consistency and low-energy effective theories
by Jens Braun, Marc Leonhardt, Jan M. Pawlowski
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Jens Braun · Jan M. Pawlowski |
| Submission information | |
|---|---|
| Preprint Link: | scipost_201902_00046v1 (pdf) |
| Date accepted: | April 18, 2019 |
| Date submitted: | Feb. 20, 2019, 1 a.m. |
| Submitted by: | Braun, Jens |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Low-energy effective theories have been used very successfully to study the low-energy limit of QCD, providing us with results for a plethora of phenomena, ranging from bound-state formation to phase transitions in QCD. These theories are consistent quantum field theories by themselves and can be embedded in QCD, but typically have a physical ultraviolet cutoff that restricts their range of validity. Here, we provide a discussion of the concept of renormalization group consistency, aiming at an analysis of cutoff effects and regularization-scheme dependences in general studies of low-energy effective theories. For illustration, our findings are applied to low-energy effective models of QCD in different approximations including the mean-field approximation. More specifically, we consider hot and dense as well as finite systems and demonstrate that violations of renormalization group consistency affect significantly the predictive power of the corresponding model calculations.
Published as SciPost Phys. 6, 056 (2019)
Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2019-4-10 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_201902_00046v1, delivered 2019-04-10, doi: 10.21468/SciPost.Report.905
Strengths
Clear and correct results
Well written
Weaknesses
Report
Expectation values of observables depend on some microscopic couplings and on the cutoff for the momentum integrations within the effective theory. Ideally, the cutoff just denotes the transition scale from some more fundamental theory to the effective theory, and observables should not depend on it. In practice, this dependence is often rather strong, such that the cutoff appears as a parameter of the effective theory. The present paper proposes renormalisation group consisteny as powerful method to reduce the cutoff dependence. They show what can be achieved with well chosen practical examples.
I recommend publication
Requested changes
none
Report #1 by Anonymous (Referee 1) on 2019-4-6 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_201902_00046v1, delivered 2019-04-06, doi: 10.21468/SciPost.Report.901
Strengths
2-understandable for a rather wide audience of people interested in effective field theories, even though examples only QCD related
3-will probably trigger further studies of RG consistency in other models
Weaknesses
Report
The manuscript is very well written and provides an extremely useful introduction to the subject for a rather general audience, even though the applications discussed focus only on QCD related examples. The presentation is technically sound and the calculations well illustrated and informative.
The authors are leading experts in the field and the quality of the investigation is very high. Though the manuscript has somewhat the character of an introductory review, the example calculations provide some very interesting new results that will certainly trigger further studies in this field of research.
I recommend publication of this very nice paper without changes.
Requested changes
- none