arXiv subjects
Publications and source records attributed to A. Agodi.
The Constraint Effective Potential (CEP) allows a determination of the mass and other quantities directly, without relying upon asymptotic correlator decays. We report and discuss the results of some mass calculations in $(λΦ^4)_4$, obtained from CEP and our improved version of CEP (ICEP).
The Constrained Effective Potential (CEP) is known to be equivalent to the usual Effective Potential (EP) in the infinite volume limit. We have carried out MonteCarlo calculations based on the two different definitions to get informations on finite size effects. We also compared these calculations with those based on an Improved CEP (ICEP) which takes into account the finite size of the lattice. It turns out that ICEP actually reduces the finite size effects which are more visible near the vanishing of the external source.
We compute numerically the effective potential for the $(λΦ^4)_4$ theory on the lattice. Three different methods were used to determine the critical bare mass for the chosen bare coupling value. Two different methods for obtaining the effective potential were used as a control on the results. We compare our numerical results with three theoretical descriptions. Our lattice data are in quite good agreement with the ``Triviality and Spontaneous Symmetry Breaking'' picture.
There are two physically different interpretations of ``triviality'' in $(λΦ^4)_4$ 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 $h(x)\equiv Φ(x)-<Φ>$ 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.
We present a critical reappraisal of the available results on the broken phase of $λ(Φ^4)_4$ theory, as obtained from rigorous formal analyses and from lattice calculations. All the existing evidence is compatible with Spontaneous Symmetry Breaking but dictates a trivially free shifted field that becomes controlled by a quadratic hamiltonian in the continuum limit. As recently pointed out, this implies that the simple one-loop effective potential should become effectively exact. Moreover, the usual naive assumption that the Higgs mass-squared $m^2_h$ is proportional to its ``renormalized'' self-coupling $λ_R$ is not valid outside perturbation theory: the appropriate continuum limit has $m_h$ finite and vanishing $λ_R$. A Monte Carlo lattice computation of the $λ(Φ^4)_4$ effective potential, both in the single-component and in the O(2)-symmetric cases, is shown to agree very well with the one-loop prediction. Moreover, its perturbative leading-log improvement (based on the concept of $λ_R$) fails to reproduce the Monte Carlo data. These results, while supporting in a new fashion the peculiar ``triviality'' of the $λ(Φ^4)_4$ theory, also imply that, outside perturbation theory, the magnitude of the Higgs mass does not give a measure of the observable interactions in the scalar sector of the standard model.
We present a lattice computation of the effective potential for O(2)-invariant $(λΦ^4)_4$ theory in the region of bare parameters corresponding to a classically scale-invariant theory. As expected from ``triviality'' and as in the one-component theory, we find very good agreement with the one-loop prediction, while a perturbative leading-log improvement of the effective potential fails to reproduce the Monte Carlo data. The mass $m_h$ of the free shifted radial field is related to the renormalized vacuum expectation value $v_R$ through the same relation $m^2_h=8π^2 v^2_R$ as in the one-component case. This confirms the prediction of a weakly interacting 2.2 TeV Higgs particle in the standard model.
The generally accepted ``triviality'' of $λΦ^4$ theories does not forbid Spontaneous Symmetry Breaking but implies a trivially free shifted field which becomes effectively governed by a quadratic hamiltonian. As a consequence, one expects the one-loop potential to be exact . We present a lattice computation of the effective potential for massless $λΦ^4$ theory which nicely confirms the expectations based on ``triviality''. Our results imply that the magnitude of the Higgs boson mass, beyond perturbation theory, does not represent a measure of the observable interactions in the scalar sector of the standard model.