Semi-analytical solution of the φ4 theory on an F4 lattice

Investigating the cutoff dependence of the Higgs mass triviality bound, the φ4 theory is formulated on an F4 lattice which preserves Lorentz invariance to a higher degree than the commonly used hypercubic lattice. I solve this model non-perturbatively by evaluating the high-temperature expansion through 13th order following the approach of Luescher and Weisz. The results are continued across the transition line into the broken phase by integrating the perturbative RG equations. In the broken phase, the renormalized coupling never exceeds two thirds of the three level unitarity bound when Λ/mR ≥ 2. The results confirm recent Monte Carlo data and I obtain as an upper bound for the Higgs mass mR/fπ ≤ 2.46±0.02HTE±0.08PT at Λ/mR = 2. (orig.)