In order to accurately describe the cutoff dependence of the Higgs mass triviality bound, the $\varphi\sp4$ theory is formulated on an $F\sb4$ lattice which preserves Lorentz invariance to a higher degree than the commonly used hypercubic lattice. / We solve this model non-perturbatively by evaluating the linked cluster expansion through 12th order following the approach of Luscher and Weisz. The results are continued across the transition line into the broken phase by integrating the perturbative renormalization group equations. In the Goldstone phase, the renormalized coupling never exceeds 2/3 of the tree level unitarity bound when $\Lambda$/$m\sb{R}\ge 2$. Our results confirm recent Monte Carlo data and we obtain as an upper bound for the Higgs mass $m\sb{R}$/$f\sb\pi=2.45(7)$ at $\Lambda$/$m\sb{R}=2$. / Attempting to produce a heavier Higgs on the lattice, additional four-derivative terms are introduced in the naive action which serve to parameterize the leading order cutoff effects. Using a cluster reflection algorithm of the Swendsen-Wang-Wolff type, we simulate this action on an $F\sb4$ lattice in a region where the region where the effects of the new terms are expected to be maximal. As an upper bound we now obtain $M\sb\sigma$/$f\sb\pi\approx 2.8$, an increase of about 20% compared to the simplest non-linear action. Despite triviality, the scalar sector may thus not be weakly interacting. / Source: Dissertation Abstracts International, Volume: 53-11, Section: B, page: 5775. / Major Professors: Urs M. Heller; Dennis W. Duke. / Thesis (Ph.D.)--The Florida State University, 1992.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_76814 |
| Contributors | Klomfass, Markus., Florida State University |
| Source Sets | Florida State University |
| Language | English |
| Detected Language | English |
| Type | Text |
| Format | 149 p. |
| Rights | On campus use only. |
| Relation | Dissertation Abstracts International |
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