Does massless (lambda Phi^4)_4 theory exhibit spontaneous symmetry breaking (SSB)? The raw 1-loop result implies that it does, but the "RG-improved" result implies the opposite. I argue that the appropriate "low-energy effective theory" is a nonlocal field theory involving an attractive, long-range interaction Phi^2(x) Phi^2(y)/z^4, where z=|x-y|. RG improvement then requires running couplings for both this interaction and the original pointlike interaction. A crude calculation in this framework yields SSB even after "RG improvement" and closely agrees with the raw 1-loop result.
Recent lattice data for the effective potential of lambda Phi^4 theory fits the massless one-loop formula with amazing precision. Any corrections are at least 100 times smaller than is reasonable, perturbatively. This is strong evidence for the "exactness conjecture" of Consoli and Stevenson.
The complex scalar quantum field theory with a lambda (phi^*phi)^2 interaction is considered in the Feshbach-Villars formulation. It is shown that exact few-particle eigenstates of the QFT Hamiltonian can be obtained. The resulting relativistic few-body equations correspond to Klein-Gordon particles interacting via delta-function, or ``contact'', potentials. Momentum-space solutions of the two-body equation yield a `trivial' unity S-matrix.
Recent calculations in one-loop and Gaussian appro- ximation, using the so-called autonomous renormalization scheme, indicate a comparatively massive, narrow Higgs excitation at about 2 TeV. Here I show that this result qualitatively persists in the framework of a post-Gaussian variational approximation for the pure O(N)-symmetric phi**4-theory for N>1. The method is based on nonlinear transformations of path-integral variables, and the optimization amounts to a Schwinger-Dyson-type summation of diagrams. In the case of O(4), for example, I find M_Higgs = 2.3 TeV, compared to 1.9 TeV and 2.1 T…
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.
We show that the shear viscosity of lambda phi^4 theory is sensitive at next-to-leading order to soft physics, which gives rise to subleading corrections suppressed by only a half power of the coupling, eta = [3033.54 + 1548.3 m_{th}/T] N T^3]/[ (N+2)/3 lambda^2], with m^2_th=(N+2)/72 lambda T^2. The series appears to converge about as well (or badly) as the series for the pressure.
Considered is the N=1 SQCD-like theory with SU(N_c) colors and 0<N_F<2N_c flavors of light quarks Q_i,\bar Q_j and with the additional N^2_F colorless flavored fields Phi_{ij} with the large mass parameter μ_{Phi}>>Lambda. The mass spectra of this Phi-theory (and its dual variant, the dPhi-theory) are calculated at different values of μ_{Phi}/Lambda >>1 within the dynamical scenario which implies the (quasi)spontaneous breaking of chiral symmetry. It is shown that, under appropriate conditions, the seemingly heavy and dynamically irrelevant fields Phi 'return back' and there appear two additio…
We explore the analytical properties of the traceless stress tensor 2-point function at zero momentum and small frequency (relevant for shear viscosity and hydrodynamic response) in hot, weakly coupled lambda phi^4 theory. We show that, rather than one or a small number of poles, the correlator has a cut along the negative imaginary frequency axis. We briefly discuss this result's relevance for constructing 2'nd order hydrodynamic models of hot relativistic field theories.
We study the domain of validity of a Schwinger-Dyson (SD) approach to non-equilibrium dynamics when there is broken symmetry. We perform exact numerical simulations of the one- and two-point functions of lambda phi^4 field theory in 1+1 dimensions in the classical domain for initial conditions where < phi(x) > not equal to 0. We compare these results to two self-consistent truncations of the SD equations which ignore three-point vertex function corrections. The first approximation, which sets the three-point function to one (the bare vertex approximation (BVA)) gives an excellent description f…
The strong evidence for the `triviality' of (lambda Phi^4)_4 theory is not incompatible with spontaneous symmetry breaking. Indeed, for a `trivial' theory the effective potential should be given exactly by the classical potential plus the free-field zero-point energy of the shifted field; i.e., by the one-loop effective potential. When this is renormalized in a simple, but nonperturbative way, one finds, self-consistently, that the shifted field does become non-interacting in the continuum limit. For a classically scale-invariant (CSI) lambda Phi^4 theory one finds m_h^2 = 8 pi^2 v^2, predicti…
We present a non-perturbative study of the lambda phi**4 model on a non-commutative plane. The lattice regularised form can be mapped onto a Hermitian matrix model, which enables Monte Carlo simulations. Numerical data reveal the phase diagram; at large lambda it contains a "striped phase", which is absent in the commutative case. We explore the question whether or not this phenomenon persists in a Double Scaling Limit (DSL), which extrapolates simultaneously to the continuum and to infinite volume, at a fixed non-commutativity parameter. To this end, we introduce a dimensional lattice spacing…
We apply the $δ$-expansion perturbation scheme to the $λϕ_{4}$ self-interacting scalar field theory in 3+1 D at finite temperature. In the $δ$-expansion the interaction term is written as $λ(ϕ^{2})^{1 + δ}$ and $δ$ is considered as the perturbation parameter. We compute, in this perturbation approach, the renormalized mass at finite temperature from which we get the critical temperature. The results are compared with the usual loop-expansion at finite temperature.
If spacetime contains large compact extra dimensions, the fundamental mass scale of nature, $Lambda$, may be close to the weak scale, allowing gravitational physics to significantly modify electroweak symmetry breaking. Operators of the form $(1/Lambda^2) |phi^* D phi|^2$ and $(1/Lambda^2) phi^* W B phi$, where $W$ and $B$ are the SU(2) and U(1) field strengths and $phi$ is the Higgs field, remove the precision electroweak bound on the Higgs boson mass for values of $Lambda$ in a wide range: $4 TeV < Lambda < 11 TeV$. Within this framework, there is no preference between a light Higgs boson, a…
We study the Landau pole in the lambda phi^4 field theory at non-zero and large temperatures. We show that the position of the thermal Landau pole Lambda_L(T) is shifted to higher energies with respect to the zero temperature Landau pole Lambda_L(0). We find for high temperatures T > Lambda_L(0), Lambda_L(T) simeq pi^2 T / log (T / Lambda_L(0)). Therefore, the range of applicability in energy of the lambda phi^4 field theory increases with the temperature.
For a 4D N=1 supersymmetric model with a low SUSY breaking scale (f) and general Kahler potential K(Phi^i,Phi_j^*) and superpotential W(Phi^i) we study, in an effective theory approach, the relation of the goldstino superfield to the (Ferrara-Zumino) superconformal symmetry breaking chiral superfield X. In the presence of more sources of supersymmetry breaking, we verify the conjecture that the goldstino superfield is the (infrared) limit of X for zero-momentum and Lambda->\infty. (Lambda is the effective cut-off scale). We then study the constraint X^2=0, which in the one-field case is known …
We use lattice simulations to examine the detailed dynamics of inflaton fragmentation during and after preheating in $λϕ^4$ chaotic inflation. The dynamics are qualitatively similar to preheating after $m^2 ϕ^2$ inflation, involving the exponential growth and subsequent expansion and collision of bubble-like inhomogeneities of the inflaton and other scalar fields. During this stage fluctuations of the fields become strongly non-Gaussian. In the quartic theory, the conformal nature of the theory allows us to extend our simulations to much greater times than is possible for the quadratic model. …
The time evolution of O(N) symmetric lambda Phi^4 scalar field theory is studied in the large N limit. In this limit the <Phi> mean field and two-point correlation function <Phi Phi> evolve together as a self-consistent closed Hamiltonian system, characterized by a Gaussian density matrix. The static part of the effective Hamiltonian defines the True Effective Potential U_eff for configurations far from thermal equilibrium. Numerically solving the time evolution equations for energy densities corresponding to a quench in the unstable spinodal region, we find results quite different from what m…
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-z…
We argue that massless (lambda Phi^4)_4 is "trivial" without being entirely trivial. It has a non-trivial effective potential which leads to spontaneous symmetry breaking, but the particle excitations above the broken vacuum are non-interacting. The key to this picture is the realization that the constant background field (the mode with zero 4-momentum) renormalizes differently from the fluctuation field (the finite-momentum modes). This picture reconciles rigorous results and lattice calculations with one-loop and Gaussian-approximation analyses. Because of "triviality", these latter two meth…
This article continues 1205.0410 [hep-th]. Considered is the N=1 SQCD-like theory with SU(N_c) colors and 3N_c/2 <N_F <2N_c flavors of light quarks Q_i,\bar Q_j, and with the additional N^2_F colorless flavored fields Phi_{ij} with the large mass parameter μ_Phi>>Lambda. The mass spectra of this Phi theory (and its dual variant, the dPhi theory) are calculated at different values of μ_Phi/Lambda >>1 within the dynamical scenario which implies that quarks can be in two different phases only: either this is the HQ (heavy quark) phase where they are confined, or they are higgsed at appropriate va…
The thermodynamics of a scalar field with a quartic interaction is studied within the linear delta expansion (LDE) method. Using the imaginary-time formalism the free energy is evaluated up to second order in the LDE. The method generates nonperturbative results that are then used to obtain thermodynamic quantities like the pressure. The phase transition pattern of the model is fully studied, from the broken to the symmetry restored phase. The results are compared with those obtained with other nonperturbative methods and also with ordinary perturbation theory. The results coming from the two …
The discovery of supernova SN 1997ff at z~1.7 has confirmed the expected switch from cosmological acceleration to deceleration, as predicted by the concordance Lambda/CDM model. However, its position in the SN Ia Hubble diagram suggestes that the switch is too pronounced, which here is taken to mean that a cosmological constant is not an adequate description of the state of the vacuum. An 'oscillessence' model is invoked, with a scalar field phi governed by a simple quadratic potential, which gives a better fit to the new data point. The field is undergoing coherent oscillations, and a key fea…
We discuss various aspects of the O(N)-model in the vacuum and at finite temperature within the Phi-derivable expansion scheme to order lambda^2. In continuation to an earlier work, we look for a physical parametrization in the N=4 case that allows to accommodate the lightest mesons. Using zero-momentum curvature masses to approximate the physical masses, we find that, in the parameter range where a relatively large sigma mass is obtained, the scale of the Landau pole is lower compared to that obtained in the two-loop truncation. This jeopardizes the insensitivity of the observables to the ult…
The K^- induced production of Lambda(1405) in the K^- d to pi Sigma n reaction is investigated having in mind the conditions of the DAFNE facility at Frascati where kaons are obtained from the decay of slow moving phi mesons. We find that the K^- d to Lambda(1405) n process favors the production of Lambda(1405) initiated by the K^- p channel, which gives largest weight to the higher mass Lambda(1405) appearing at 1420 MeV in chiral theories. We find that the fastest kaons from the decay of the phi are well suited to see this resonance, particularly if one selects forward going neutrons in the …
We investigate photoproduction of $ϕ$-mesons off protons within a coupled-channel effective-Lagrangian method which is based on the K-matrix approach. Since the threshold energy of the $KΛ(1520)$ channel is close to that of $ϕN$, the contribution of this channel to $ϕ$-photoproduction near the threshold energy region may give rise to some unexpected structures. In the transition amplitude $KΛ(1520) \to ϕN$, the kinematics allows an intermediate kaon to be on-shell. This happens in the energy region where a peak structure has been observed in $ϕ$-photoproduction. In our calculations the on-shel…
We provide outstanding numerical evidence that in large-N massless QCD the joint spectrum of the masses squared, for fixed integer spin s and unspecified parity and charge conjugation, obeys exactly the following laws: m_k^2 = (k+s/2) Lambda_QCD^2 for s even, m_k^2 = 2(k+s/2) Lambda_QCD^2 for s odd, k = 1,2,... for glueballs, and m_n^2 = 1/2 (n+s/2) Lambda_QCD^2, n = 0,1,... for mesons. One of the striking features of these laws is that they imply that the glueball and meson masses squared form exactly-linear Regge trajectories in the large-N limit of massless QCD, all the way down to the low-…
Cosmological scaling solutions, which give rise to a scalar-field density proportional to a background fluid density during radiation and matter eras, are attractive to alleviate the energy scale problem of dark energy. In the presence of multiple scalar fields the scaling solution can exit to the epoch of cosmic acceleration through the so-called assisted inflation mechanism. We study cosmological dynamics of a multi-field system in details with a general Lagrangian density p=sum_{i=1}^n X_i g(X_i e^{lambda_i phi_i}), where X_i=-(nabla phi_i)^2/2 is the kinetic energy of the i-th field phi_i,…
We study the optimized perturbation theory (OPT) at finite temperature, which is a self-consistent resummation method. Firstly, we generalize the idea of the OPT to optimize the coupling constant in lambda phi^4 theory, and give a proof of the renormalizability of this generalized OPT. Secondly, the principle of minimal sensitivity and the criterion of the fastest apparent convergence, which are conditions to determine the optimal parameter values, are examined in lambda phi^4 theory. Both conditions exhibit a second-order transition at finite temperature with critical exponent beta = 0.5 in t…
We summarize the physics topics which can be addressed by measurements of high-Q^2 exclusive electroproduction of strange mesons, gamma* N -> phi N, K* Lambda, K Lambda, K Sigma, at Jefferson Lab with 11 GeV beam energy. The proposed investigations are aimed both at exploring the reaction mechanism (dominance of point-like configurations) and extracting information about baryon structure from the data (generalized parton distributions, or GPDs). They include (a) probing the t-dependence of the nucleon's gluon GPD (transverse spatial distribution of gluons) in phi meson production; (b) separati…
A simple realization of inflation consists of adding the following operators to the Einstein-Hilbert action: (partial phi)^2, lambda phi^4, and xi phi^2 R, with xi a large non-minimal coupling. Recently there has been much discussion as to whether such theories make sense quantum mechanically and if the inflaton phi can also be the Standard Model Higgs. In this note we answer these questions. Firstly, for a single scalar phi, we show that the quantum field theory is well behaved in the pure gravity and kinetic sectors, since the quantum generated corrections are small. However, the theory like…
The operator product expansion is used to obtain model-independent predictions for the first two moments of the renormalized B-meson light-cone distribution amplitude phi_+(omega,mu), defined with a cutoff omega<Lambda_UV. The leading hadronic power corrections are given in terms of the parameter Lambda(bar)=m_B-m_b. From the cutoff dependence of the zeroth moment an analytical expression for the asymptotic behavior of the distribution amplitude is derived, which exhibits a negative radiation tail for omega>>mu. By solving the evolution equation for the distribution amplitude, an integral repr…
The renormalization group flows of the coupling constants for the gauged U(N) vector model, with N_f massless fermions in the defining representation, are studied in the large N limit, to all orders in the scalar coupling lambda, leading order in 1/N, and lowest two orders in the gauge coupling g^2. It is shown that the restrictions of asymptotic freedom, and the reality of the coupling constants throughout the flows, places important restrictions on N_f/N. For the case with massless mesons, these conditions are sufficiently restrictive to imply the existence of an infrared fixed-point (g_*,la…
We report on the non-perturbative computation of the running coupling of two-flavour QCD in the Schr"odinger functional scheme. The corresponding Lambda-parameter, which describes the coupling strength at high energy, is related to a low energy scale which still remains to be connected to a hadronic ``experimentally'' observable quantity. We find the non-perturbative evolution of the coupling indispensable to avoid untolerable errors in the estimated Lambda-parameter.
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.
It has been proposed that the $Λ$ and $\overlineΛ$ polarizations observed in heavy-ion collisions are due to the interaction between quark spin and thermal vorticity. In this work we report on a computation of the relaxation time required for this alignment to occur at finite temperature and baryon chemical potential, considering quarks with a finite mass. The calculation is performed after modelling the interaction by means of an effective vertex which couples the thermal gluons and quarks within the vortical medium. We show that the effect of the quark mass is to reduce the relaxation time a…
Massless $ϕ^{4}$-theory is investigated in zero and four space-time dimensions. Path-integral linearisation of the $ϕ^{4}$-interaction defines an effective theory, which is investigated in a loop-expansion around the mean field. In zero dimensions this expansion converges rapidly to the exact potential obtained numerically. In four dimensions its lowest order (mean-field approximation) produces a real and convex effective potential. Two phases are found. In one the renormalisation group improved one-loop effective potential is recovered as the leading contribution near the classical minimum. T…
We give a more precise characterisation of the end of the electroweak phase transition in the framework of the effective 3d SU(2)--Higgs lattice model than has been given before. The model has now been simulated at gauge couplings beta_G=12 and 16 for Higgs masses M_H^*=70, 74, 76 and 80 GeV up to lattices 96^3 and the data have been used for reweighting. The breakdown of finite volume scaling of the Lee-Yang zeroes indicates the change from a first order transition to a crossover at lambda_3/g_3^2=0.102(2) in rough agreement with results of Karsch et al (hep-lat/9608087) at β_G=9 and smaller …
