The lattice Georgi-Glashow model in three dimensions

We find the phase diagram of the 3-DSU(2) lattice gauge-Higgs model with the scalar fields transforming as triplets underSU(2). The model is studied for several values of λ, the Higgs self-coupling. When λ is sufficiently small, the Higgs phase transition continues to new regions of the coupling constant space, due to the radial fluctuations.     

Gaussian effective potential for the U(1) Higgs model

In order to investigate the Higgs mechanism nonperturbatively, we compute the Gaussian effective potential of the U(1) Higgs model (“scalar electrodynamics”). We show that the same simple result is obtained in three different formalisms. A general covariant gauge is used, with Landau gauge proving to be optimal. The renormalization generalizes the “autonomous” renormalization for λ?⁴ theory and requires a particular relationship between the bare gauge coupling e _B and the bare scalar self-coupling λ _B. When both couplings are small, then λ is proportional to e⁴ and the scalar/vector mass-squared ratio is of order e², as in the classic 1-loop analysis of Coleman and Weinberg. However, as λ increases, e reaches a maximum value and then decreases, and in this “nonperturbative” regime the Higgs scalar can be much heavier than the vector boson. We compare our results to the autonomously renormalized 1-loop effective potential, finding close agreement in the physical predictions. The main phenomenological implication is a Higgs mass of about 2 TeV.     

Bianchi type IX asymptotical behaviours with a massive scalar field: chaos strikes back

We use numerical integrations to study the asymptotical behaviour of a homogeneous but anisotropic Bianchi type IX model in General Relativity with a massive scalar field. As it is well known, for a Brans-Dicke theory, the asymptotical behaviour of the metric functions is ruled only by the Brans-Dicke coupling constant ₀ with respect to the value –3/2. In this paper we examine if such a condition still exists with a massive scalar field. We also show that, contrary to what occurs for a massless scalar field, the singularity oscillatory approach may exist in the presence of a massive scalar field having a positive energy density.     

Vector boson in the constant electromagnetic field

The propagator and the complete sets of in-and out-solutions of the wave equation, together with the Bogoliubov coefficients relating these solutions are obtained for the vector W-boson (with the gyromagnetic ratio g=2) in a constant electromagnetic field. When only the electric field is present, the Bogoliubov coefficients are independent of the boson polarization and are the same as for the scalar boson. For the collinear electric and magnetic fields, the Bogoliubov coefficients for states with the boson spin perpendicular to the field are again the same as in the scalar case. For the W ^? spin parallel (antiparallel) to the magnetic field, the Bogoliubov coefficients and the one-loop contributions to the imaginary part of the Lagrange function are obtained from the corresponding expressions for the scalar case by the substitution m ² → m ²+2eH (m ² → m ²-2eH). For the gyromagnetic ratio g=2, the vector boson interaction with the constant electromagnetic field is described by the functions that can be expected by comparing the scalar and Dirac particle wave functions in the constant electromagnetic field.     

Radiatively induced spontaneous symmetry breaking and phase transitions in curved spacetime

Local gauge symmetries which are spontaneously broken in flat spacetime are shown to be restored for large spacetime curvatures. The case of symmetry breaking due to radiative quantum corrections in gauge theories with elementary scalar fields is considered explicitly. In spacetimes with a positive Ricci curvature scalar R and a cosmological event horizon, the critical curvature R_C is of O(m_H²) or O(m_W²), depending on whether the theory is formulated with conformal or minimal scalar fields. In Ricci flat spacetimes with a conventional event horizon the symmetry is expected to be restored when the temperature of the Hawking thermal radiation is of O(m_W). This phenomenon is described in detail, using functional integral methods and dimensional renormalization, for massless scalar electro-dynamics in de-Sitter spacetime. For conformal scalars, the symmetry restoring phase transition is first order, the critical curvature being R_C = 0.910 m_H². For minimal scalars, an anomalous, curvature dependent mass counterterm is required. The phase transition in this case is second order, and occurs at R_C = 83.57 m_W². Symmetry restoration at finite temperature in flat spacetime is considered in an appendix. The critical temperature at which a first-order phase transition occurs in the Weinberg-Salam model is found to be T_C = 0.329 m_W.     

Accurate energy levels for the anharmonic oscillator and a summable series for the double-well potential in perturbation theory

We introduce a generalization of Wick-ordering which maps the anharmonic oscillator (AO) Hamiltonian for mass m and coupling λ exactly into a “Wick-ordered” Hamiltonian with an effective mass M which is a simple analytic function of λ and m. The effective coupling $\text{Λ =}\text{λ}\text{M}{}^3$ is bounded. We transform the AO perturbation series in λ into one in Λ. This series may then be summed using Borel summation methods. We also introduce a new summation method for the AO series (which is a practical necessity to obtain accurate energy levels of the excited states). We obtain a numerical accuracy for $\text{(E}{}_{\mathrm{PT}}\text{? E}{}_{\mathrm{exact}}\text{)}\text{E}{}_{\mathrm{exact}}$ of at least 10^?7 (using 20 orders of perturbation theory) and 10^?3 (using only 2 orders of perturbation theory) for all couplings and all energy levels of the anharmonic oscillator. The methods are applicable also to the double-well potential (DWP, the AO with a negative mass-squared). The only change is that now the effective coupling is unbounded as λ → 0. The series in Λ is, however, still summable. The relative accuracy in the energy levels for 20 orders of perturbation theory varies from 10^?7 for large coupling to 1% at λ = 0.1 and to 10% at λ = .05. We also present results for the sextic oscillator.     

An effective lagrangian for multiphoton processes and a non-linear Born-Infeld lagrangian

An effective lagrangian for multiphoton processes (of Euler-Heisenberg type) is computed for an electromagnetic field interacting with massive scalar, fermion and vector particles. It is found that if the charges g_I, masses m_I and numbers N_I of massive particles satisfy the “supersymmetric” conditions, N_Sm_S⁴+3N_Vm_V⁴?2N_Fm_F⁴=0 and g_I²/m_I⁴ is I-independent, where I=S, F, V stands for scalars, fermions and vectors respectively, then not only quartic divergences (poles at n=0 in dimensional regularization) proportional to constant terms cancel out but also maximally helicity changing interaction terms vanish in the effective lagrangian. A possibility to relate a non-linear Born-Infeld lagrangian to the effective lagrangian is examined.     

Neutron spectroscopy study of magnons in the austenite and martensite phases of a Ni-Mn-Ga Heusler alloy

The low energy region of magnon excitations of an off-stoichiometric Ni_49.1Mn_29.4Ga_21.5 single crystal has been investigated by neutron spectroscopy. The lowest magnetic exchange stiffness constant D of 97±2 meV Å² has been found in the cubic austenite phase. In the two martensitic phases the exchange stiffness constants are significantly larger with values of 149±4 meV Å² in the tetragonal phase and 198±7 meV Å² in the low temperature martensite. The large value of D in the low temperature phase compared to the other phases cannot be explained solely by renormalization effects due to magnon-magnon interaction and is attributed to a stronger magnetic coupling. In both the martensitic phases a gap of magnon excitation at the Γ-point of about 0.2 meV was observed.     

Search for macroscopic CP violating forces using a neutron EDM spectrometer

The search for CP violating forces between nucleons in the so-called axion window of force ranges λ between 2 × 10^?5 m and 0.02 m is interesting because only little experimental information is available there. Axionlike particles would induce a pseudo-magnetic field for neutrons close to bulk matter. A laboratory search investigates neutron spin precession close to a heavy mirror using ultracold neutrons in a magnetic resonance spectrometer. From the absence of a shift of the magnetic resonance we established new constraints on the coupling strength of axion-like particles in terms of the product g _s g _p of scalar and pseudo-scalar dimensionless constants, as a function of the force range λ, g _s g _p λ² ≤ 2 × 10^?21 [cm²] (C.L.95%) for 10^?4 cm < λ < 1 cm. For 0.1 cm < λ < 1 cm previous limits are improved by 4 to 5 orders of magnitude.     

A QCD analysis of the 〈p2T〉 behaviour observed in recent semi-inclusive neutrino data

Relying on a recent recalculation of the β-function in massive QCD, we show that a theory with infinitely many quark flavors is asymptotically free if the quark masses grow as m_n² = n^σM₀², 1 < σ ? 3.6; the precise definition of the (via the three-gluon vertex) enters in an essential way. In these models the running coupling constant decays like an inverse power of Q² as Q² → ∞. Some phenomenological implications of this curious result are discussed.     

Low energy theorems in a nonlocal chiral quark model at finite temperature

We solve the Dyson equation and the Bethe-Salpeter equation for a nonlocal effective quark interaction kernel which is instantaneous and separable. The momentum-dependent dynamical quark mass, the scalar and pseudoscalar meson masses, the pion decay constant and the quark meson coupling constant are calculated at finite temperature in the Hartree approximation for the quark self energy. We obtain relations between these quantities, which coincide to leading order in the current quark mass (m ₀/Δm) with the basic low energy theorems: the Goldstone theorem, the Gell-Mann-Oakes-Renner relation and the Goldberger-Treimann relation at finite temperature. A formula for the σ?π mass gap is obtained which exhibits an additional contribution from the momentum dependence of the quark mass.     

The Bethe-Salpeter equation with fermions

The Bethe-Salpeter (BS) equation in the ladder approximation is studied within a fermion theory: two fermion fields (constituents) with mass m interacting via an exchange of a scalar field with mass μ. The BS equation can be written in the form of an integral equation in the configuration Euclidean x-space with the symmetric kernel K for which Tr K ² = ∞ due to the singular character of the fermion propagator. This kernel is represented in the form K = K ₀ + K _I . The operator K ₀ with Tr K ₀ ² = ∞ is of the “fall at the center” potential type and describes a continuous spectrum only. Besides the presence of this operator leads to a restriction on the value of the coupling constant. The kernel K _I with Tr K _I ² < ∞ is responsible for bound fermion-fermion states. Our approach is that the eigenvalue problem of the equation $\Lambda\Psi = g^2(K_0 + K_I)\Psi \qquad {\rm with}\qquad \Lambda = 1The Bethe-Salpeter (BS) equation in the ladder approximation is studied within a fermion theory: two fermion fields (constituents) with mass m interacting via an exchange of a scalar field with mass μ. The BS equation can be written in the form of an integral equation in the configuration Euclidean x-space with the symmetric kernel K for which Tr K ² = ∞ due to the singular character of the fermion propagator. This kernel is represented in the form K = K ₀ + K _I . The operator K ₀ with Tr K ₀ ² = ∞ is of the “fall at the center” potential type and describes a continuous spectrum only. Besides the presence of this operator leads to a restriction on the value of the coupling constant. The kernel K _I with Tr K _I ² < ∞ is responsible for bound fermion-fermion states. Our approach is that the eigenvalue problem of the equation can be rewritten in the form The kernel of the last equation is finite for g ² < g _c ² and the variational procedure of calculations of eigenvalues and eigenfunctions can be applied. The quantum pseudoscalar and scalar mesodynamics is considered. The binding energy of the state 1⁺ (deuteron) as a function of the coupling constant is calculated in the framework of the procedure formulated above. It is shown that this bound state is absent in the pseudoscalar mesodynamics and does exist in the scalar mesodynamics. A comparison with the non-relativistic Schr?dinger picture is made. Correspondence: G. V. Efimov, Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna, Russia     

On condensation of the vortex solitons in a 2 + 1 dimensional abelian Higgs model

We study the roles of the vortex solitons in a 2 + 1 dimensional abelian Higgs model. From the effective lagrangian L_eff for the soliton field χ, it is found that the appearance of the solitons reduces the dielectric constant to a value smaller than one. If the Higgs field 〈H〉_vac does not vanish, the vacuum is in the Higgs phase and the solitons are not important. If it does vanish, the solitons become massless and L_eff has an infinite number of classically degenerate vacua. In the quantum theory of L_eff with large coupling constant e, no evidence of 〈χ〉_vac ≠ 0 has been discovered. For this conclusion to hold it is crucial that the free energy of scalar QED monotonically increases with e².     

Unnatural oscillon lifetimes in an expanding background

We consider a classical toy model of a massive scalar field in 1+1$1+1$ dimensions with a constant exponential expansion rate of space. The nonlinear theory under consideration supports approximate oscillon solutions, but they eventually decay due to their coupling to the expanding background. Although all the parameters of the theory and the oscillon energies are of order one in units of the scalar field mass m  , the oscillon lifetime is exponentially large in these natural units. For typical values of the parameters, we see oscillon lifetimes scaling approximately as τ∝exp(kE/m)/m$\tau \propto \exp (kE/m)/m$ where E is the oscillon energy and the constant k   is on the order of 5 to 15 for expansion rates between H=0.02m$H=0.02m$ and H=0.01m$H=0.01m$.     

Dark energy,induced gravity and broken scale invariance

We study the cosmological evolution of an induced gravity model with a self-interacting scalar field σ and in the presence of matter and radiation. Such model leads to Einstein gravity plus a cosmological constant as a stable attractor among homogeneous cosmologies and is therefore a viable dark-energy (DE) model for a wide range of scalar field initial conditions and values for its positive γ   coupling to the Ricci curvature γσ²R$\gamma {\sigma }^{2}R$.     

Temperature dependence of magnetic anisotropy constant in cobalt ferrite nanoparticles

The temperature dependence of the effective magnetic anisotropy constant K(T) of CoFe₂O₄ nanoparticles is obtained based on the SQUID magnetometry measurements and Mössbauer spectroscopy. The variation of the blocking temperature T_B as a function of particle radius r is first determined by associating the particle size distribution and the anisotropy energy barrier distribution deduced from the hysteresis curve and the magnetization decay curve, respectively. Finally, the magnetic anisotropy constant at each temperature is calculated from the relation between r and T_B. The resultant effective magnetic anisotropy constant K(T) decreases markedly with increasing temperature from 1.1×10⁷ J/m³ at 5 K to 0.6×10⁵ J/m³ at 280 K. The attempt time τ₀ is also determined to be 6.1×10⁻¹² s which together with the K(T) best explains the temperature dependence of superparamagnetic fraction in Mössbauer spectra.     

A numerical estimate of the upper limit for the Higgs boson mass

TheSU (2) Higgs model with a scalar doublet field is studied by Monte Carlo calculations on 12⁴ and 16⁴ lattices. The gauge coupling is chosen to be similar in magnitude to the physical value in the standard model. The numerical results at large scalar self-coupling imply an upper limitm _H /m _W ?9 for the ratio of the Higgs boson mass to the W-mass.     

The pressure influence on the incommensurate-commensurate ferroelectric phase transition in [4-NH2C5H4NH][SbCl4]

The dielectric properties of the [4-NH₂C₅H₄NH] SbCl₄ (abbreviated as 4-APCA) crystal were investigated under hydrostatic pressure up to 300 Mpa. The pressure-temperature phase diagram was given. The paraelectric-ferroelectric phase transition (II→III) temperature (T_c) increases linearly with increasing pressure with a slope dT_c/dp=21×10⁻² K/MPa. The pressure dependence of Curie-Weiss constants has been evaluated also. In the paraelectric phase (II) the Curie constant (C₊) was pressure dependent whereas the C₋ constant over the ferroelectric phase (III) was almost constant. The results are interpreted in terms of improper and displacive type phase transition model with a soft phonon at a zone boundary.     

Phase transition of [(C6H5)3PCH3]+(TCNQ)-2 and electrical transport properties

The electrical conductivity at 10GHz, the dielectric constant, and the thermoelectric power (TEP) of [(C₆H₅)₃PCH₃]⁺(TCNQ)^-₂, from 230 up to 400 K, have been measured. This organic quasi-one-dimensional solid undergoes a first order phase transition at 314 K. At the transition the conductivity increases by a factor of 2.2 and the activation energy drops to 0.26 from 0.31 eV. At 314 K TEP decreases abruptly from -75 to -60μVK^-1 and remains almost constant for T > 314 K. The dielectric permeability ?₀ is constant and equal to 5 in the low temperature phase, increases abruptly by 7% at the transition, and then depends strongly on temperature in the high temperature phase. Results of the high temperature phase are interpreted in terms of a strongly correlated salt.     

N = 2 harmonic superspace with central charges and its application to self-interacting massive hypermultiplets

We investigate the structure of the harmonic superspace formalism with central charges for N = 2 supersymmetry, which is applicable to a wide class of N = 2 theories. As a simple application, the Lagrangian for self-interacting N = 2 massive scalar hypermultiplets is constructed in this formalism, and the interactions are explicitly obtained in terms of physical fields in the lowest order in the coupling constant. Although the theory looks highly unrenormalizable, remarkable cancellations take place so that all radiative corrections vanish in the lowest nontrivial order in the coupling constant.