Probing top-quark operators with precision electroweak measurements

In the standard model effective field theory, operators involving the top quark are generally difficult to probe and can generate sizable loop contributions to electroweak precision observables measured by past and future lepton colliders. Could the high precision of electroweak measurements compensate for loop suppression and provide competitive reaches on these operators? Would the inclusion of these contributions introduce too many additional parameters for a meaningful global electroweak analysis to be performed? In this paper, we perform a detailed phenomenological study to address these two important questions. Focusing on eight dimension-6 operators that generate anomalous couplings between electroweak gauge bosons and third-generation quarks, we calculate their one loop contributions to \begin{document}$ e^+e^- \to f\bar{f} $\end{document} processes, both on and off the Z-pole, and the \begin{document}$ e^-e^+ \to WW $\end{document} process. A global analysis is performed with these eight operators and those that contribute to the above processes at tree level using measurements at the LEP, SLC, and several low energy experiments. We find that although current electroweak precision measurements are sensitive to the one-loop effects of top-quark operators, it is difficult to separate them from the operators that contribute at tree level, making a global analysis rather challenging. Under further assumptions (for instance, new physics contributes to only third generation quark operators and the S and T parameters), competitive reaches may be obtained in a global fit. Another important finding of our study is that the two operators that generate the dipole interactions of the bottom quark have a significant impact on the Z-pole measurements and should not be omitted. We also discuss the implications of the recently reported W-boson mass measurement at the CDF for our results. Finally, we estimate the reaches of future lepton colliders in probing top-quark operators with precision electroweak measurements.     

Confronting electroweak precision measurements with New Physics models

Precision experiments, such as those performed at LEP and SLC, offer us an excellent opportunity to constrain extended gauge model parameters. To this end, it is often assumed that in order to obtain more reliable estimates, one should include the sizable one-loop standard model (SM) corrections, which modify the couplings as well as other observables. This conviction is based on the belief that the higher order contributions from the “extension sector” will be numerically small. However, the structure of higher order corrections can be quite different when comparing the SM with its extension; thus one should avoid assumptions which do not take account of such facts. This is the case for all models with . As an example, both the manifest left–right symmetric model and the model, with an additional boson, are discussed, and special attention to the top contribution to is given. We conclude that the only sensible way to confront a model with the experimental data is to renormalize it self-consistently. If this is not done, parameters which depend strongly on quantum effects should be left free in fits, though essential physics is lost in this way. We should note that the arguments given here allow us to state that at the level of loop corrections (indirect effects) there is nothing like a “model-independent global analysis” of the data. Received: 9 September 1999 / Published online: 25 February 2000     

Light bottom squark and gluino confront electroweak precision measurements

We address the compatibility of a light sbottom (mass approximately 2-5.5 GeV) and a light gluino (mass approximately 12-16 GeV) with electroweak precision measurements. Such light particles have been suggested to explain the observed excess in the b quark production cross section at the Tevatron. The electroweak observables may be affected by the sbottom and gluino through the supersymmetric-QCD (SUSY-QCD) corrections to the Zbb vertex. We examine, in addition to the SUSY-QCD corrections, the gauge boson propagator corrections from the stop which are allowed to be light from the SU(2)(L) symmetry. We find that this scenario is strongly disfavored from electroweak precision measurements.     

The effective electroweak theory

The effective electroweak Lagrange function appropriate to dynamic mass generation is obtained on the basis of the variational approach to the (super-)string inspiredSU(2)_L ×U(1)_y × XU(1)_E gauge field theory.This work was supported in part by the Ministry of Science and Higher Education under the contract CPBP 01.03.The authors would like to thank the Referee for a fruitful discussion.     

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 of ${cal O}(M_Z)$: $$M_{H}=76 {+ 152 ?op -50}{? GeV}.$$ 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 of $←pha (M_Z)$ and ${←pha_s} (M_Z)$.     

Reconsidering harmonic and anharmonic coherent states: Partial differential equations approach

This article presents a new approach to dealing with time dependent quantities such as autocorrelation function of harmonic and anharmonic systems using coherent states and partial differential equations. The approach that is normally used to evaluate dynamical quantities involves formidable operator algebra. That operator algebra becomes insurmountable when employing Morse oscillator coherent states. This problem becomes even more complicated in case of Morse oscillator as it tends to exhibit divergent dynamics. This approach employs linear partial differential equations, some of which may be solved exactly and analytically, thereby avoiding the cumbersome noncommutative algebra required to manipulate coherent states of Morse oscillator. Additionally, the arising integrals while using the herein presented method feature stability and high numerical efficiency. The correctness, applicability, and utility of the above approach are tested by reproducing the partition and optical autocorrelation function of the harmonic oscillator. A closed-form expression for the equilibrium canonical partition function of the Morse oscillator is derived using its coherent states and partial differential equations. Also, a nonequilibrium autocorrelation function expression for weak electron–phonon coupling in condensed systems is derived for displaced Morse oscillator in electronic state. Finally, the utility of the method is demonstrated through further simplifying the Morse oscillator partition function or autocorrelation function expressions reported by other researchers in unevaluated form of second-order derivative exponential. Comparison with exact dynamics shows identical results.     

Quantum–classical correspondence and the role of the dipole function in molecular dissociation

We consider the quantum and classical dissociation dynamics of heteronuclear diatomic molecules induced by infrared laser pulses. The field–molecule interaction is given by the product of the time-dependent electric field and the molecule permanent dipole. We investigate the influence of the dipole function in molecular dissociation. We show that the dissociation can be suppressed at certain external field frequencies for a nonlinear and finite-range dipole function. The correspondence between quantum and classical results is established by relating classical Fourier amplitudes to discrete–continuum quantum matrix elements.     

The role of spurions in Higgs-less electroweak effective theories

Inspired by recent developments of moose models, we reconsider low-energy effective theories of Goldstone bosons, gauge fields and chiral fermions applied to low-energy QCD and to Higgs-less electroweak symmetry breaking. Couplings and the corresponding reduction of symmetry are introduced via constraints enforced by a set of non-propagating covariantly constant spurion fields. Relics of the latter are used as small expansion parameters conjointly with the usual low-energy expansion. Certain couplings can only appear at higher orders of the spurion expansion and, consequently, they become naturally suppressed independently of the idea of dimensional deconstruction. At leading order this leads to a set of generalized Weinberg sum rules and to the suppression of non-standard couplings to fermions in Higgs-less EWSB models with the minimal particle content. Within the latter, higher spurion terms allow for a fermion mass matrix with the standard CKM structure and C P violation. In addition, Majorana masses for neutrinos are possible. Examples of non-minimal models are briefly mentioned.Received: 8 January 2004, Revised: 7 February 2004, Published online: 2 April 2004     

受迫振子的对称性与守恒量

讨论受迫振子体系的对称性和守恒量,导出了其含时位势的具体形式,给出了相应的对称变换算符,并讨论了线谐振子体系的含时守恒量.     

Analytical Solution for Single—Mode Time—Dependent Oscillator

Based on the general theory of time-dependent quantum transformation,we use the “time evolution operator” method to solve the single-mode time-dependent oscillator.     

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.     

Conditional stability of diatomic molecule driven by a weak laser field

Using a direct perturbation method, we investigate the stability of a diatomic molecule modelled by a weakly laser-driven Morse oscillator. It is shown that stationary state solution of the system is stable in the sense of Lyapunov and the periodical one possesses conditional stability, namely its stability depends on the initial conditions and system parameters. The corresponding sufficient and necessary conditions are established that indicate the stable states associated with some discrete energies. The results reveal how a diatomic molecule can be stabilized or dissociated with a weak laser, and demonstrate that the mathematical conditional stability works in the considered physical system.     

Algebraic methods applied to the study of energy transfer in anharmonic systems

We make use of two different methodologies to study the transition probabilities in a molecular anharmonic system in the presence of an external perturbation. For the first method, we use a series expansion of the displacement coordinate keeping up to fourth order terms; for the second method we use a deformed algebra to approximate the anharmonic Hamiltonian via a harmonic oscillator's Hamiltonian written in terms of deformed operators. We evaluate vibrational transition probabilities as a function of the collision energy and compare the results obtained with the two approaches.     

Analysis of electroweak precision data and prospects for future improvements

We update our previous work on an analysis of the electroweak data by including new and partly preliminary data available up to the 1996 summer conferences. The new results on the partial decay widths into and hadrons now offer a consistent interpretation of all data in the minimal standard model. The value extracted for the strong interaction coupling constant agrees well with determinations in other areas. New constraints on the universal parameters , and are obtained from the updated measurements. No signal of new physics is found in the , , analysis once the SM contributions with GeV and those of not a too heavy Higgs boson are accounted for. The naive QCD-like technicolor model is now ruled out at the 99% CL even for the minimal model with . In the absence of a significant new physics effect in the electroweak observables, constraints on masses of the top quark, , and Higgs boson, , are derived as a function of and the QED effective coupling . The preferred range of depends rather strongly on the actual value of : for , while for at 95% CL. Prospects due to forthcoming improved measurements of asymmetries, the mass of the weak boson , and are discussed. Anticipating uncertainties of 0.00020 for , 20 MeV for , and 2 GeV for , the new physics contributions to the , , parameters will be constrained more severely, and, within the SM, the logarithm of the Higgs mass can be constrained to about . The better constraints on , , and on within the minimal SM should be accompanied with matching precision in . Received: 18 June 1997     

Enhanced electroweak radiative corrections in SUSY and precision data

Enhanced radiative corrections generated in SUSY extensions of the Standard Model spoil the fit of the precision data (Z-boson decay parameters and W-boson mass). This negative effect is washed out for heavy enough squarks, because of the decoupling property of SUSY models. We find that even for light squarks the enhanced radiative corrections can be small. In this case substantial mixing is necessary.