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.     

Renormalization scheme dependence of electroweak radiative corrections

We compare two renormalization schemes of the electroweak standard model: the on-shell scheme withe, M _W ,M _Z ,M _H , and the fermion masses {m _f } as free parameters, and an intermediate scheme where theW boson self energy is renormalized atq ²=0 instead ofq ²=M _W ². TheM _W ?M _Z interdependence, and the differentiale ⁺ e ^?→μ ⁺ μ ^? cross section including polarized beams are calculated in both schemes to one-loop order. We find striking differences between the forward-backward asymmetries and the polarization asymmetries near theZ resonance after inclusion of weak and QED corrections.     

The fundamental-electroweak scale hierarchy in the standard model

The multiple-point principle, according to which several vacuum states with the same energy density exist, is put forward as a fine-tuning mechanism predicting the ratio between the fundamental and electroweak scales in the Standard Model (SM). It is shown that this ratio is exponentially huge: ∼e ⁴⁰. Using renormalization group equations for the SM, we obtain the effective potential in the two-loop approximation and investigate the existence of its postulated second minimum at the fundamental scale. The investigation of the evolution of the top-quark Yukawa coupling constant in the two-loop approximation shows that, with initial values of the top-quark Yukawa coupling in the interval h(M _t )=0.95±0.03 (here, M _t is the top-quark pole mass), a second minimum of the SM effective potential can exist in the region ϕ_min2≈10¹⁶−10²² GeV. A prediction is made of the existence of a new bound state of six top quarks and six antitop quarks, formed owing to Higgs boson exchanges between pairs of quarks-antiquarks. This bound state is supposed to condense in a new phase of the SM vacuum. This gives rise to the possibility of having a phase transition between vacua with and without such a condensate. The existence of three vacuum states (new, electroweak, and fundamental) solves the hierarchy problem in the SM. The text was submitted by the authors in English.     

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.     

Polarized bhabha scattering in multiboson electroweak gauge models

The general expression for the differential cross section of the reactione ⁺ e ^?→γ,Z ₁ ⁰ ,Z ₂ ⁰ , ..., →e ⁺ e ^? with an arbitrary initial polarization state is derived in the context of electroweak gauge models with more than one neutral boson. Angular distributions, azimuthal asymmetries in the case of natural polarization, and longitudinal polarization asymmetries for models of the typeSU(2)×U(1)×G (G=?(1),S?(2)) and left-right symmetric models are compared with the standard model results. For the angular distributions withe ^± having equal helicities a～10% deviation from the standard model is predicted already below 50 GeV for models of the first type withZ ₁ ⁰ masses up to 80 GeV. At energies around the firstZ ₁ ⁰ a study of azimuthal and polarization asymmetries yields the possibility of distinguishing between different models.     

Two-loop corrections to the potential of a pointlike charge in a superstrong magnetic field

The potential of the pointlike charge in a superstrong homogeneous magnetic field B ? m _e ² /e ³ ≈ 6 × 10¹⁵ G is considered. It is well known that Coulomb potential is significantly modified by taking into account vacuum polarization (calculated in one loop approximation). We consider electron selfenergy and correction to the vertex function at one loop, and show that these diagrams are not enhanced by magnetic field like eB.We calculate two-loop corrections to the vacuum polarization and find that these contributions are small.     

On the connection between the vacuum polarization potential in muonic atoms andg-2 of the muon

A simple connection, between the vacuum polarization potential used in muonic atoms and the muon anomaly arising from the second-order vertex graph with electron vacuum polarization insertions, is established. In particular, the leading log-term and the orderm _e/m _μ term are essentially the same in the two cases. We make use of this connection to determine the vacuum polarization potential in order α³(Zα).     

On the metastability of the Standard Model vacuum

If the Higgs mass m_H is as low as suggested by present experimental information, the Standard Model ground state might not be absolutely stable. We present a detailed analysis of the lower bounds on m_H imposed by the requirement that the electroweak vacuum be sufficiently long-lived. We perform a complete one-loop calculation of the tunnelling probability at zero temperature, and we improve it by means of two-loop renormalization-group equations. We find that, for m_H=115 GeV, the Higgs potential develops an instability below the Planck scale for m_t>(166±2) GeV, but the electroweak vacuum is sufficiently long-lived for m_t<(175±2) GeV.     

Hadronic contributions to electroweak parameter shifts

Usinge ⁺ e ^?-data, an updated analysis of hadronic contributions to electroweak parameter renormalizations is presented. We emphasize the estimate of uncertainties which is important for precision tests at LEP and SLC. ForM _z =93 GeV and sin² Θ ₀=0.22 hadronic contributions from 5 flavors are found to be $$\Delta r_{had}^{(5)} = 0.0326 \pm 0.0007(\Delta r_{QED,had}^{(5)} = 0.0286 \pm 0.0007)$$ and $$\Delta g_{had}^{(5)} = 0.0602 \pm 0.0016(\Delta g_{3\gamma ,had}^{(5)} = 0.0619 \pm 0.0016)$$ for the renormalization of α and α _g =α/sin² Θ ₀, respectively. Parameter shifts are calculated and uncertainties due to higher order effects are estimated.     

A comparison of direct and indirect determinations of the masses of the Higgs Boson and the top quark

The indirect estimation of the Higgs Boson mass from electroweak radiative corrections within the Standard Model is compared with the directly measured value obtained by the ATLAS and CMS Collaborations at the CERN LHC collider. Treating the direct measurement of m_H as input, the Standard Model indirect estimation of the top-quark mass is also obtained and compared with its directly measured value. A model-independent analysis finds an indirect value of m_H of ■70 GeV, below the directly measured value of 125.7±0.4 GeV and an indirect value:m_t = 177.3±1.0 GeV, above the directly measured value: 173.21±0.87 GeV. A goodness-of-fit test to the Standard Model using all Z-pole observables and mW has a χ~2 probability of ■2%. The reason why probability values about a factor of ten larger than this, and indirect estimates of m H about 30 GeV higher, have been obtained in recent global fits to the same data is recalled.     

Bound on the Higgs boson mass with no zero-charge behaviour in a magnetic field

The upper boundm<280 GeV/c² on the Higgs boson mass is obtained by considering the requirement that the electroweak theory must be consistent in a magnetic fieldH. The restriction emerges naturally by studying the effective potential in a magnetic field as a function of mass, and the values ofm when there is no zero-charge, in the fieldsH～H ₀=M _w ² /e are obtained.     

A precise determination of the electroweak mixing angle from semileptonic neutrino scattering

The cross-section ratio of neutral-current and charged-current semileptonic interactions of muon-neutrinos on isoscalar nuclei has been measured with the result:R ^v =0.3093±0.0031 for hadronic energy larger than 4 GeV. From this ratio we determined the electroweak mixing angle sin² θ _W , wherem _c is the charm-quark mass in GeV/c². Comparison with direct measurements ofm _w andm _z determines the radiative shift of the intermediate boson mass Δr=0.077±0.025(exp.)±0.038(syst.), in agreement with the prediction. Assuming the validity of the electroweak standard theory we determined ?=0.990?0.013(m _c ?1.5)±0.009(exp.)±0.003(theor.).     

Vector resonances from a strong electroweak sector at linear colliders

We explore the usefulness of very energetic lineare ⁺ e ^? colliders in the TeV range in studying an alternative scheme of electroweak symmetry breaking based on a strong interacting sector. The calculations are performed within the BESS model which contains new vector resonances. If the massM _V of the new boson multiplet lies not far from the maximum machine energy, or if it is lower, such a resonant contribution would be quite manifest. A result of our analysis is that also virtual effects are important. It appears that annihilation into a fermion pair in such machines, at the considered luminosities, would improve only marginally on existing limits if polarized beams are available and left-right asymmetries are measured. On the other hand, the process ofW-pair production bye ⁺ e ^? annihilation would allow for sensitive tests of the hypothesized strong sector, especially if theW polarizations are reconstructed from their decay distributions, and the more so the higher the energy of the machine. Ane ⁺ e ^? collider with c.m. energy \(\sqrt s = 500\) GeV could improve the limits on the model for the range 500<M _V (GeV)<1000 whenW polarization is not reconstructed. IfW polarizations are reconstructed, then the bounds improve for the entire expected range ofM _V . These bounds become more stringent for larger energy of the collider. We have also studied the detectability of the new resonances through the fusion subprocesses, but this channel does not seem to be interesting even for a collider with a c.m. energy \(\sqrt s = 2\) TeV.     

Role of heavy fermions and heavy Higgs scalars in the electroweak correction to the MW − MZ relation

The role of heavy fermions and heavy Higgs-scalars in the M_W ? M_Z relation resulting from the one-loop-corrected μ decay width Γ⁽¹⁾ and its experimental data Γ^exp is studied in the framework of the standard electroweak theory. Exact and approximate formulae are both given for these heavy particle effects. The quadratic dependence of Γ⁽¹⁾ on large fermion mass m_heavy gives a positive contribution to the calculation of M_W from Γ⁽¹⁾ = Γ^exp for a given M_Z, and cancels the light fermion contributions of the form ～ αln(m_light/M_W) at the value of m_heavy ～ 200 GeV. On the other hand, the Higgs mass dependence of the calculation is, at best, logarithmic, and does not produce visible effects. Applications for deriving constraints for the top-quark mass (or heavier fermion mass) are discussed, and a concrete example is given of the relation between experimental uncertainties in measurements of M_W,Z and the corresponding allowed region for m_t.     

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.     

New physics sum rules from polarized electron-positron asymmetries on the Z resonance

We propose a strategy to express some of the electroweak parameters characterizing a certain type of new physics beyond the standard model through “new physics sum rules” involving experimentally measureable e⁺e⁻ polarization asymmetries on (near) the Z resonance. In the case of a single E₆-generated new Z′, our sum rules would provide an unambiguous measurement of the mixing angle for |θ_M|⩾0.04.     

Standard model Higgs field and energy scale of gravity

The effective potential of the Higgs scalar field in the Standard Model may have a second degenerate minimum at an ultrahigh vacuum expectation value. This second minimum then determines, by radiative corrections, the values of the top-quark and Higgs-boson masses at the standard minimum corresponding to the electroweak energy scale. An argument is presented that this ultrahigh vacuum expectation value is proportional to the energy scale of gravity, E _Planck ≡ √?c ⁵/G _N, considered to be characteristic of a spacetime foam. In the context of a simple model, the existence of kink-type wormhole solutions places a lower bound on the ultrahigh vacuum expectation value and this lower bound is of the order of E _Planck.     

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.     

The quasi-fixed Minimal Supersymmetric Standard Model

The infra-red fixed points are determined for all the parameters of the MSSM. They dominate the renormalisation group running when the top-Yukawa is in the quasi-fixed point regime (i.e. large at the GUT scale). We examine this behaviour analytically, by solving the full set of one-loop renormalisation group equations in the approximation that the electroweak contributions are negligible, and also numerically. We find the quasi-fixed points for the top-quark trilinear couplings; A_Uα3=A_U3α=−0.59m_g independently of the input parameters at the unification scale. All the remaining parameters are significantly focused towards their true fixed points at the weak scale. We examine how this increases the predictivity of the MSSM in this regime.     

Updated status of the global electroweak fit and constraints on new physics

We present an update of the Standard Model fit to electroweak precision data. We include newest experimental results on the top-quark mass, the W mass and width, and the Higgs-boson mass bounds from LEP, Tevatron and the LHC. We also include a new determination of the electromagnetic coupling strength at the Z pole. We find for the Higgs-boson mass $91^{+30}_{-23}~\mbox{GeV}$ and $120^{+12}_{-5}~\mbox{GeV}$ when not including and including the direct Higgs searches, respectively. From the latter fit we indirectly determine the W mass to be $(80.360^{+0.014}_{-0.013})~\mbox{GeV}$ . We exploit the data to determine experimental constraints on the oblique vacuum polarisation parameters, and confront these with predictions from the Standard Model (SM) and selected SM extensions. By fitting the oblique parameters to the electroweak data we derive allowed regions in the BSM parameter spaces. We revisit and consistently update these constraints for a fourth fermion generation, two Higgs doublet, inert Higgs and littlest Higgs models, models with large, universal or warped extra dimensions and technicolour. In most of the models studied a heavy Higgs boson can be made compatible with the electroweak precision data.