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.     

Revisiting the global electroweak fit of the Standard Model and beyond with Gfitter

The global fit of the Standard Model to electroweak precision data, routinely performed by the LEP electroweak working group and others, demonstrated impressively the predictive power of electroweak unification and quantum loop corrections. We have revisited this fit in view of (i) the development of the new generic fitting package, Gfitter, allowing for flexible and efficient model testing in high-energy physics, (ii) the insertion of constraints from direct Higgs searches at LEP and the Tevatron, and (iii) a more thorough statistical interpretation of the results. Gfitter is a modular fitting toolkit, which features predictive theoretical models as independent plug-ins, and a statistical analysis of the fit results using toy Monte Carlo techniques. The state-of-the-art electroweak Standard Model is fully implemented, as well as generic extensions to it. Theoretical uncertainties are explicitly included in the fit through scale parameters varying within given error ranges. This paper introduces the Gfitter project, and presents state-of-the-art results for the global electroweak fit in the Standard Model (SM), and for a model with an extended Higgs sector (2HDM). Numerical and graphical results for fits with and without including the constraints from the direct Higgs searches at LEP and Tevatron are given. Perspectives for future colliders are analysed and discussed. In the SM fit including the direct Higgs searches, we find M _H =116.4_−1.3^+18.3 GeV, and the 2σ and 3σ allowed regions [114,145] GeV and [[113,168] and [180,225]] GeV, respectively. For the strong coupling strength at fourth perturbative order we obtain α _S (M _Z ²)=0.1193_−0.0027^+0.0028(exp )±0.0001 (theo). Finally, for the mass of the top quark, excluding the direct measurements, we find m _t =178.2_−4.2^+9.8 GeV. In the 2HDM we exclude a charged-Higgs mass below 240 GeV at 95% confidence level. This limit increases towards larger tan β, e.g., is excluded for tan β=70.     

Renormalization of seesaw neutrino masses in the standard model with two-Higgs doublets

Using the theoretical ambiguities inherent in the seesaw mechanism, we derive the new analytic expressions for both quadratic and linear seesaw formulae for neutrino masses at low energies, with either up-type quark masses or charged lepton masses. This is possible through full radiative corrections arising out of the renormalizations of the Yukawa couplings, the coefficients of the neutrino-mass-operator in the standard model with two-Higgs doublets, and also the QCD-QED rescaling factors below the top-quark mass scale, at one-loop level. We also investigate numerically the unification of top-b-τ Yukawa couplings at the scale M ₁=0.59×10⁸ GeV for a fixed value of tan β=58.77, and then evaluate the seesaw neutrino masses which are too large in magnitude to be compatible with the presently available solar and atmospheric neutrino oscillation data. However, if we consider a higher but arbitrary value of M ₁=0.59×10¹¹ GeV, the predictions from linear seesaw formulae with charged lepton masses, can accommodate simultaneousely both solar atmospheric neutrino oscillation data.     

Analysis of various polarization asymmetries in the inclusive b→s?+?? decay in the fourth-generation standard model

In this study a systematical analysis of various polarization asymmetries in inclusive b→s ℓ ⁺ ℓ ⁻ decay in the standard model (SM) with four generation of quarks is carried out. We found that the various asymmetries are sensitive to the new mixing and quark masses for both of the μ and τ channels. Sizable deviations from the SM values are obtained. Hence, b→s ℓ ⁺ ℓ ⁻ decay is a valuable tool for searching physics beyond the SM, especially in the indirect searches for the fourth-generation of quarks (t′,b′).     

About the Stability of the Dodecatoplet

A new investigation is done of the possibility of binding the “dodecatoplet”, a system of six top quarks and six top antiquarks, (t ⁶ t̄ ⁶), using the Yukawa potential mediated by Higgs exchange. A simple variational method gives a upper bound close to that recently estimated in a mean-field calculation. It is supplemented by a lower bound provided by identities among the Hamiltonians describing the system and its subsystems.     

(Non)decoupling of the Higgs triplet effects

We consider the electroweak theory with an additional Higgs triplet at one loop, using the hybrid renormalization scheme based on α_EM, G_F and M_Z as input observables. We show that in this scheme loop corrections can in a natural way be split into a standard model part and corrections due to “new physics”. The latter, however, do not decouple in the limit of an infinite triplet mass parameter, if the triplet trilinear coupling to the SM Higgs doublets grows with the triplet mass. For electroweak observables computed at one loop this effect can be attributed to the radiative generation in this limit of a nonvanishing vacuum expectation value of the triplet. We also point out that whenever tree level expressions for the electroweak observables depend on vacuum expectation values of scalar fields other than the standard model Higgs doublet, a tadpole contribution to the “oblique” parameter T should in principle be included. The origin of nondecoupling is discussed also on the basis of symmetry principles in a simple scalar field theory.     

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.     

Electroweak quantum effects in theM w -M z relation

Quantum effects in theM _w -M _z relation are studied in the framework of the standard SU(2)×U(1) electroweak theory. After reviewing this relation in detail, numerical analysis is carried out by using recent data of ALEPH, DELPHI, L3, OPAL and MARK II collaborations onM _z , and those of CDF and UA2 collaborations onM _w . For the weighted averageM _z ^exp =91.157±0.032 GeV, theW mass is calculated asM _w ⁽⁰⁾ =80.90±0.04 GeV,M _w ^(l.l) =79.75±0.04±0.02 GeV andM _w =80.21±0.04±0.04 GeV at the tree, leading-log and full correction level (form _top=140 GeV andm _Higgs=100 GeV) respectively. Remarkable is that only the fully correctedM _w is consistent withM _w ^exp =80.24±0.37 GeV, which clearly demands the heavy top-quark correction, and therefore gives a strong phenomenological support, independent of the neutral current data, to the electroweak theory as a renormalizable quantum field theory with the spontaneous symmetry breakdown.     

Two-loop effect on the heavy quark mass near the fixed point

We have studied the two-loop effect on the infrared fixed point of the Yukawa couplings. The two-loop contribution to the large Yukawa coupling for the quark is found to be within 4.5% at the electroweak scale, but that for the lepton is up to 8%. It is noticed that the fixed point structure obtained by the one-loop renormalization group equations is credible enough, at least to the two-loop approximation.     

Non-linear scission/recombination kinetics of living polymerization

Living polymers are formed by reversible association of primary units (unimers). Generally the chain statistical weight involves a factor σ < 1 suppressing short chains in comparison with free unimers. Living polymerization is a sharp thermodynamic transition for σ ≪ 1 which is typically the case. We show that this sharpness has an important effect on the kinetics of living polymerization (one-dimensional association). The kinetic model involves i) the unimer activation step (a transition to an assembly-competent state); ii) the scission/recombination processes providing growth of polymer chains and relaxation of their length distribution. Analyzing the polymerization with no chains but unimers at t = 0 , with initial concentration of unimers M ≳ M ^* (M^* is the critical polymerization concentration), we determine the time evolution of the chain length distribution and find that: 1) for M ^* ≪ M ≪ M ^*/σ the kinetics is characterized by 5 distinct time stages demarcated by 4 characteristic times t₁, t₂, t₃ and t^*; 2) there are transient regimes (t ₁ ≲ t ≲ t ₃) when the molecular-weight distribution is strongly non-exponential; 3) the chain scissions are negligible at times shorter than t₂. The chain growth is auto-accelerated for t ₁ ≲ t ≲ t ₂ : the cut-off chain length (= polymerization degree 〈n〉_w N ₁ ∝ t ² in this regime. 4) For t ₂ < t < t ₃ the length distribution is characterized by essentially 2 non-linear modes; the shorter cut-off length N₁ is decreasing with time in this regime, while the length scale N₂ of the second mode is increasing. (5) The terminal relaxation time of the polymer length distribution, t^*, shows a sharp maximum in the vicinity of M^*; the effective exponent is as high as ∼ σ^-1/3 just above M^*.     

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.     

Probing top-quark couplings indirectly at Higgs factories

We perform a global effective-field-theory analysis to assess the combined precision of Higgs couplings,triple gauge-boson couplings, and top-quark couplings, at future circular e~+e~- colliders, with a focus on runs below the tt production threshold. Deviations in the top-quark sector entering as one-loop corrections are consistently taken into account in the Higgs and diboson processes. We find that future lepton colliders running at center-of-mass energies below the tt production threshold can still provide useful information on top-quark couplings, by measuring virtual top-quark effects. With rate and differential measurements, the indirect individual sensitivity achievable is better than at the high-luminosity LHC. However, strong correlations between the extracted top-quark and Higgs couplings are also present and lead to much weaker global constraints on top-quark couplings. This implies that a direct probe of top-quark couplings above the tt production threshold is also helpful for the determination of Higgs and triple-gauge-boson couplings. In addition, we find that below the e~+e~-→tth production threshold, the top-quark Yukawa coupling can be determined by its loop corrections to all Higgs production and decay channels. Degeneracy with the ggh coupling can be resolved, and even a global limit is competitive with the prospects of a linear collider above the threshold. This provides an additional means of determining the top-quark Yukawa coupling indirectly at lepton colliders.     

Gauge coupling and fermion mass relations in low string scale brane models

We analyze the gauge coupling evolution in brane inspired models with U(3) x U(2) x U(1)^N symmetry at the string scale. We restrict our work to the case of brane configurations with two and three abelian factors (N = 2,3) and where only one Higgs doublet is coupled to down quarks and leptons and only one to the up quarks. We find that the correct hypercharge assignment of the standard model particles is reproduced for six viable models distinguished by different brane configurations. We investigate the third generation fermion mass relations and find that the correct low energy m_b/m_τ ratio can be obtained for b-τ Yukawa coupling equality at a string scale as low as M_S~10³ TeV. Received: 30 August 2005, Published online: 16 November 2005 PACS: 11.25.Wx, 11.25.Uv, 12.10.Kt     

On the two-loop $$ \ma thcal{O} $$( αs2) correc tions to the pole mass of the t quark in the MSSM

The paper is devoted to the calculation of two-loop (α _s ²) MSSM corrections to the relation between the pole mass of the t quark and its running mass in the scheme. Firstly, the value of the second-order contribution from large-mass expansion in mt/M _SUSY is studied. Contrary to our expectations, this contribution turned out to be negligible. As a by-product of this calculation, the two-loop anomalous dimension of the running quark mass is obtained in the supersymmetric QCD. Secondly, the influence of the two-loop corrections to the t-quark mass on the predicted superpartner masses is investigated. The text was submitted by the authors in English.     

Production of slow muonic hydrogen isotopes in vacuum

Muonic hydrogen isotopes (μ⁻ p, μ⁻ d, and μ⁻t) are simple quantum mechanical systems ideally suited for studies of numerous fundamental phenomena in electroweak and strong interactions as well as in applied areas such as muon chemistry or muon catalyzed fusion. Emission of muonic hydrogen isotopes into vacuum helps to overcome the limitations which are normally imposed on conventional investigations with gaseous and liquid targets. A proof of principle experiment for this new technique was performed at TRIUMF last year. Negative muons with 30 MeV/c momentum were stopped in a thin film of solid hydrogen and produced very low energy μ⁻d in vacuum. The distribution center of the normal velocity components of emitted μ⁻d atoms was measured to be ∼1 cm/μs. The yield of μ⁻d in vacuum is an increasing function of H₂ film thickness δ up to a value of δ≥1 mm.     

A Condensed Matter Interpretation of SM Fermions and Gauge Fields

We present the bundle (Aff(3)⊗ℂ⊗Λ)(ℝ³), with a geometric Dirac equation on it, as a three-dimensional geometric interpretation of the SM fermions. Each (ℂ⊗Λ)(ℝ³) describes an electroweak doublet. The Dirac equation has a doubler-free staggered spatial discretization on the lattice space (Aff(3)⊗ℂ)(ℤ³). This space allows a simple physical interpretation as a phase space of a lattice of cells. We find the SM SU(3) _c ×SU(2) _L ×U(1) _Y action on (Aff(3)⊗ℂ⊗Λ)(ℝ³) to be a maximal anomaly-free gauge action preserving E(3) symmetry and symplectic structure, which can be constructed using two simple types of gauge-like lattice fields: Wilson gauge fields and correction terms for lattice deformations. The lattice fermion fields we propose to quantize as low energy states of a canonical quantum theory with ℤ₂-degenerated vacuum state. We construct anticommuting fermion operators for the resulting ℤ₂-valued (spin) field theory. A metric theory of gravity compatible with this model is presented too.     

Some top-quark propertie s mea sured in $$p\bar p$$ colli sion s u sing CDF detector at √ s = 1.96 TeV (Review)

This review considers important properties of the top-quark. The top-quark decays before hadronization, and the spin information is directly transferred to the decay products. Therefore the structure of the weak interaction is investigated by measuring the helicity fractions, f, of the W boson—the top-quark decay product. Other investigations: search for the presence of V+A interaction, search for exotic top-quark charge — 4/3 and for t[`(t)]t\bar t — resonances—all of them, so far, were not found in the experiments — testifies against of going out of the Standard Model.     

Single production of fourth-family quarks at the LHC

We study the single production of fourth-family quarks through the process pp→Q′jX at the Large Hadron Collider (LHC). We have calculated the decay widths and branching ratios of the fourth-family quarks (b′ and t′) in the mass range 300–800 GeV. The cross sections for the signal and background processes have been calculated in a Monte Carlo framework. It is shown that the LHC can discover single t′ and b′ quarks if the CKM matrix elements |V _t′q |,|V _qb′|≳0.01.     

Determination of the probability of existence of pair interactions in the formation of M2tX2t?1Superstructures in MXy nonstoichiometric compounds

An analytical method has been proposed for calculating the probabilities P _i ^(2)(s) of existence of X-X, X−□, and □−□ pair interactions in the nonmetal sublattice of M _2tX_2t−1 superstructures formed in strongly nonstoichiometric compounds MX _y (MX _y □_1−y) and M ₂X _y (MX_y/2□_1−y/2) with a high content of structural vacancies □. The main characteristics necessary for the quantitative determination of the probabilities P_i(2)(s) as functions of the composition, degree of long-range order, symmetry, and structure type have been determined for all the known superstructures M _2tX_2t−1.