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M. Consoli

Publications and source records attributed to M. Consoli.

At least 73 records · Page 4Linked to original sources
arXiv1999

Further lattice evidence for a large re-scaling of the Higgs condensate

Using a high-statistics lattice simulation of the Ising limit of $(λΦ^4)_4$ theory, we have measured the susceptibility and propagator in the broken phase. We confirm our earlier finding of a discrepancy between the field re-scaling implied by the propagator data and that implied by the susceptibility. The discrepancy becomes {\it worse} as one goes closer to the continuum limit; thus, it cannot be explained by residual perturbative effects. The data are consistent with an unconventional description of symmetry breaking and ``triviality'' in which the re-scaling factor for the finite-momentum fluctuations tends to unity, but the re-scaling factor for the condensate becomes larger and larger as one approaches the continuum limit. In the Standard Model this changes the interpretation of the Fermi-constant scale and its relation to the Higgs mass.

hep-lat↗
arXiv1999

Physical mechanisms generating spontaneous symmetry breaking and a hierarchy of scales

We discuss the phase transition in 3+1 dimensional lambda Phi^4 theory from a very physical perspective. The particles of the symmetric phase (`phions') interact via a hard-core repulsion and an induced, long-range -1/r^3 attraction. If the phion mass is sufficiently small, the lowest-energy state is not the `empty' state with no phions, but is a state with a non-zero density of phions Bose-Einstein condensed in the zero-momentum mode. The condensate corresponds to the spontaneous-symmetry-breaking vacuum with neq 0 and its excitations ("phonons" in atomic-physics language) correspond to Higgs particles. The phase transition happens when the phion's physical mass m is still positive; it does not wait until m^2 passes through zero and becomes negative. However, at and near the phase transition, m is much, much less than the Higgs mass M_h. This interesting physics coexists with `triviality;' all scattering amplitudes vanish in the continuum limit, but the vacuum condensate becomes infinitely dense. The ratio m/M_h, which goes to zero in the continuum limit, can be viewed as a measure of non-locality in the regularized theory. An intricate hierarchy of length scales naturally arises. We speculate about the possible implications of these ideas for gravity and inflation.

hep-ph↗
arXiv1998

First lattice evidence for a non-trivial renormalization of the Higgs condensate

General arguments related to ``triviality'' predict that, in the broken phase of $(λΦ^4)_4$ theory, the condensate $<Φ>$ re-scales by a factor $Z_ϕ$ different from the conventional wavefunction-renormalization factor, $Z_{prop}$. Using a lattice simulation in the Ising limit we measure $Z_ϕ=m^2 χ$ from the physical mass and susceptibility and $Z_{prop}$ from the residue of the shifted-field propagator. We find that the two $Z$'s differ, with the difference increasing rapidly as the continuum limit is approached. Since $Z_ϕ$ affects the relation of $<Φ>$ to the Fermi constant it can sizeably affect the present bounds on the Higgs mass.

hep-lat↗
arXiv1997

lambda Phi^4 Theory From a Particle-Gas Viewpoint

We discuss the physics of the 3+1 dimensional lambda Phi^4 quantum field theory in terms of the statistical mechanics of a gas of particles (`atoms') that interact via a -1/r^3-plus-hard-core potential. The hard-core potential, delta^(3)(r), arises from the bare vertex diagram, while the attractive, long-range -1/r^3 potential is due to exchange of a particle pair via the t,u-channel "fish" diagram. (Higher-order diagrams preserve this form of the interparticle potential.) For sufficiently small atom mass, the lowest-energy state is not the `empty' state with no atoms, but a state with a non-zero density of spontaneously created atoms, Bose-condensed in the zero-momentum mode. This corresponds to the spontaneous-symmetry-breaking phase transition, and the `phonon' excitations of the Bose condensate correspond to Higgs particles. The important point is that the phase transition happens while the atom's physical mass m is still positive: it does not wait until m^2 passes through zero and becomes negative, contrary to the assumption of a second-order transition, on which renormalization-group-improved perturbation theory is based.

hep-ph↗
arXiv1997

The $(λΦ^4)_4$ theory on the lattice: effective potential and triviality

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.

hep-lat↗
arXiv1997

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

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.

hep-ph↗
arXiv1996

Response to Tarrach's "Mode Dependent Field Renormalization and Trivialty"

We respond to Tarrach's criticisms (hep-th/9511034) of our work on lambda Phi^4 theory. Tarrach does not discuss the same renormalization procedure that we do. He also relies on results from perturbation theory that are not valid. There is no "infrared divergence" or unphysical behaviour associated with the zero-momentum limit of our effective action.

hep-th↗
arXiv1996

Lattice effective potential of $(λΦ^4)_4$: nature of the phase transition and bounds on the Higgs mass

We present a detailed discussion of Spontaneous Symmetry Breaking (SSB) in $(λΦ^4)_4$. In the usual approach, inspired by perturbation theory, one predicts a second-order phase transition, the Higgs mass $m_h$, related to the value of the renormalized 4-point coupling, gets smaller when increasing the ultraviolet cutoff and this leads to the generally quoted upper bounds $m_h<$700-900 GeV. On the other hand, by exploring the structure of the effective potential in those approximation consistent with `triviality', where the Higgs mass does not represent a measure of any observable interaction, SSB does not require an ultraviolet cutoff, the phase transition is first-order, such that the massless `Coleman-Weinberg' regime lies in the broken phase, and one gets only $m_h<$3 TeV from vacuum stability. To separate out the two alternatives, we present a precise lattice computation of the slope of the effective potential in the region of bare parameters indicated by the Luscher~\&~Weisz and Brahm's analysis of the critical line. Our lattice data strongly support the latter description of SSB. Indeed, our data cannot be reproduced in perturbation theory, and then they confirm the existence on the lattice of a remarkable phase of $(λΦ^4)_4$ where SSB is generated through ``dimensional transmutation'', and show no evidence for residual self-interaction effects of the shifted ``Higgs'' field $h(x)=Φ(x)-\langleΦ\rangle$, in agreement with ``triviality''.

hep-th↗
arXiv1995

Remarks on the Cosmological Constant and the $λΦ^4$ Phase Transition

We reanalyze the problem of the cosmological constant associated with the phase transition in a self-interacting scalar theory. It is pointed out that the generally accepted ``triviality'' of $(λΦ^4)_4$ implies a first-order phase transition. As a consequence, Spontaneous Symmetry Breaking can be consistent with zero cosmological constant if one assumes that it vanishes in the symmetric phase $<Φ>=0$.

hep-ph↗
arXiv1995

Strategy for the 1995 LEP Energy Scan

We propose a procedure to measure the Z$^{0}$ line shape and take full advantage of the superb performance of the CERN $e^+e^-$ Collider LEP. A precise determination of the total cross section at 5 energies is needed for a model-independent analysis of the data and for a precision test of the QED initial state radiation from the fully inclusive hadronic channel.

hep-ph↗
arXiv1995

Lattice effective potential of massless $(λΦ^4)_4$: `triviality' and spontaneous symmetry breaking

We present a precise lattice computation of the slope of the effective potential for massless $(λΦ^4)_4$ theory in the region of bare parameters indicated by the Brahm's analysis of lattice data. Our results confirm the existence on the lattice of a remarkable phase of $(λΦ^4)_4$ where Spontaneous Symmetry Breaking is generated through ``dimensional transmutation''. The resulting effective potential shows no evidence for residual self-interaction effects of the shifted `Higgs' field $h(x)=Φ(x)-\langleΦ\rangle$, as predicted by ``triviality'', and cannot be reproduced in perturbation theory. Accordingly the mass of the Higgs particle, by itself, does not represent a measure of any observable interaction.

hep-th↗
arXiv1995

Indications on the Higgs-Boson Mass from the LEP Data

We update our previous analysis on the Higgs mass $m_h$ and the QCD coupling $α_s(=α_s(M_z))$ by using the LEP data after the 1995 Winter Conferences. For $m_t=180$ GeV we find evidence for a rather large value of the Higgs mass in the range 500-1000 GeV, in agreement with the indications from the W mass.

hep-ph↗
arXiv1994

Lattice $(Φ^4)_4$ Effective Potential Giving Spontaneous Symmetry Breaking and the Role of the Higgs Mass

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.

hep-lat↗
arXiv1994

"TRIVIALITY" MADE EASY: the real (lambda Phi^4)_4 story

The real meaning of `triviality' of (lambda Phi^4)_4 theory is outlined. Assuming `triviality' leads to an effective potential that is just the classical potential plus the zero-point energy of the free-field fluctuations. This V_{eff} gives spontaneous symmetry breaking. Its proper renormalization has the consequence that all scattering amplitudes vanish, self-consistently validating the original assumption. Nevertheless, the theory is physically distinguishable from a free field theory; it has a symmetry-restoring phase transition at a finite critical temperature.

hep-ph↗
arXiv1994

Lattice Computation of the Effective Potential in O(2)-Invariant $λΦ^4$ Theory

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.

hep-lat↗
arXiv1994

Triviality" and the Perturbative Expansion in $λΦ^4$ Theory

The "triviality" of $(λΦ^4)_4$ quantum field theory means that the renormalized coupling $λ_R$ vanishes for infinite cutoff. That result inherently conflicts with the usual perturbative approach, which begins by postulating a non-zero, cutoff-independent $λ_R$. We show how a "trivial" solution $λ_R=0$ can be compatible with the known structure of perturbation theory to arbitrarily high orders, by a simple re-arrangement of the expansion. The "trivial" solution reproduces the result obtained by non-perturbative renormalization of the effective potential. The physical mass is finite, while the renormalized coupling strength vanishes: the two are NOT proportional. The classically scale-invariant $λΦ^4$ theory coupled to the Standard Model predicts a 2.2 TeV Higgs, but does NOT imply strong interactions in the scalar sector.

hep-ph↗
arXiv1994

The Real Test of ``Triviality'' on the Lattice

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.

hep-th↗