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.     

Critical bubbles and fluctuations at the electroweak phase transition

We discuss the critical bubbles of the electroweak phase transition using an effective high-temperature 3-dimensional action for the Higgs field ϕ. The separate integration of gauge and Goldstone boson degrees of freedom is conveniently described in the 't Hooft-Feynman covariant background gauge. The effective dimensionless gauge coupling g3 (T) z in the broken phase is well behaved throughout the phase transition. However, the behavior of the one-loop Z(ϕ) factors of the Higgs and gauge kinetic terms signalizes the breakdown of the derivative expansion and of the perturbative expansion for a range of small ϕ values increasing with the Higgs mass m_H Taking a functional S_z [ϕ] with constant Z(ϕ) = z instead of the full non-local effective action in some neighborhood of the saddle point we are calculating the critical bubbles for several temperatures. The fluctuation determinant is calculated to high accuracy using a variant of the heat kernel method. It gives a strong suppression of the transition rate compared to previous estimates.     

Effective scalar field theory for the electroweak phase transition

We investigate an effective model for the finite-temperature symmetry-restoration phase transition of the electroweak theory. It is obtained by dimensional reduction of the (3 + 1)-dimensional full theory and by subsequent integration over all static gauge degrees of freedom. The resulting theory corresponds to a 3-dimensional O(4) ferromagnet containing cubic and quartic terms of the field in its potential function. Possible nonperturbative effects of a magnetic screening mass are parametrically included in the potential. We analyse the theory using mean-field and numerical Monte Carlo (MC) simulation methods. At the value of the physical Higgs mass, m_H = 37 GeV, considered in the present investigation, we find a discontinuous symmetry-restoring phase transition. We determine the critical temperature, order parameter jump, interface tension and latent heat characteristics of the transition. The Monte Carlo results indicate a somewhat weaker first-order phase transition as compared to the mean-field treatment, demonstrating that non-perturbative fluctuations of the Higgs field are relevant. This effect is especially important for the interface tension. Any observation of hard first-order transition could result only from non-perturbative effects related to the gauge degrees of freedom.     

First-order electroweak phase transition powered by additional F-term loop effects in an extended supersymmetric Higgs sector

We investigate the one-loop effect of new charged scalar bosons on the Higgs potential at finite temperatures in the supersymmetric standard model with four Higgs doublet chiral superfields as well as a pair of charged singlet chiral superfields. In this model, the mass of the lightest Higgs boson h is determined only by the D-term in the Higgs potential at the tree-level, while the triple Higgs boson coupling for hhh can receive a significant radiative correction due to nondecoupling one-loop contributions of the additional charged scalar bosons. We find that the same nondecoupling mechanism can also contribute to realize stronger first order electroweak phase transition than that in the minimal supersymmetric standard model, which is definitely required for a successful scenario of electroweak baryogenesis. Therefore, this model can be a new candidate for a model in which the baryon asymmetry of the Universe is explained at the electroweak scale.     

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 higgs boson mass from precision electroweak data

We present a new global fit to precision electroweak data, including new low- and high-energy data and analyzing the radiative corrections arising from the minimal symmetry breaking sectors of the Standard Model (SM) and its supersymmetric extension (MSSM). It is shown that present data favor a Higgs mass ofO(M _z):M _H=76 _?50 ⁺¹⁵² GeV. We confront our analysis with (meta) stability and perturbative bounds on the SM Higgs mass, and the theoretical upper bound on the MSSM Higgs mass. Present data do not discriminate significantly between the SM and MSSM Higgs mass ranges. We comment in passing on the sensitivity of the Higgs mass determination to the values ofα(M _z) andα _s(M _z).     

Strongly first order electroweak phase transition induced by primordial hypermagnetic fields

We consider the effect of the presence of a hypermagnetic field at the electroweak phase transition. Screening of the Z-component inside a bubble of the broken phase delays the phase transition and makes it stronger first order. We show that the sphaleron constraint can be evaded for m_H up to 100 GeV if a B_Y0.3T² exists at the time of the EW phase transition, thus resurrecting the possibility for baryogenesis within the minimal standard model (provided enough CP violation can be obtained). We estimate that for m_H100 GeV the Higgs condensate behaves like a type II superconductor with Z-vortices penetrating the bubble. Also, for such high Higgs masses the minimum B_Y field required for a strong first order phase transition is large enough to render the W-field unstable towards forming a condensate which changes the simple picture of the symmetry breaking.     

Singlino-driven electroweak baryogenesis in the next-to-MSSM

We explore a new possibility of electroweak baryogenesis in the next-to-minimal supersymmetric standard model. In this model, a strong first-order electroweak phase transition can be achieved due to the additional singlet Higgs field. The new impact of its superpartner (singlino) on the baryon asymmetry is investigated by employing the closed-time-path formalism. We find that the CP violating source term fueled by the singlino could be large enough to generate the observed baryon asymmetry of the Universe without any conflicts with the current constraints from the non-observation of the thallium, neutron and mercury electric dipole moments.     

Monte carlo study of anSU(2) lattice gauge-Higgs theory at finite temperature

AnSU(2) gauge theory coupled to a Higgs field in the fundamental representation is studied at finite temperature by Monte Carlo method. Calculations are done on 8⁴, 8³×4 and 8³×2 lattices with a small Higgs self-coupling constant. In the parameter region we studied both the location and the order of the Higgs transition are found to be insensitive to the system's temperature. As for the deconfining transition at finite temperature, our data suggest that it disappears within the symmetric region as the Higgs bare mass decreases. Results on the Higgs energy density and the gauge energy density are also presented.     

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.     

Non-perturbative contributions to the hot electroweak potential and the crossover

We discuss non-perturbative contributions to the three-dimensional 1-loop effective potential of the electroweak theory at high temperatures in the framework of the stochastic vacuum model. It assumes a gauge-field background with Gaussian correlations which leads to confinement. The instability of 〈F²〉 = 0 in Yang-Mills theory appears for small Higgs expectation value 〈φ²〉 in an IR regularized form. The gauge-boson propagator obtains a positive momentum-dependent “diamagnetic” effective (mass)² due to confinement effects and a negative one due to “paramagnetic” spin-spin interactions which are related to the 〈F²〉 = 0 instability. Numerical evaluation of an approximate effective potential containing these masses shows qualitatively the fading away of the first-order phase transition with increasing Higgs mass which was observed in lattice calculations. The crossover point can be roughly determined postulating that the effective φ⁴ and φ² terms vanish there.     

On the role of the higgs mechanism in present electroweak precision tests

Based on the observablesM _W, Γ _l ,s _W ^?2 (M _Z ² ), we evaluate the parameters Δx, Δy and ε at one-loop level within an electroweak massive vector-boson theory, which does not employ the Higgs mechanism. The theoretical results are consistent with the experimental ones on Δx, Δy, ε. The theoretical prediction for Δy coincides with the standard-model one (apart from numerically irrelevant terms which vanish forM _H→∞). Nonrenormalizability only affects Δx and ε, which differ from the standard-model results by the replacement logM _H→log Λ for a heavy Higgs mass,M _H (where Λ denotes an effective UV cut-off).     

Phase structure and critical behavior of multi-Higgs U(1) lattice gauge theory in three dimensions

We study the three-dimensional (3D) compact U(1) lattice gauge theory coupled with N-flavor Higgs fields by means of the Monte Carlo simulations. This model is relevant to multi-component superconductors, antiferromagnetic spin systems in easy plane, inflational cosmology, etc. It is known that there is no phase transition in the N = 1 model. For N = 2, we found that the system has a second-order phase transition line in the c₂ (gauge coupling)-c₁ (Higgs coupling) plane, which separates the confinement phase and the Higgs phase. Numerical results suggest that the phase transition belongs to the universality class of the 3D XY model as the previous works by Babaev et al. and Smiseth et al. suggested. For N = 3, we found that there exists a critical line similar to that in the N = 2 model, but the critical line is separated into two parts; one for c₂<c_2tc=2.4±0.1 with first-order transitions, and the other for c_2tc<c₂ with second-order transitions, indicating the existence of a tricritical point. We verified that similar phase diagram appears for the N = 4 and N = 5 systems. We also studied the case of anistropic Higgs coupling in the N = 3 model and found that there appear two second-order phase transitions or a single second-order transition and a crossover depending on the values of the anisotropic Higgs couplings. This result indicates that an “enhancement” of phase transition occurs when multiple phase transitions coincide at a certain point in the parameter space.     

Velocity of electroweak bubble walls

We study the velocity of bubble walls in the electroweak phase transition. For several extensions of the Standard Model, we estimate the friction and calculate the wall velocity, taking into account the hydrodynamics. We find that deflagrations are generally more likely than detonations. Nevertheless, for models with extra bosons, which give a strongly first-order phase transition, the deflagration velocity is in general quite high, 0.1v_w0.6. Therefore, such phase transitions may produce an important signal of gravitational waves. On the other hand, models with extra fermions which are strongly coupled to the Higgs boson may provide a strongly first-order phase transition and small velocities, 10⁻²v_w10⁻¹, as required by electroweak baryogenesis.     

On the radiative corrections to the electroweak parameters and precision tests of the electroweak theory

The radiative corrections to the electroweak parameters are reconsidered with an emphasis on analysing prospects for future tests of the as yet untested parts of the electroweak theory, in particular the “new physics” of vector-boson self-interactions and the Higgs scalar. The vacuum polarization due to the light fermions is treated in the leading-long approximation, while the top-quark is taken into account exactly. A detailed analysis of the errors involved in our approximations and a comparison with the results of complete one-loop calculations shows that vacuum polarization due to bosons is negligible, ifm _H =100 GeV, while it may become visible in precision tests ine ⁺ e ^? annihilation, ifm _H ?1 TeV. We also give detailed results (as a function of the top-quark mass) on the radiatively correceted parameters used in model-independent fits to neutrino-scattering and in the interpretation of atomic-parity violation experiments. Technically, we diagonalize the γ-Z propagator for anyq ², and we show, when treating the top-quark vacuum polarization exactly, that the intuitively appealing notion of running coupling constants can be used beyond the leading-log approximation.     

Nonperturbative contribution to the fermion propagator and dynamical electroweak symmetry breaking

We examine the field-theoretical contribution of fermion-antifermion condensates arising from a weak-SU(2) doublet of condensing fermions to electroweak vacuum polarization functions. For the custodial-SU(2) case of equal condensates and masses, we find that the condensate contributions to vacuum polarization functions uphold the electroweak signature relationm _w=m _zcosθ_w, and that these contributions are decoupled entirely from oblique radiative corrections. If only the upper member of the doublet forms a fermion-antifermion condensate, the relationm _w=m _zcosθ_w is again upheld in the limit that the mass of the lower member of the doublet is small compared to that of the upper member. For this case, the upper-member's fermion-antifermion condensate is shown to enter oblique radiative corrections. In the absense of an explicit Higgs mechanism, identification of this doublet with (t, b) is shown to be excluded by present empirical bounds onS, T, andU parameters. Further phenomenological consequences of fermion-antifermion condensate contributions to theW-Z mass matrix are discussed, both in the absense and in the presence of an explicit Higgs mechanism.     

On electroweak symmetry breaking in the littlest Higgs model

In SU(5)/SO(5) little Higgs models radiative corrections give rise to SU(2)_L×U(1)_Y symmetry breaking. In this work we start a program for a detailed determination of the relevant terms of the effective Higgs potential by computing the contribution of the t, b and T quarks at the one-loop level, as a starting point for a higher-loop computation. In spite of the fact that some two-loop level contributions are well known to be important, we use our preliminary one-loop result to illustrate that, by demanding the effective potential to reproduce exactly the standard model Higgs potential, and in particular the relation m_H ²=2λv²=2μ², it will be possible to set new constraints on the parameter space of the littlest Higgs model when the computation of all the relevant contributions to the effective Higgs potential is completed.     

The higgs boson mass in standard electroweak theory

The Higgs—boson mass in standardSU(2)×U(1) electroweak theory is obtained by requiring the one-loop effective potential to be an exact solution of the renormalization—group equation. Neglecting fermion couplings one getsm _H =35 GeV.     

Baryon asymmetry from a two stage electroweak phase transition?

We investigate an extension of the Standard Model with a second Higgs doublet, showing a two stage phase transition. Wash-out of a baryon asymmetry after the phase transition can be easily avoided in this class of models.B+L transitions are more strongly suppressed in the intermediate phase than in the high temperature symmetric phase, however. Therefore, it becomes more difficult if not impossible to generate a sufficient baryon asymmetry during the phase transition.supported by Landes Graduierten Förderungs Gesetz