Higgs mass trivality bounds on F4 lattices

In order to accurately describe the cutoff dependence of the Higgs mass triviality bound, the var-phi 4 theory is formulated on an F4 lattice which preserves Lorentz invariance to a higher degree than the commonly used hypercubic lattice. The authors solve this model non-perturbatively by evaluating the linked cluster expansion through 12th order following the approach of Luescher 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 λ/mR ≥ 2. The results confirm recent Monte Carlo data and the authors obtain as an upper bound for the Higgs mass mR/fπ = 2.45(7) at λ/mR = 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, the authors simulate this action on an F4 lattice in a region where the effects of the new terms are expected to be maximal. As an upper bound the authors now obtain Mσ/fπ ∼ 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