The Technical Fine-Tuning Problem in Renormalized Perturbation Theory.
We study the technical--as opposed to physical --fine-tuning problem, i.e. the stability of tree-level gauge hierarchies at higher orders in renormalized perturbation theory, in a number of different models. These include softly-broken supersymmetric models, and non-supersymmetric ones with a hierarchy of spontaneously-broken gauge symmetries. The models are renormalized using the BPHZ prescription, with momentum subtractions. Explicit calculations indicate that the tree-level hierarchy is not upset by the radiative corrections, and consequently no further fine-tuning is required to maintain it. Furthermore, this result is shown to run counter to that obtained via Dimensional Renormalization, (the only scheme used in previous literature on the subject). The discrepancy originates in the inherent local ambiguity in the finite parts of subtracted Feynman integrals. We conclude that--within fully-renormalized perturbation theory--the answer to the technical fine-tuning question (in the sense of whether the radiative corrections will "readily" respect the tree level gauge hierarchy or not) is contingent on the renormalization scheme we use to define the model at the quantum level, rather than on the model itself. In other words, the need for fine-tuning, when it arises, is an artifact of the application of a certain class of renormalization schemes. We emphasize that the issue is purely technical in nature, and that this result does not imply that physical properties are renormalization scheme dependent.
- Pub Date:
- Physics: Elementary Particles and High Energy