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.     

The thermodynamics of SU(3) lattice gauge theory with a light isodoublet of quarks

Using hybrid differential equations with stochastic pseudo-fermion fields, we simulated SU(3) lattice gauge theory with a light isodoublet of quarks on a 4 × 8³ lattice. The bare quark mass is 0.0125 in lattice units which corresponds to 7.75 MeV if the finite temperature chiral transition occurs at T_c=155 MeV as suggested by phenomenology. The transition is first order and metastable states are found over a narrow range in temperature. Results for 4⁴ lattices are also presented for 2 and 3 light flavors.     

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.     

First-order chiral phase transition in lattice QCD

The chiral phase transition in lattice QCD has been studied for light fermions of mass ma=0.025 on lattices of size 4⁴ and 8³×4 using the hybrid algorithm. We find evidence for a first-order chiral phase transition with a large latent heat. A comparison with 10³×6 data shows violations of asymptotic scaling for T_ch which are similar in magnitude to those observed in the pure gauge sector.     

The standard model from a gauge theory in ten dimensions via CSDR

We present a gauge theory in ten dimensions based on the gauge group E₈ which is dimensionally reduced, according to the coset space dimensional reduction (CSDR) scheme, to the standard model SU_3c×SU_2L×U₁, which breaks further to SU_3c×U_1em. We use the coset space Sp₄/(SU₂×U₁)×Z₂. The model gives similar predictions for sin²θ_w and proton decay as the minimal SU₅ GUT. Natural choices of parameters suggest that the Higgs masses are as predicted by the Coleman-Weinberg radiative mechanism.     

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.     

Upper bound estimate for the Higgs mass from the lattice regularized Weinberg-Salam model

There are indications that, as a consequence of the trivality of the scalar φ⁴ theory, the Weinberg-Salam model is massive free field theory. However, considering theWS model as an effective field theory, an upper bound for the Higgs mass can exist. We have studied this phenomenon by simulating the SU(2) gauge Higgs model on a lattice. The results indicate that R_max = m_H/m_W|_max = 9.3 ± 1. However, serious finite size effects make it unfeasible to explore the region m_H ⩽ Λ_cutoff with Monte Carlo simulation.     

On the thermodynamics and scaling behaviour of SU(2) gauge theory with fermion feedback

We study SU(2) lattice gauge theory with four species (N_f = 4) of light dynamical fermions by microcanonical simulation methods. Relatively large lattices, long runs and small quark masses are considered. On a 8³ × 16 lattice $\text{〈}\text{ψ}\text{ψ〉}$ is measured and good evidence for asymptotic freedom with fermion feedback is found. The scaling window begins at β = 4/g² ≈ 1.85. On a 12³ × 6 lattice SU(2) thermodynamics is studied systematically. The chiral symmetry restoration transition is found at β = 1.925 ± .025. The crossover from hadronic matter to the quark-gluon plasma is abrupt.     

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).     

Z′ mass limits,masses and coupling of higgs bosons,and Z′ decays in an E6 superstring based model

We demonstrate that current phenomenological constraints on Z-Z′ mixing for an E₆ grand unified group with low energy gauge group SU(2)_L×U(1)_Y×U(1)_Y, allow only a narrow range of Higgs vacuum expectation values consistent with possibilities favored by renormalization group expectations. Modest improvements in bounds on this mixing will lead to substantial bounds on the Z′ mass if alternative renormalization group solutions are not found. We then explore the constraints upon relations between Higgs masses in this model. In addition we explore the couplings of these Higgs to the gauge particles of the theory and emphasize the associated implications for Higgs detection in decays of the Z′.     

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.     

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.     

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 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.     

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.     

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.     

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)