Seminarium Kosmologia i Fizyka Cząstek

We have computed Wilsonian effective action in a simple model with spontaneously broken chiral parity. Knowledge of Wilsonian running of relevant parameters makes it possible to discuss in a consistent manner the issues of fine-tuning and stability of the scalar potential. This has been compared with the standard picture based on Gell-Mann–Low running. Since Wilsonian running includes automatically integration of heavy degrees of freedom, the running differs markedly from the Gell-Mann–Low version. However, similar behaviour 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. However, care must be taken when drawing conclusions, because of the truncation of higher dimension operators. 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. The Wilsonian version of the radiative symmetry breaking mechanism has been described.