arXiv subjects

G. Weiglein

Publications and source records attributed to G. Weiglein.

196 records · Page 11Linked to original sources

arXiv1997

Higgs-mass dependence of two-loop corrections to Delta r

The Higgs-mass dependence of the Standard Model contributions to the correlation between the gauge-boson masses is studied at the two-loop level. Exact results are given for the Higgs-dependent two-loop corrections associated with the fermions, i.e. no expansion in the top-quark and the Higgs-boson mass is made. The results for the top quark are compared with results of an expansion up to next-to-leading order in the top-quark mass. Agreement is found within 30% of the two-loop result. The remaining theoretical uncertainties in the Higgs-mass dependence of Delta r are discussed.

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arXiv1997

Higher-order corrections to precision observables in the Standard Model and the MSSM

A summary of recent results obtained for higher-order corrections to precision observables in the Standard Model and the Minimal Supersymmetric Standard Model is given. In the Standard Model electroweak two-loop results valid for arbitrary values of the masses of the top quark, the Higgs boson and the gauge bosons are discussed. For the example of two specific diagrams the exact two-loop result is compared with the result of an expansion in the top-quark mass up to next-to-leading order. Furthermore the Higgs-mass dependence of the two-loop corrections to the relation between the gauge-boson masses is analyzed. In the MSSM the exact gluonic corrections to $Δr$ are derived. They are compared with the leading contribution entering via the $ρ$ parameter.

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arXiv1997

Leading QCD Corrections to Scalar Quark Contributions to Electroweak Precision Observables

In the supersymmetric extension of the Standard Model we derive the two-loop QCD corrections to the scalar quark contributions to the electroweak precision observables entering via the rho parameter. A very compact expression is derived for the gluon-exchange contribution. The complete analytic result for the gluino-exchange contribution is very lengthy; we give expressions for several limiting cases that were derived from the general result. The two-loop corrections, generally of the order of 10 to 30% of the one-loop contributions, canbe very significant. Contrary to the Standard Model case, where the QCD corrections are negative and screen the one-loop value, the corresponding corrections in the supersymmetric case are in general positive, therefore increasing the sensitivity in the search for scalar quarks through their virtual effects in high-precision electroweak observables.

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arXiv1997

Precise Predictions for the W-Boson Mass

Recent results for higher-order corrections to the relation between the vector-boson masses in the Standard Model and Supersymmetry are summarized. In the Standard Model, the Higgs-mass dependence of the two-loop contributions to Delta r is studied. Exact results are given for the Higgs-dependent two-loop corrections associated with the fermions, i.e. no expansion in the top-quark and the Higgs-boson mass is made. The results for the top quark are compared with results of an expansion up to next-to-leading order in the top-quark mass. Agreement is found within 30 % of the two-loop result. In Supersymmetry, the two-loop QCD corrections to the stop- and sbottom-loop contributions to the rho parameter are presented. The two-loop corrections modify the one-loop contribution by up to 30 %; the gluino decouples for large masses. Contrary to the SM case where the QCD corrections are negative and screen the one-loop value, the corresponding corrections in the supersymmetric case are in general positive, increasing the sensitivity in the search for scalar quarks through their virtual effects in high-precision electroweak observables.

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arXiv1996

Supersymmetric contributions to electroweak precision observables: QCD corrections

We calculate the two-loop QCD correction to the scalar quark contributions to the electroweak gauge-boson self-energies at zero momentum-transfer in the supersymmetric extension of the Standard Model. We then derive the $O(α_s)$ correction to the contribution of the scalar top and bottom quark loops to the rho parameter, which is the most sizable supersymmetric contribution to the electroweak mixing angle and the W-boson mass. The two-loop corrections modify the one-loop contribution by up to 30%; the gluino decouples for large masses. Contrary to the SM case where the QCD corrections are negative and screen the one-loop value, the corresponding corrections in the supersymmetric case are in general positive, increasing the sensitivity in the search for scalar quarks through their virtual effects in high-precision electroweak observables.

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arXiv1996

Calculation of two-loop top-quark and Higgs-boson corrections in the electroweak Standard Model

A combination of algebraical and numerical techniques for calculating two-loop top-quark and Higgs-boson corrections to electroweak precision observables like $Δr$ or the $ρ$-parameter is presented. The renormalization is performed within the on-shell scheme. The results of the calculations are valid for arbitrary values of $m_t$, $M_H$ and of the gauge-boson masses. An example is treated where the full result is compared to the result obtained via an expansion up to next-to-leading order in $m_t$. As an application, results for the Higgs-mass dependent top-contributions to $Δr$ are given.

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arXiv1996

The background-field formulation of the electroweak Standard Model

The application of the background-field method to the electroweak Standard Model and its virtues are reviewed. Special emphasis is directed to the Ward identities that follow from the gauge invariance of the background-field effective action. They are compatible with on-shell renormalization and imply a decent behavior of the background-field vertex functions. Via the usual construction of connected Green functions they transfer to Ward identities for connected Green functions which, in distinction to the conventional formalism, remain exactly valid in finite orders of perturbation theory even if a Dyson summation of self-energies (within a systematic use of one-particle irreducible building blocks) is performed. Finally, we comment on the interplay between gauge invariance and gauge-parameter (in-)dependence of vertex and Green functions and the uniqueness of resummation procedures.

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arXiv1996

How reliably can the Higgs-Boson Mass be predicted from Electroweak Precision Data?

From the LEP precision data and the measurement of the W-boson mass, upon excluding the observables Rb, Rc in a combined fit of the top-quark mass, Mt, and the Higgs-boson mass, MH, within the Standard Model, we find the weak 1sigma bound of MH<900GeV. Stronger upper bounds on MH, sometimes presented in the literature, rely heavily on the inclusion of Rb in the data sample. Upon including Rb, the quality of the fit drastically decreases, and by carefully analyzing the dependence of the fit results on the set of experimental input data we conclude that these stronger bounds are not reliable. Moreover, the stronger bounds on MH are lost if the deviation between theory and experiment in Rb is ascribed to contributions of new physics. Replacing swbar^2(LEP) by the combined value swbar^2(LEP+SLD) in the data sample leads to a bound of MH<430GeV at the 1sigma level. The value of swbar^2(SLD) taken alone, however, gives rise to fit results for MH which are in conflict with MH<65.2GeV from direct searches.

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arXiv1996

Implications of Electroweak Precision Data on Bounds on the Higgs-Boson Mass

Carefully analyzing the dependence of the bounds on the Higgs-boson mass $\MH$ derived from the observables $\swbar^2(\LEP)$, $\swbar^2(\SLD)$, $\Gl$, $\MW$, $\GT$, $\Gh$, as well as $\Rb$ and $\Rc$, and considering the uncertainties in $α(\MZ^2)$ and $α_s(\MZ^2)$, we find that a stronger bound than $40\GeV\lsim\MH\lsim 1\TeV$ at the $1σ$ level can hardly be deduced at present, even if the experimental information on the top-quark mass $\Mt$ from direct production is taken into account.

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arXiv1996

On the Observation of Bosonic Loop Corrections in Electroweak Precision Experiments

We investigate the structure of the experimentally significant electroweak bosonic loop corrections to the leptonic weak mixing angle, the leptonic Z-boson decay width, and the W-boson mass. It is shown that the bosonic corrections that have a sizable effect at the present level of experimental accuracy are directly related to the use of the Fermi constant G_F as input parameter for analyzing the LEP observables. Indeed, if the (theoretical value of the) leptonic width of the W boson is used as input parameter instead of the low-energy parameter G_F determined from muon decay, fermion-loop corrections are sufficient for compatibility between theory and experiment.

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arXiv1995

Which Bosonic Loop Corrections are Tested in Electroweak Precision Measurements?

The nature of the electroweak bosonic loop corrections to which current precision experiments are sensitive is explored. The set of effective parameters $\De x$, $\De y$, and $\eps$, which quantify SU(2) violation in an effective Lagrangian, is shown to be particularly useful for this purpose. The standard bosonic corrections are sizable only in the parameter $\De y$, while $\De x$ and $\eps$ are sufficiently well approximated by the pure fermion-loop prediction. By analyzing the contributions to $\De y$ it is shown that the bosonic loop corrections resolved by the present precision data are induced by the change in energy scale between the low-energy process muon decay and the energy scale of the LEP1 observables. If the (theoretical value of the) leptonic width of the W boson is used as input parameter instead of the Fermi constant $\GF$, no further bosonic loop corrections are necessary for compatibility between theory and experiment.

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arXiv1994

Application of the Background-Field Method to the electroweak Standard Model

Application of the background-field method yields a gauge-invariant effective action for the electroweak Standard Model, from which simple QED-like Ward identities are derived. As a consequence of these Ward identities, the background-field Green functions are shown to possess very desirable theoretical properties. The renormalization of the Standard Model in the background-field formalism is studied. A consistent on-shell renormalization procedure retaining the full gauge symmetry is presented. The structure of the counterterms is shown to greatly simplify compared to the conventional formalism. A complete list of Feynman rules for the Standard Model in the background-field method is given for arbitrary values of a quantum gauge parameter including all counterterms necessary for one-loop calculations.

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arXiv1994

Green functions from a gauge-invariant effective action for the electroweak Standard Model

Application of the background-field method to the electroweak Standard-Model yields a gauge-invariant effective action giving rise to simple Ward identities. We find that in the background-field `t Hooft-Feynman gauge the resulting vertex functions are exactly those that are obtained using the pinch technique. Thus, the background-field method provides a general framework that generalizes the pinch technique directly and uniquely to arbitrary Green functions and arbitrary orders of perturbation theory. Moreover, the desirable properties of the pinch-technique vertex functions hold for arbitrary gauge parameters and have a simple explanation within the background- field method.

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arXiv1994

Calculation of two-loop self-energies in the electroweak Standard Model

Motivated by the results of the electroweak precision experiments, studies of two-loop self-energy Feynman diagrams are performed. An algebraic method for the reduction of all two-loop self-energies to a set of standard scalar integrals is presented. The gauge dependence of the self-energies is discussed and an extension of the pinch technique to the two-loop level is worked out. It is shown to yield a special case of the background-field method which provides a general framework for deriving Green functions with desirable theoretical properties. The massive scalar integrals of self-energy type are expressed in terms of generalized multivariable hypergeometric functions. The imaginary parts of these integrals yield complete elliptic integrals. Finally, one-dimensional integral representations with elementary integrands are derived which are well suited for numerical evaluation.

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arXiv1994

Gauge Invariance of Green Functions: Background-Field Method versus Pinch Technique

Application of the background-field method to QCD and the electroweak Standard Model yields gauge-invariant effective actions giving rise to simple Ward identities. Within this method, we calculate the quantities that have been treated in the literature using the pinch technique. Putting the quantum gauge parameter equal to one, we recover the pinch-technique results as a special case of the background-field method. The one-particle-irreducible Green functions of the background-field method fulfil for arbitrary gauge parameters the desirable theoretical properties that have been noticed within the pinch technique. Therefore the background-field formalism provides a general framework for the direct calculation of well-behaved Green functions. Within this formalism, the pinch technique appears as one of arbitrarily many equivalent possibilities.

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arXiv1993

Reduction of general two-loop self-energies to standard scalar integrals

We present a method for reducing general two-loop self-energies to standard scalar integrals in massive gauge theories with special emphasis on the electroweak Standard Model. It includes the tensor integral reduction for all two-loop integrals appearing in self-energy calculations. The results are valid for arbitrary values of the invariant momentum $p^2$, all particle masses, the space-time dimension $D$ and the gauge parameters $ξ_i \; (i = γ, Z, W)$. The algebraic structure of the results clearly displays the gauge dependence of the considered quantities and allows to perform very stringent checks. We explicitly verify Slavnov-Taylor identities by calculating several thousand Feynman-diagrams and adding them up algebraically. As an application we calculate the light fermion contributions to the two-loop gauge boson self-energies of the electroweak SM. We study their gauge dependence and discuss the occurring standard integrals.

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