Semi-Analytical Solution of the $φ^4$ Theory on an $F_4$ Lattice

Details Semi-Analytical Solution of the $φ^4$ Theory on an $F_4$ Lattice Semi-Analytical Solution of the $φ^4$ Theory on an $F_4$ Lattice

1993-07-14

arxiv.org/abs/hep-lat/9307013v1

Nucl.Phys. B412 (1994) 621-656

Physics

High Energy Physics

High Energy Physics - Lattice

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

Scientific paper

10.1016/0550-3213(94)90395-6

Investigating the cutoff dependence of the Higgs mass triviality bound, the $\phi^4$ 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 L\"uscher 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 $\Lambda/m_R \geq 2$. The results confirm recent Monte Carlo data and I obtain as an upper bound for the Higgs mass $m_R/f_\pi \leq 2.46 \pm 0.02_{\rm HTE} \pm 0.08_{\rm PT}$ at $\Lambda/m_R=2$.

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