Semi-Analytical Solution of the ${\varphi }^4$ Theory on an $F_4$ Lattice

Abstract

Investigating the cutoff dependence of the Higgs mass triviality bound, the ${\varphi }^4$ theory is formulated on an $F_4$ 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 Lüscher 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 2/3 of the tree level unitarity bound when $\Lambda /m_R\ge 2$. The results confirm recent Monte Carlo data and I obtain as an upper bound for the Higgs mass $m_R/f_{\pi }\le 2.46\pm 0.02_{\mathrm{HTE}}\pm 0.08_{\mathrm{PT}}$ at $\Lambda /m_R=2$.

36 pages, CU-TP-603, Latex, 3 PS figures included, uuencoded compressed shar file

References in corpus (1)

• Numerical analysis of the Higgs mass triviality bound

Cited by in corpus (3)

• N-vector spin models on the sc and the bcc lattices: a study of the critical behavior of the susceptibility and of the correlation length by high temperature series extended to order beta^{21}
• New extended high temperature series for the N-vector spin models on three-dimensional bipartite lattices
• The ϕ_3^4 lattice field theory viewed from the high-temperature side