Electroweak baryon number violation at finite temperature

We consider baryon and lepton number violating processes in the electroweak theory induced by gauge and Higgs fields passing the sphaleron solution at finite temperature. We show that for temperatures larger than 19 GeV the anomalous baryon and lepton number violating processes are suppressed by the Boltzmann factor exp (?βE _sp), whereE _sp is the sphaleron energy, rather than by the instanton tunneling factor exp (?8π²/g ²). We caculate the rate of baryon and lepton number violating processes at finite temperature and determine the freezing temperature of the anomalous processes in the early universe as a function of the Higgs mass. We compare the freezing temperature with the critical temperature of the electroweak phase transition infered from the one-loop finite-temperature effective potential. We obtain a critical Higgs mass of the order of 100 GeV, slightly depending on the top mass and the magnitude of the pre-exponential factor in the rate of theB non-conservation, above which the anomalous processes are certainly in equilibrium after the electroweak phase transition. Assuming that the temperature-dependence of the sphaleron energy is given by that found from the one-loop finitetemperature effective potential, this critical Higgs mass is lowered to a value of the order of 50 GeV.     

Numerical tests of the electroweak phase transition and thermodynamics of the electroweak plasma

The finite temperature phase transition in the SU(2) Higgs model at a Higgs boson mass M_H ≅ 34 GeV is studied in numerical simulations on four-dimensional lattices with time-like extensions up to L_t = 5. The effects of the finite volume and finite lattice spacing on masses and couplings are studied in detail. The errors due to uncertainties in the critical hopping parameter are estimated. The thermodynamics of the electroweak plasma near the phase transition is investigated by determining the relation between energy density and pressure.     

Polyakov loop distributions near deconfinement inSU(2) lattice gauge theory

The distribution function of the Polyakov loop is investigated on a 16³×3 lattice in the neighbourhood of the deconfinement transition ofSU(2) gauge theory. We find, that well above the transition the distribution is a Gaussian; when the coupling approaches the critical point it is modified due to phase flip attempts of the system. Corresponding distributions for the plaquettes remain, however, Gaussian. For one coupling close to the transition we study the distributions on 8³, 12³ and 18³×4 lattices and show that strong finite size effects are present. Using the maximum values of the Gaussian parts of the distributions we construct a more physical (and therefore scaling) order parameter whose critical exponent is in excellent agreement with the universality hypothesis.     

Variation of potential energy surface height and bound state depth induced by laser phase along the reaction path in atom-molecule reactions: Application to Li + CH<Subscript>4</Subscript> → LiH + CH<Subscript>3</Subscript>

Laser atom-molecule reaction interaction through polarizability and dipole moment contribution leads to potential energy surface barrier reshaping and bound states along the reaction path. The polarizability is maximum in the transition state. We will show here by using gauge representation (electric field gauge) for wave length λ = 20.6 μm, intensity I = 1 × 10¹² W/cm², I = 5 × 10¹² W/cm², I = 1 × 10¹³ W/cm², I = 3 × 10¹³ W/cm², that we can create laser induced potential energy surface barrier reshaping in the transition state region (–1–0.5 a. u.). We illustrate such effects for the LiH + CH₃ ? Li + CH₄ reaction with a barrier using ab-initio methods for calculating the reaction path, polarizability and dipole moment contribution of the atom-molecule reaction.     

Baryon asymmetry of the universe and the electroweak phase transition

The present baryon asymmetry of the universe has finally been determined at the finite temperature electroweak phase transition. The strength of this transition plays a crucial role. The effective action is presented to higher orders, including wave function correction factors and the fullg ⁴, λ² effective potential. An upper bound for the Higgs massm _H～70 GeV is concluded for the reliability of the perturbative approach. The finite temperature electroweak, phase transition is studied on the lattice and the most important results of Monte-Carlo simulations are collected.     

Gauge hierarchy in the presence of discrete symmetry

We discuss the gauge hierarchy problem in theories that posses an additional discrete symmetry. As examples, we consider two models based on the gauge groups U(1)_L×U(1)_Rand SU(2)_L×SU(2)_R×U(1), with parity transformation as the discrete symmetry. By employing a minimal choice of Higgs multiplets there is no freedom, in the semi-classical approximation, to arrange for an arbitrary hierarchy. Either one has a left-right symmetric phase (no hierarchy) or a totally asymmetric phase (infinite hierarchy). It is shown that radiative corrections, à la Coleman-Weinberg, do not smooth out the transition region separating the two phases. A finite gauge hierarchy is not realized.     

Linked cluster expansions for U(1) lattice gauge theory in 2 + 1 and 3 + 1 dimensions

Compact U(1) lattice gauge theory is studied in 2 + 1 and 3 + 1 dimensions using strong coupling series expansions and the recently proposed exact linled cluster expansion alborithm Results for the vacuum energy, specific heat and axial string tension in 2 + 1 dimensions are in agreement with previous finite lattice estimates. In 3 + 1 dimensions, we present new strong coupling series results (order g^?40) which together with the ELCE estimates show evidence of a continuous phase transition at x = 1/g⁴ = 0.72 ± 0.08. The associated critical index for the vanishing string tension is μ = 0.65 ± 0.12. The axial string tension in D = 3 + 1 appears to undergo a non-deconfining roughening transition at smaller x (0.56 ± 0.07).     

A non-linear Rζ gauge condition for the electroweak SU(2) × U(1) model

A non-linear R_ζ gauge condition is presented and explicitly developed in the framework of the SU(2)×U(1) gauge model. We give the corresponding Feynman rules, which are simpler than in R_ζ gauges, because couplings involving unphysical Higgs and gauge bosons disappear or simplify. The Faddeev-Popov sector is more elegant, the ghosts coupling to neutral gauge bosons like in scalar electrodynamics. Finally, as a practical example, the transition Higgs→γγ is considered and compared with the usual calculation in linear gauges.     

Finite temperature QCD in the presence of dynamical quarks

By using Monte Carlo (MC) methods we study the deconfining transition of QCD with color group SU(3) at finite temperature. The fermion polarization effects are kept in account by implementing the pseudo-fermion method. We use two different lattice volumes (6³ × 4, 8³ × 4) to check finite size effects. Even in the presence of light quarks we find a discontinuous transition. The existence of this transition is observed both creating metastable states and using mixed phase runs.     

Black hole/string transition for the small Schwarzschild black hole of AdS 5 × S5 and critical unitary matrix models

In this paper we discuss the black hole–string transition of the small Schwarzschild black hole of AdS ₅×S⁵ using the AdS/CFT correspondence at finite temperature. The finite temperature gauge theory effective action, at weak and strong coupling, can be expressed entirely in terms of constant Polyakov lines which are SU(N) matrices. In showing this we have taken into account that there are no Nambu–Goldstone modes associated with the fact that the 10-dimensional black hole solution sits at a point in S⁵. We show that the phase of the gauge theory in which the eigenvalue spectrum has a gap corresponds to supergravity saddle points in the bulk theory. We identify the third order N=∞ phase transition with the black hole–string transition. This singularity can be resolved using a double scaling limit in the transition region where the large N expansion is organized in terms of powers of N^-2/3. The N=∞ transition now becomes a smooth crossover in terms of a renormalized string coupling constant, reflecting the physics of large but finite N. Multiply wound Polyakov lines condense in the crossover region. We also discuss the implications of our results for the resolution of the singularity of the lorenztian section of the small Schwarzschild black hole.     

On the characterization of the higgs phase in lattice gauge theories

We consider Higgs models on a lattice in 3 or 4 dimensions. Higgs scalars are assumed to transform trivially under a finite subgroup Γ of the compact gauge groupG. We adopt 't Hooft's definition of the Higgs phase, it is characterized by a nonvanishing free energy per unit length (area) of a vortex in 3 (4) dimensions. By using a Peierls argument we show that the models are in the Higgs phase in this sense for suitable coupling constants.     

Proton-induced F-centers in LiF and MgF2

The growth of F-centers in LiF irradiated at room temperature with 40- and 85-MeV protons and with ⁹⁰Sr electrons was found to be proportional to the square root of the absorbed energy over the range 0.5 to 2.3 Mrad which corresponds to an F-center density range of 1 × 10¹⁶ to 1.5 × 10¹⁷ per cm³. The production efficiency was 5 × 10³eV per F-center at an absorbed energy of 2.3 Mrad. The density of F-centers produced in MgF₂ by 40- and 85-MeV protons was measured over an absorbed energy range of 0.2 to 29 Mrad which corresponds to a maximum F-center density of 2 × 10¹⁶ per cm³. The production efficiency for MgF₂ was 4 × 10⁵eV per F-center at an absorbed energy of 16 Mrad.     

On Nambu monopole dynamics in a SU(2) lattice Higgs model

It is shown that an SU(2) Higgs model on a lattice is equivalent to the Georgi-Glashow model in the limit of a small coupling constant between the Higgs and gauge fields. It can therefore be concluded that the transition between the confinement and symmetric phases in a 3 + 1 dimensional SU(2) Higgs model at finite temperature is accompanied by condensation of Nambu monopoles. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 9, 577–580 (10 November 1997)     

Proton decay in locally supersymmetric GUT

Proton decay is studied in the supergravity model with “the hidden sector” as the source of supersymmetry breaking. Each dimension-five operator is found to accompany ΔB ≠ 0 four-scalar interactions. The Higgs fermion exchange for loop diagrams at low energies can be as important as the gauge fermion exchange, if the associated Yukawa coupling is significant as suggested by the radiatively induced SU(2) × U(1) breaking mechanism. The experimental bound for p → K⁰μ⁺ gives the lower bound of the order of 10¹⁶ GeV for the mass of the baryon-number violating Higgs particle.     

Temperature dependence of the critical magnetic field of the structural transition in MBBA-based ferronematics

We studied the structural transitions in ferronematics based on the thermotropic nematic liquid crystal MBBA (4^′ -methoxybenzylidene-4-n-butylaniline) having a nematic-to-isotropic transition temperature T _N–I?=?48.0^○C and in MBBA-based ferronematics doped with a magnetic suspension consisting of Fe₃O₄ particles (10?nm in diameter) coated with oleic acid as a surfactant. The ferronematic samples were prepared with different volume concentrations of magnetic particles φ?=,1× 10^?4, 2× 10^?4 and 5×10^?4. The temperature dependences of the critical magnetic fields in a bias electric field under strong applied magnetic fields are presented. We calculated the surface density of anchoring energy W at the nematic–magnetic particle boundary. Scaling of the structural transition in the MBBA and MBBA-based ferronematics with the temperature of the nematic-to-isotropic transition was observed.     

Virtual effects of Higgs particles

The possibility of observing Higgs particles through virtual effects is considered in detail for a general gauge theory. The effect of charged Higgs particles on low-energy weak interaction processes, like muon decay, tau decay, nuclear beta decay, pion decay, and some higher-order processes is analyzed. The effect of flavor-changing neutral Higgs particles on rare decay modes of the muon and kaon, μe conversion, K^o-$\text{K}$^o and D^o-$\text{D}$^o mixing is also studied. We discuss constraints on possible extensions of the Weinberg-Salam model and experiments sensitive to their Higgs particles. In particular, we analyze the neutral Higgs which couple to fermions in the minimal SU(2)_L×SU(2)_R×U(1) model and find that they probably have mass greater than 100 GeV.     

THE EVIDENCE OF DECONFINEMENT PHASE TRANSITION OF SU(2) LATTICE GAUGE MODEL BY MONTE CARLO METHOD

In this paper,we have calculated the SU(2) lattice gauge by the Monte Carlo method.For the finite temperature problem 8³×4 lattice is used and for the zero temperature problem 8⁴ lattice.From the calculations of the energy density,heat capacity and entropy density,the results indicate that there is a deconfinement phase transition when T/Λ_L=40—50.     

Non-Abelian Vortices on Riemann Surfaces: an Integrable Case

We consider U(n + 1) Yang–Mills instantons on the space Σ × S ², where Σ is a compact Riemann surface of genus g. Using an SU(2)-equivariant dimensional reduction, we show that the U(n + 1) instanton equations on Σ × S ² are equivalent to non-Abelian vortex equations on Σ. Solutions to these equations are given by pairs (A,?), where A is a gauge potential of the group U(n) and ? is a Higgs field in the fundamental representation of the group U(n). We briefly compare this model with other non-Abelian Higgs models considered recently. Afterwards we show that for g > 1, when Σ × S ² becomes a gravitational instanton, the non-Abelian vortex equations are the compatibility conditions of two linear equations (Lax pair) and therefore the standard methods of integrable systems can be applied for constructing their solutions.     

Higgs boson emission in very rare decays of an extra vector boson

We explore the phenomenological structure of E ₆-inspired grand unified group with the gauge group SU(3)_c×SU(2)_L×U(1)_Y×U(1), the emphasis being laid upon its implications for Higgs boson observation. In particular, we discuss the probability for the mass eigenstate Z ₂ to decay into a Higgs particle and a bound state composed of heavy quarks. Constraints on and relations between the Z ₂ and Higgs masses are presented.     

Pressure dependence of the absorption edge for Cd1-xMnxTe

The effect of pressure on the optical absorption edge of mixed crystals Cd_1-xMn_xTe with different manganese concentrations is reported. The observed absorption edge shifts to higher energy with increasing pressure at a rate of α=7?8×10^?3 eV/kbar and a second order coefficient of β=-4×10^?5 eV/kbar² for x<0.5, to lower energy with increasing pressure at a rate of α=-5.0 ×10^?3 eV/kbar for x?0.5. A phase transition occurs for all the samples studied. The absorption edge of the new phase is outside the wavenumber range of the instrument. The physical origins of different pressure coefficients are discussed in the light of the deformation potentials of energy band states and the hybridization of the Mn²⁺ 3d levels with the p-like states in the valence band.