A lattice test of alternative interpretations of ``triviality'' in $(λΦ^4)_4$ theory

Details A lattice test of alternative interpretations of ``triviality'' in $(λΦ^4)_4$ theory A lattice test of alternative interpretations of ``triviality'' in $(λΦ^4)_4$ theory

1997-02-24

arxiv.org/abs/hep-ph/9702407v2

Mod.Phys.Lett. A12 (1997) 1011-1024

Physics

High Energy Physics

High Energy Physics - Phenomenology

16 pages, LaTeX, 2 eps figures (acknowledgements added in the replaced version)

Scientific paper

10.1142/S0217732397001035

There are two physically different interpretations of ``triviality'' in $(\lambda\Phi^4)_4$ theories. The conventional description predicts a second-order phase transition and that the Higgs mass $m_h$ must vanish in the continuum limit if $v$, the physical v.e.v, is held fixed. An alternative interpretation, based on the effective potential obtained in ``triviality-compatible'' approximations (in which the shifted `Higgs' field $h(x)\equiv \Phi(x)-<\Phi>$ is governed by an effective quadratic Hamiltonian) predicts a phase transition that is very weakly first-order and that $m_h$ and $v$ are both finite, cutoff-independent quantities. To test these two alternatives, we have numerically computed the effective potential on the lattice. Three different methods were used to determine the critical bare mass for the chosen bare coupling value. All give excellent agreement with the literature value. Two different methods for obtaining the effective potential were used, as a control on the results. Our lattice data are fitted very well by the predictions of the unconventional picture, but poorly by the conventional picture.

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