Naturalness of effective theories in Wilsonian approach
Abstract
We have computed Wilsonian effective action in a simple model containing scalar field with quartic self-coupling which interacts via Yukawa coupling with a Dirac fermion. The model is invariant under a chiral parity operation, which can be spontaneously broken by a vev of the scalar field. We have computed explicitly Wilsonian running of relevant parameters which makes it possible to discuss in a consistent manner the issue of fine-tuning and stability of the scalar potential. This has been compared with the typical picture based on Gell-Mann-Low running. Since Wilsonian running includes automatically integration out of heavy degrees of freedom, the running differs markedly from the Gell-Mann-Low version. However, similar behavior can be observed: scalar mass squared parameter and the quartic coupling can change sign from a positive to a negative one due to running which causes spontaneous symmetry breaking or an instability in the renormalizable part of the potential for a given range of scales. As for the issue of fine-tuning, since in the Wilsonian approach power-law terms are not subtracted, one can clearly observe the quadratic sensitivity of fine-tuning measure to the change of the cut-off scale.
Keywords
Cite
@article{arxiv.1510.02154,
title = {Naturalness of effective theories in Wilsonian approach},
author = {Tomasz Krajewski and Zygmunt Lalak},
journal= {arXiv preprint arXiv:1510.02154},
year = {2015}
}
Comments
12 pages, 6 figures, proceeding of a talk given at "18th International Conference From the Planck Scale to the Electroweak Scale" held in Ioannina, Greece, 25-29 May 2015