Dissertations / Theses on the topic 'Quark mixing'

Das Standardmodell einer zusätzlichen sequentiellen Fermiongeneration (SM4) war 2012 auf Basis eines Fits an elektroschwache Präzisionsobservable und die Higgs-Signalstärken mit einer Signifikanz von 5.3 sigma ausgeschlossen worden. Komplementär dazu wurden in der vorliegenden Arbeit Fits des SM4 an eine Kombination eines typischen Satzes von Flavour-Observablen mit den Ergebnissen des zuvor durchgeführten Elektroschwachen Präzisionsfits durchgeführt. Im SM3-Kontext extrahierte Größen wurden gemäß ihrer Bedeutung im SM4 reinterpretiert und die angepassten theoretischen Ausdrücke angegeben. Die resultierenden Einschränkungen der CKM-Matrix des SM4, ihrer potentiell CP-verletzenden Phasen sowie der Masse des up-type-Quarks der 4. Generation t'' werden angegeben. Zum Vergleich des SM4 mit dem SM3 werden die erreichten chi^2-Werte genutzt. chi^2=15.53 im SM4 und 9.56 im SM3 passen fast vollkommen zu einer gleich guten Beschreibung der Experimente durch beide Modelle, wobei das SM3 aber sechs Freiheitsgrade mehr besitzt. Außerdem wurden die Vorhersagen des SM3 und des SM4 für die Dimyon-Ladungsasymmetrie ASL mit experimentellen Werten verglichen. Die Vorhersage des SM3 ist ca. 2 sigma vom experimentellen Wert entfernt, die des SM4 ca. 3 sigma.\par Die Ergebnisse deuten nicht darauf hin, dass die Signifikanz des 2012 erreichten Ausschlusses des SM4 durch die Hinzunahme von Flavour-Observablen zu den damals verwendeten elektroschwachen Präzisionsobservablen und Higgs-Querschnitten bedeutend verringert würde.\par Es konnte jedoch keine genaue quantitative Aussage über die Auswirkungen der Flavourobservablen auf diese Signifikanz getroffen werden, weil das Programm CKMfitter likelihood-ratio-Berechnung nur durchführen kann, wenn sich eines der untersuchten Modelle durch Fixierung von Parametern aus dem anderen ergibt (nested models), was hier nicht der Fall ist.
The Standard Model extended by an additional sequential generation of Dirac fermions (SM4) was excluded with a significance of 5.3 sigma in 2012. This was achieved in a combined fit of the SM4 to Electroweak Precision Observables and signal strengths of the Higgs boson. This thesis complements this excludion by a fit of the SM4 to a typical set of Flavour physics observables and the results of the previously performed Electroweak Precision fit. Quantities extracted in an SM3 framework are reinterpreted in SM4 terms and the adapted theoretical expressions are given. The resultant constraints on the SM4''s CKM matrix, its potentially CP-violating phases and the mass of the new up-type quark t'' are given. To compare the relative performance of the SM4 and the SM3, this work uses the chi^2 values achieved in the fit. The values of 15.53 for the SM4 and 9.56 for the SM4 are almost perfectly consistent with both models describing the experimental data equally well with the SM3 having six degrees of freedom more. The dimuon charge asymmetry ASL was not used as a fit input because the interpretation of its measurement was subject to debate at the time when the fits were produced, but its prediction in the fit was used as an additional test of the SM4. The SM3''s prediction differs from the experimental values by about 2 sigma, and the SM4''s prediction by about 3 sigma. \par In summary, these results do not suggest that any significant reduction of the 5.3 sigma exclusion could be achieved by combining the Electroweak Precision Observables and Higgs inputs with Flavour physics data. However, the exact effect of the Flavour physics input on the significance of the SM4''s exclusion cannot be given at this point because the CKMfitter software is currently not able to perform a statistically stringent likelihood comparison of non-nested models.

In this thesis, several properties of baryons are studied using the chiral quark model. The chiral quark model is a theory which can be used to describe low energy phenomena of baryons. In Paper 1, the chiral quark model is studied using wave functions with configuration mixing. This study is motivated by the fact that the chiral quark model cannot otherwise break the Coleman–Glashow sum-rule for the magnetic moments of the octet baryons, which is xperimentally broken by about ten standard deviations. Configuration mixing with quark-diquark components is also able to reproduce the octet baryon magnetic moments very accurately. In Paper 2, the chiral quark model is used to calculate the decuplet baryon magnetic moments. The values for the magnetic moments of the ++and− are in good agreement with the experimental results. The total quark spin polarizations are also calculated and are found to be significantly smaller than the non-relativistic quark model results. In Paper 3, the weak form factors for semileptonic octet baryon decays are studied in the chiral quark model. The “weak magnetism” form factors are found to be consistent with the conserved vector current (CVC) results and the induced pseudotensor form factors, which seem to be model independent, are small. The results obtained are in general agreement with experiments and are also compared with other model calculations.
QC 20100618

This thesis reports a measurement of the charm-mixing observable yCP using D^0->K^+K^−, D^0->pi^+pi^−, and D^0->K^−pi^+ decays, where the D^0 meson originates from semileptonic B-meson decays. The analysis is performed on the full Run 2 dataset collected by LHCb with pp collisions at a centre-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 5.57 fb^−1 . The dataset is divided into 18 exclusive D^0 decay-time bins, in which an invariant mass fit is performed to extract the signal yield for each decay channel. The ratios of KK/Kpi and pipi/Kpi yields in each bin, corrected for the efficiency as function of the decay-time estimated from a Monte Carlo sample, are then fitted to extract the difference between the decay widths of KK (pipi) and Kpi channels, ∆Γ^{KK} (∆Γ^{pipi}). Finally, y_CP is computed as ∆Γt(D^0), where t(D^0) is the precisely known D^0 lifetime. The values obtained from the two decay channels with preliminary systematic uncertainties are y_CP^{KK} = (75.98 ± 0.07 (stat) ± 0.06 (syst))%, y_CP^{pipi} = (76.29 ± 0.14 (stat) ± 0.05 (syst))%, which are consistent with each other (the central values are blind), and when combined yield a result of y_CP = (76.08 ± 0.06 (stat) ± 0.04 (syst))%. The analysis aims at updating the previous LHCb measurement with a larger data sample size, and is expected to improve the precision by a factor two with respect to the current world average y_CP = (0.715 ± 0.111)%.

This thesis is arranged in two distinct parts. The first part involves the construction of a novel dynamical scheme which is capable of generating the masses of the quarks and the elements of the Kobayashi-Maskawa matrix, and which does not rely upon the Higgs mechanism. The up quarks acquire their masses by coupling to a new heavy fermion via emission and reabsorption of a new scalar boson. The down quarks, on the other hand, obtain their masses via a correction to the up mass matrix as a result of an anomalous flavour changing interaction of the $W sp pm$. Extensions of the mass generation model are proposed and discussed. The second part involves the leading-log s study of hadron-hadron elastic scattering to order $ alpha sb{s} sp3$. By introducing wave functions, it is found that there are three types of form factor for the proton, and two for the pion. These form factors turn out to cancel the infrared divergence which occurs in quark-quark scattering. To this order in $ alpha sb{s}$, the amplitude of such elastic scattering is shown to have the form $ sim$(1 + log(s)($ alpha sb{o}$ + $ alpha sp prime t$ + $O(t sp2))$ for the imaginary part and a constant $ sim alpha sb{odd}$ for the real part, where s and t are the usual Mandelstam variables, and the $ alpha$'s are constants.

The Standard Model of Elementary Particle Physics (SM) is the present theoryfor the elementary particles and their interactions and is a well-established theorywithin the physics community. The SM is a combination of Quantum Chromodynamics(QCD) and the Glashow{Weinberg{Salam (GWS) electroweak model. QCDis a theory for the strong force, whereas the GWS electroweak model is a theoryfor the weak and electromagnetic forces. This means that the SM describes allfundamental forces in Nature, except for the gravitational force. However, the SMis not a nal theory and some of its problems will be discussed in this thesis.In the rst part of this thesis, several properties of baryons are studied suchas spin structure, spin polarizations, magnetic moments, weak form factors, andnucleon quark sea isospin asymmetries, using the chiral quark model (QM). TheQM is an eective chiral eld theory developed to describe low energy phenomena of baryons, since perturbative QCD is not applicable at low energies. The resultsof the QM are in good agreement with experimental data.The second part of the thesis is devoted to the concept of quantum mechanicalneutrino oscillations. Neutrino oscillations can, however, not occur within the GWSelectroweak model. Thus, this model has to be extended in some way. All studiesincluding neutrino oscillation are done within three avor neutrino oscillationmodels. Both vacuum and matter neutrino oscillations are considered. Especially,global ts to all data of candidates for neutrino oscillations are presented and alsoan analytical formalism for matter enhanced three avor neutrino oscillations usingtime evolution operators is derived. Furthermore, investigations of matter eectswhen neutrinos traverse the Earth are included.The thesis begins with an introductory review of the QM and neutrino oscillationsand ends with the research results, which are given in the nine accompanyingscientic articles.
QC 20100616

This thesis presents an analysis of inclusive semileptonic $B \to X_u e \nu$ decays using approximately 454 million $\Upsilon(4S) \to B \bar{B}$ decays collected during the years 1999 to 2008 with the BABAR detector. The electron energy, $E_e$, and the invariant mass squared of the electron-neutrino pair,$ q^2$, are reconstructed, where the neutrino kinematics is deduced from the decay products of both B mesons. The final hadronic state,$ X_u$, consists of a sum of many hadronic channels, each of which contains at least one $u$ quark. The variables $q^2$ and $E_e$ are then combined to compute the maximum kinematically allowed invariant mass squared of the hadronic system, $s_h^{max}$. Using these kinematic quantities, the partial branching fraction, $\Delta BR(B \to X_u e \nu)$, unfolded for detector effects, is measured to be $\Delta BR(E_e>2.0 GeV, s_h^{max}<3.52 GeV^2) = (3.33 \pm 0.18 \pm 0.21) \times 10^{-4} in the $\Upsilon(4S)$ and \Delta \tilde{\BR}(\tilde E_e>1.9 GeV, \tilde {s}^{max}_{h} < 3.5 GeV^2) = (4.57 \pm 0.24 \pm 0.32) \times 10^{-4} in the $B$ meson rest frames. The quoted errors are statistical and systematic, respectively. The CKM matrix element $|V_{ub}|$ is determined from the measured $\Delta \tilde{\BR}$ using theoretical calculation based on Heavy Quark Expansion. The result is $|V_{ub}| = (4.19 \pm 0.18{}^{+0.26}_{-0.20} {}^{+0.26}_{-0.25}) \times 10^{-3}, where the errors represent experimental uncertainties, uncertainties from HQE parameters and theoretical uncertainties, respectively.

In this analysis the decay B- --> D*° e- nu is measured. The underlying data sample consists of about 226 million B-meson pairs accumulated on the Y(4S) resonance by the BABAR detector at the asymmetric e+e- collider PEP II. The reconstruction of the decay uses the channels D*° --> D° pi°, D° --> K- pi+ and pi° --> gamma gamma. The neutrino is not reconstructed. Since the rest frame of the B meson is unknown, the boost w of the D*° meson in the B meson rest frame is estimated by w'. The w' spectrum of the data is described in terms of the partial decay width dGamma/dw given by theory and the detector simulation translating each spectrum dGamma/dw into an expectation of the measured w' spectrum. dGamma/dw depends on a form factor F(w) parameterizing the strong interaction in the decay process. To find the best descriptive dGamma/dw a fit to the data determines the following two parameters of dGamma/dw: (i) F(1)|Vcb|, the product between F at zero D*°-recoil and the Quark mixing parameter |Vcb|; (ii) rho^2, a parameter of the form factor F(w). The former parameter scales the height of dGamma/dw and rho^2 varies the shape of it. The determined values of F(1)|Vcb|, rho^2 and the branching fraction BF(B- --> D*° e- nu) are F(1)|Vcb| = (35.8 +- 0.5 +- 1.5) x 10e-03, rho^2 = (1.08 +- 0.05 +- 0.09) and BF(B- --> D*° e- nu) = (5.60 +- 0.08 +- 0.42)%, where the uncertainties are statistical and systematic, respectively. The value of BF(B- --> D*° e- nu) has been determined by an integration of dGamma/dw over the allowed w range using the fitted values of F(1)|Vcb| and rho^2.

In this analysis the decay B- --> D*° e- nu is measured. The underlying data sample consists of about 226 million B-meson pairs accumulated on the Y(4S) resonance by the BABAR detector at the asymmetric e+e- collider PEP II. The reconstruction of the decay uses the channels D*° --> D° pi°, D° --> K- pi+ and pi° --> gamma gamma. The neutrino is not reconstructed. Since the rest frame of the B meson is unknown, the boost w of the D*° meson in the B meson rest frame is estimated by w'. The w' spectrum of the data is described in terms of the partial decay width dGamma/dw given by theory and the detector simulation translating each spectrum dGamma/dw into an expectation of the measured w' spectrum. dGamma/dw depends on a form factor F(w) parameterizing the strong interaction in the decay process. To find the best descriptive dGamma/dw a fit to the data determines the following two parameters of dGamma/dw: (i) F(1)|Vcb|, the product between F at zero D*°-recoil and the Quark mixing parameter |Vcb|; (ii) rho^2, a parameter of the form factor F(w). The former parameter scales the height of dGamma/dw and rho^2 varies the shape of it. The determined values of F(1)|Vcb|, rho^2 and the branching fraction BF(B- --> D*° e- nu) are F(1)|Vcb| = (35.8 +- 0.5 +- 1.5) x 10e-03, rho^2 = (1.08 +- 0.05 +- 0.09) and BF(B- --> D*° e- nu) = (5.60 +- 0.08 +- 0.42)%, where the uncertainties are statistical and systematic, respectively. The value of BF(B- --> D*° e- nu) has been determined by an integration of dGamma/dw over the allowed w range using the fitted values of F(1)|Vcb| and rho^2.

L’étude de la décroissance β est un outil fantastique pour approfondir notreconnaissance de l’interaction faible décrite par le Modèle Standard. Ce modèle et laphysique au-delà peuvent être testés par des mesures précises de paramètres caractérisantces décroissances. Parmi ces tests, la vérification de l’hypothèse de la conservation ducourant vectoriel (CVC) et de l’unitarité de la matrice de mélange des quarks de Cabibbo-Kobayashi-Maskawa (CKM) sont d’un grand intérêt. Pour cela, les paramètres caractérisantles transitions β doivent être déterminés très précisément. Les meilleures précisions ont étéobtenues pour les transitions super-permises de Fermi de type 0+ → 0+. Cependant, il existed’autres types de décroissances pour réaliser ces tests, par exemple, les décroissances βmiroir. À ce jour, elles ne permettent pas d’atteindre les précisions obtenues avec lestransitions de type 0+ → 0+. Pour améliorer cela, de nouvelles mesures très précises desparamètres expérimentaux caractérisant ces transitions, comme la demi-vie et le rapportd’embranchement, sont nécessaires. C’est pourquoi une expérience a été réalisée àl’université de Jyväskylä en Finlande, afin d’étudier la décroissance β des noyaux miroir 23Mget 27Si et de mesurer ces paramètres. Les valeurs des demi-vies obtenues pour ces deuxnoyaux sont respectivement dix fois et sept fois plus précises que les moyennes de lalittérature. La valeur obtenue pour le rapport d’embranchement de 23Mg est trois fois plusprécise que la moyenne de la littérature, celui de 27Si étant déjà connu avec une très grandeprécision (0,02%), n’a pas été déterminé avec une meilleure précision
Beta decays are a fantastic tool to study the weak interaction described by theStandard Model. This model and the physics beyond can be tested by precisemeasurements of nuclear β decays. Among these tests, the conserved vector current (CVC)hypothesis and the unitarity of the Cabibbo-Kobayashi-Maskawa (CKM) quark-mixing matrixare of great interest. For these, the parameters of β transitions must be precisely determined.The highest precisions have been obtained with superallowed 0+ → 0+ Fermi β decays.However, there are other possibilities to make these tests, for example mirror β decays. Fornow, they do not allow to achieve the precision of the 0+ → 0+ transitions. To improve this,new accurate measurements of experimental parameters characterizing these transitions,such as the half-life and the branching ratio, are needed. For this purpose, an experimenthas been carried out at the University of Jyväskylä to study the mirror β decays of 23Mg and27Si and to measure these parameters. The half-life values obtained for these two nuclei are,respectively, ten times and seven times more precise than the literature averages. The valueof the branching ratio obtained for 23Mg is three times more precise than the literatureaverage; the one of 27Si has not been improved as it is already precisely known (0.02%)

Bien qu'ayant beaucoup de succès pour décrire la grande variété de phénomènes de la physique des particules, le Modèle Standard (MS) laisse certaines propriétés de la nature sans explication. Ici, nous allons mettre l'accent sur le traitement différent des chiralités de type gauche et droite dans le cadre du MS. Une façon naturelle d'expliquer cela est de plonger le MS dans un modèle plus fondamental, capable de traiter les chiralités d'une manière symétrique. Cette classe de modèles, connue sous le nom de "modèles à symétrie droite-gauche" (LR models, en anglais), introduit une nouvelle interaction qui couple préférentiellement aux champs "droitiers". Puis, à une haute échelle d'énergie, la symétrie reliant droite et gauche est brisée spontanément donnant naissance au MS et aux phénomènes de violation de symétrie de parité. La manière spécifique par laquelle le mécanisme Brout-Englert-Higgs (BEH) se produit dans les modèles LR peut être sondée par des observables électrofaibles de précision, ce qui sert de premier test de l'extension du MS dans le secteur électrofaible. Comme conséquence du mécanisme BEH dans les modèles LR, de nouveaux bosons de jauge sont présents. Ce sont W’ et Z’, censés être beaucoup plus lourds que les bosons de jauge W et Z afin d'expliquer pourquoi ils n'ont jamais été vus jusqu'à présent. Ces nouvelles particules sont accompagnées d'une riche phénoménologie, comme de nouvelles sources de violation de CP au-delà de celle du MS. En outre, un nouveau secteur scalaire neutre introduit des courants qui changent la saveur (FCNC, en anglais) au niveau des arbres, un processus fortement restreint dans le MS, où il arrive seulement à l'ordre des boucles. L'existence de FCNCs fournit des contraintes extrêmement puissantes sur les modèles LR, et mérite donc une attention spéciale, en particulier lors du calcul des corrections venant de la QCD. Nous calculons donc les corrections au Next-to-Leading Order des effets à de courtes distances venant de la QCD aux contributions du modèle LR aux observables liées au mélange de mésons neutres et sensibles donc aux FCNC.Ensuite, nous considérons l'étude phénoménologique des modèles LR afin de tester leur viabilité et leur structure. Plus particulièrement, nous considérons le cas où des doublets scalaires sont responsables de la brisure du groupe de jauge des modèles LR. A cet effet, nous menons une étude combinée des observables de précision électrofaible, des bornes directes sur la masse des nouveaux bosons de jauge et des observables qui dérivent de l'oscillation des mésons neutres, dans le cas plus simple où la matrice de mixing dans le secteur droit est égal à la matrice CKM. Ces observables sont combinées dans le cadre du paquet CKMfitter d'analyse statistique. La combinaison de différentes classes d'observables doit prendre en compte la particularité des incertitudes théoriques, qui ne sont pas de nature statistique comme d'autres sources d'incertitude. A ce propos, nous considérons aussi la comparaison de différentes modèles d'incertitude théorique, afin de trouver des méthodes bien adaptées à la situation actuelle de notre connaissance des incertitudes théoriques impliquées dans un fit global en physique de la saveur
Though very successful in explaining a wide variety of particle physics phenomena, the Standard Model (SM) leaves unexplained some properties of nature. Here we focus on the different behaviours of left- and right-handed chiralities, or in other words the violation of parity symmetry. A possible and somewhat natural avenue to explain this feature is to embed the SM into a more symmetric framework, which treats the chiralities on equal footing. This class of models, the Left-Right (LR) Models, introduces new gauge interactions that couple preferentially to right-handed fields. Then, at an energy scale high enough, LR symmetry is spontaneously broken through the Brout-Englert-Higgs (BEH) mechanism, thus giving origin to the SM and to parity violating phenomena. The specific way in which the BEH mechanism operates in LR Models can be probed by EW Precision Observables, consisting of quantities that have been very accurately measured, serving as a first test of consistency for extensions of the SM in the EW sector. We revisit a simple realization of LR Models containing doublet scalars, and consider the phenomenological study of this doublet scenario in order to test the viability and structure of the LR Models. In particular, there is a rich phenomenology associated to the new gauge bosons W’ et Z’ introduced by LR Models, such as new sources of CP violation beyond the one of the SM. Moreover, the extended neutral scalar sector introduces Flavour Changing Neutral Couplings (FCNC) at tree level, which are strongly suppressed in the SM where they arrive first at one loop. FCNCs typically lead to extremely powerful constraints since they contribute to meson-mixing processes, and therefore deserve close attention. For this reason, we consider the calculation of short-distance QCD effects correcting the LR Model contributions to meson-mixing observables up to the Next-to-Leading Order (NLO), a precision required to set solid lower bounds on the LR Model scales. Finally, we combine in a global fit electroweak precision observables, direct searches for the new gauge bosons and meson oscillation observables in the simple case where the right-handed analogous of the CKM mixing-matrix is equal to the CKM matrix itself (a scenario called CKMfitter symmetry). The full set of the observables is combined by using the CKMfitter statistical framework, based on a frequentist analysis and a particular scheme for modeling theoretical uncertainties. We also discuss other possible modelings of theoretical uncertainties in a prospective study for future global flavour fits made by the CKMfitter Collaboration

In der Z-Boson-Resonanzphysik sind mehrere Präzisionsobservablen in einem perfekten Zustand, bei dem die theoretische Unsicherheit niedriger ist als die gegenwärtige experimentelle Unsicherheit. Das Konzept für den zukünftigen Teilchenbeschleuniger Future Circular Collider (FCC), will eine Verbesserung der Messungen für die Präzisionsobservablen um ein bis zwei signifikante Stellen erreichen. Damit werden die Vorhersagen des elektroschwachen Standardmodells in eine Situation versetzt, in der vollständige Zweischleifenkorrekturen zusammen mit den führenden Dreischleifenkorrekturen obligatorisch werden. 2016 wurden die vollständigen Zweischleifenkorrekturen für den effektiven schwachen Mischungswinkel für die bottom Quarks sin^2/theta/^b_eff berechnet, indem die fehlenden bosonischen Zweischleifenkorrekturen bereitgestellt wurden. Dabei liegt die Schwierigkeit in der Berechnung der entsprechenden Zwei-Schleifen Vertex-Feynman-Integrale, die mehrere massive Teilchen einschließen. Gegenwärtig ist die analytische Rechnung der meisten dieser Integrale schwierig und deswegen werden rein numerische Techniken, mittels Sektorzerlegungsansatz und der Integralansatz nach Mellin-Barnes, angewandt. Es war bis vor kurzem nicht bekannt, wie Mellin-Barnes-Integraldarstellungen in den minkowskischen Integrationsgebieten numerisch behandelt werden können. Um dieses Problem anzugehen, stellen wir eine Vielzahl von ein- und mehrdimensionaler Techniken vor, die ein Teil des neuen Programms MBnumerics.m sind, welches in dieser Dissertation entwickelt wurde. Der Sektorzerlegungsansatz und der Integralansatz nach Mellin-Barnes sind zusammen ausreichend, um elektroschwache Zweischleifenkorrekturen für die Präzisionsobservablen der Annihilation von e^+e^- in zwei Fermionen in der Z-Bosonresonanz auszurechnen. Aktuell führt dies zu der genauesten Vorhersage für den effektiven elektroschwachen Mischungswinkel für bottom Quarks sin^2/theta/^b_eff = 0.232312.
In the Z-boson resonance physics several precision observables are in a perfect state, where the theory uncertainty is lower than the present experimental uncertainty. The ambitious concepts for the future collider, Future Circular Collider (FCC), aim for an improvement of measurements for the precision observables by one to two significant digits. This will put the Electroweak Standard Model predictions in a situation where complete two-loop corrections together with the leading three-loop corrections will become mandatory. The complete two-loop corrections for effective weak mixing angle for bottom quarks sin^2/theta/^b_eff were reported recently, by providing the missing bosonic two-loop corrections. The difficult task in this computation is the calculation of the corresponding two-loop vertex Feynman integrals which include several massive particles. At present the analytic evaluation for most of these integrals is out of reach and purely numerical techniques were applied. Only two methods, sector decomposition approach and the Mellin-Barnes integral approach, are known to extract infrared and ultraviolet singularities in a systematic way for a general Feynman integral with fully automatized algorithms. It was not known until recently how to treat Mellin-Barnes integral representations in Minkowskian regions numerically. To address this problem we introduce and discuss in detail a variety of one- and multi-dimensional techniques, which are part of a new program MBnumerics.m developed in this thesis work. Two techniques, sector decomposition and Mellin-Barnes integral approach, are together sufficient to treat electroweak two-loop corrections to the precision observables for the e^+e^- annihilation into two fermions at the Z-boson resonance. This leads to the most precise prediction at present for the effective weak mixing angle for bottom quarks: sin^2/theta/^b_eff=0.232312.