O (alpha 4 s) loop-by-loop contributions to heavy quark pair production in hadronic collisions

The present state of the theoretical predictions for the hadronic heavy hadron production is not quite satisfactory. The full next-to-leading order (NLO) ${cal O} (alpha_s^3)$ corrections to the hadroproduction of heavy quarks have raised the leading order (LO) ${cal O} (alpha_s^2)$ estimates but the NLO predictions are still slightly below the experimental numbers. Moreover, the theoretical NLO predictions suffer from the usual large uncertainty resulting from the freedom in the choice of renormalization and factorization scales of perturbative QCD.In this light there are hopes that a next-to-next-to-leading order (NNLO) ${cal O} (alpha_s^4)$ calculation will bring theoretical predictions even closer to the experimental data. Also, the dependence on the factorization and renormalization scales of the physical process is expected to be greatly reduced at NNLO. This would reduce the theoretical uncertainty and therefore make the comparison between theory and experiment much more significant. In this thesis I have concentrated on that part of NNLO corrections for hadronic heavy quark production where one-loop integrals contribute in the form of a loop-by-loop product. In the first part of the thesis I use dimensional regularization to calculate the ${cal O}(ep^2)$ expansion of scalar one-loop one-, two-, three- and four-point integrals. The Laurent series of the scalar integrals is needed as an input for the calculation of the one-loop matrix elements for the loop-by-loop contributions. Since each factor of the loop-by-loop product has negative powers of the dimensional regularization parameter $ep$ up to ${cal O}(ep^{-2})$, the Laurent series of the scalar integrals has to be calculated up to ${cal O}(ep^2)$. The negative powers of $ep$ are a consequence of ultraviolet and infrared/collinear (or mass ) divergences. Among the scalar integrals the four-point integrals are the most complicated. The ${cal O}(ep^2)$ expansion of the three- and four-point integrals contains in general classical polylogarithms up to ${rm Li}_4$ and $L$-functions related to multiple polylogarithms of maximal weight and depth four. All results for the scalar integrals are also available in electronic form. In the second part of the thesis I discuss the properties of the classical polylogarithms. I present the algorithms which allow one to reduce the number of the polylogarithms in an expression. I derive identities for the $L$-functions which have been intensively used in order to reduce the length of the final results for the scalar integrals. I also discuss the properties of multiple polylogarithms. I derive identities to express the $L$-functions in terms of multiple polylogarithms. In the third part I investigate the numerical efficiency of the results for the scalar integrals. The dependence of the evaluation time on the relative error is discussed. In the forth part of the thesis I present the larger part of the ${cal O}(ep^2)$ results on one-loop matrix elements in heavy flavor hadroproduction containing the full spin information. The ${cal O}(ep^2)$ terms arise as a combination of the ${cal O}(ep^2)$ results for the scalar integrals, the spin algebra and the Passarino-Veltman decomposition. The one-loop matrix elements will be needed as input in the determination of the loop-by-loop part of NNLO for the hadronic heavy flavor production.

Polarization in heavy quark decays

In this thesis I concentrate on the angular correlations in top quark decays and their next--to--leading order (NLO) QCD corrections. I also discuss the leading--order (LO) angular correlations in unpolarized and polarized hyperon decays. In the first part of the thesis I calculate the angular correlation between the top quark spin and the momentum of decay products in the rest frame decay of a polarized top quark into a charged Higgs boson and a bottom quark in Two-Higgs-Doublet-Models: $t(uparrow)rightarrow b+H^{+}$. The decay rate in this process is split into an angular independent part (unpolarized) and an angular dependent part (polar correlation). I provide closed form formulae for the ${mathcal O}(alpha_{s})$ radiative corrections to the unpolarized and the polar correlation functions for $m_{b}neq 0$ and $m_{b}=0$. The results for the unpolarized rate agree with the existing results in the literature. The results for the polarized correlations are new. I found that, for certain values of $tanbeta$, the ${mathcal O}(alpha_s)$ radiative corrections to the unpolarized, polarized rates, and the asymmetry parameter can become quite large. In the second part I concentrate on the semileptonic rest frame decay of a polarized top quark into a bottom quark and a lepton pair: $t(uparrow) to X_b + ell^+ + nu_ell$. I analyze the angular correlations between the top quark spin and the momenta of the decay products in two different helicity coordinate systems: system 1a with the $z$--axis along the charged lepton momentum, and system 3a with the $z$--axis along the neutrino momentum. The decay rate then splits into an angular independent part (unpolarized), a polar angle dependent part (polar correlation) and an azimuthal angle dependent part (azimuthal correlation). I present closed form expressions for the ${mathcal O}(alpha_{s})$ radiative corrections to the unpolarized part and the polar and azimuthal correlations in system 1a and 3a for $m_{b}neq 0$ and $m_{b}=0$. For the unpolarized part and the polar correlation I agree with existing results. My results for the azimuthal correlations are new. In system 1a I found that the azimuthal correlation vanishes in the leading order as a consequence of the $(V-A)$ nature of the Standard Model current. The ${mathcal O}(alpha_{s})$ radiative corrections to the azimuthal correlation in system 1a are very small (around 0.24% relative to the unpolarized LO rate). In system 3a the azimuthal correlation does not vanish at LO. The ${mathcal O}(alpha_{s})$ radiative corrections decreases the LO azimuthal asymmetry by around 1%. In the last part I turn to the angular distribution in semileptonic hyperon decays. Using the helicity method I derive complete formulas for the leading order joint angular decay distributions occurring in semileptonic hyperon decays including lepton mass and polarization effects. Compared to the traditional covariant calculation the helicity method allows one to organize the calculation of the angular decay distributions in a very compact and efficient way. This is demonstrated by the specific example of the polarized hyperon decay $Xi^0(uparrow) to Sigma^+ + l^- + bar{nu}_l$ ,($l^-=e^-, mu^-$) followed by the nonleptonic decay $Sigma^+ to p + pi^0$, which is described by a five--fold angular decay distribution.

Top-quark pair production at hadron colliders

In this thesis we investigate several phenomenologically important properties of top-quark pair production at hadron colliders. We calculate double differential cross sections in two different kinematical setups, pair invariant-mass (PIM) and single-particle inclusive (1PI) kinematics. In pair invariant-mass kinematics we are able to present results for the double differential cross section with respect to the invariant mass of the top-quark pair and the top-quark scattering angle. Working in the threshold region, where the pair invariant mass M is close to the partonic center-of-mass energy sqrt{hat{s}}, we are able to factorize the partonic cross section into different energy regions. We use renormalization-group (RG) methods to resum large threshold logarithms to next-to-next-to-leading-logarithmic (NNLL) accuracy. On a technical level this is done using effective field theories, such as heavy-quark effective theory (HQET) and soft-collinear effective theory (SCET). The same techniques are applied when working in 1PI kinematics, leading to a calculation of the double differential cross section with respect to transverse-momentum pT and the rapidity of the top quark. We restrict the phase-space such that only soft emission of gluons is possible, and perform a NNLL resummation of threshold logarithms. The obtained analytical expressions enable us to precisely predict several observables, and a substantial part of this thesis is devoted to their detailed phenomenological analysis. Matching our results in the threshold regions to the exact ones at next-to-leading order (NLO) in fixed-order perturbation theory, allows us to make predictions at NLO+NNLL order in RG-improved, and at approximate next-to-next-to-leading order (NNLO) in fixed order perturbation theory. We give numerical results for the invariant mass distribution of the top-quark pair, and for the top-quark transverse-momentum and rapidity spectrum. We predict the total cross section, separately for both kinematics. Using these results, we analyze subleading contributions to the total cross section in 1PI and PIM originating from power corrections to the leading terms in the threshold expansions, and compare them to previous approaches. We later combine our PIM and 1PI results for the total cross section, this way eliminating uncertainties due to these corrections. The combined predictions for the total cross section are presented as a function of the top-quark mass in the pole, the minimal-subtraction (MS), and the 1S mass scheme. In addition, we calculate the forward-backward (FB) asymmetry at the Tevatron in the laboratory, and in the ttbar rest frames as a function of the rapidity and the invariant mass of the top-quark pair at NLO+NNLL. We also give binned results for the asymmetry as a function of the invariant mass and the rapidity difference of the ttbar pair, and compare those to recent measurements. As a last application we calculate the charge asymmetry at the LHC as a function of a lower rapidity cut-off for the top and anti-top quarks.

Factorization and non-local 1/m b corrections in the decay B X s gamma

In this thesis, a systematic analysis of the bar B to X_sgamma photon spectrum in the endpoint region is presented. The endpoint region refers to a kinematic configuration of the final state, in which the photon has a large energy m_b-2E_gamma = O(Lambda_QCD), while the jet has a large energy but small invariant mass. Using methods of soft-collinear effective theory and heavy-quark effective theory, it is shown that the spectrum can be factorized into hard, jet, and soft functions, each encoding the dynamics at a certain scale. The relevant scales in the endpoint region are the heavy-quark mass m_b, the hadronic energy scale Lambda_QCD and an intermediate scale sqrt{Lambda_QCD m_b} associated with the invariant mass of the jet. It is found that the factorization formula contains two different types of contributions, distinguishable by the space-time structure of the underlying diagrams. On the one hand, there are the direct photon contributions which correspond to diagrams with the photon emitted directly from the weak vertex. The resolved photon contributions on the other hand arise at O(1/m_b) whenever the photon couples to light partons. In this work, these contributions will be explicitly defined in terms of convolutions of jet functions with subleading shape functions. While the direct photon contributions can be expressed in terms of a local operator product expansion, when the photon spectrum is integrated over a range larger than the endpoint region, the resolved photon contributions always remain non-local. Thus, they are responsible for a non-perturbative uncertainty on the partonic predictions. In this thesis, the effect of these uncertainties is estimated in two different phenomenological contexts. First, the hadronic uncertainties in the bar B to X_sgamma branching fraction, defined with a cut E_gamma > 1.6 GeV are discussed. It is found, that the resolved photon contributions give rise to an irreducible theory uncertainty of approximately 5 %. As a second application of the formalism, the influence of the long-distance effects on the direct CP asymmetry will be considered. It will be shown that these effects are dominant in the Standard Model and that a range of -0.6 < A_CP^SM < 2.8 % is possible for the asymmetry, if resolved photon contributions are taken into account.

Heavy neutrinos and rare decays

In dieser Dissertation wird der seltene Zerfall K_L->emu imRahmen eines verallgemeinerten Standardmodells detailliertstudiert. In diesem Prozess bleibt die zu einer gegebenen Familie gehoerende Leptonenzahl nicht erhalten. Deswegenwerden unsere Untersuchungen im Rahmen der SU(2)_L x U(1)_Y-und SU(2)_R x SU(2)_L x U(1)_{B-L}-Modelle mit schwerenMajorana-Neutrinos ausgefuehrt. Die wichtigsten Ergebnisse dieser Arbeit betreffen dieBerechnung des Verzweigungsverhaeltnisses fuer den ZerfallK_L->emu. Im SU(2)_L x U(1)_Y-Modell mit schwerenMajorana-Neutrinos wird eine deutliche Steigerung desVerzweigungsverhaeltnisses gefunden, jedoch liegen dieerhaltenen Ergebnisse um einige Groessenordnungen unter derjetzigen experimentellen Grenze. Benutzt man das gewaehlte,auf der SU(2)_R x SU(2)_L x U(1)_{B-L}$-Eichgruppebasierende Modell mit Links-Rechts-Symmetrie, dann erhoehtdie Anwesenheit der links- und rechtshaendigen Stroeme inden Schleifendiagrammen deutlich den Wert desVerzweigungsverhaeltnisses. Dadurch koennen sich Werte inder Naehe der aktuellen experimentellen Grenze vonB(K_L->emu) < 4.7 x 10^{-12} ergeben. Um unsere Ergebnisse zu untermauern, wird die Frage derEichinvarianz bei diesem Zerfallsprozess auf demEin-Schleifen-Niveau mit besonderer Aufmerksamkeitbehandelt. Ein sogenanntes ,,on-shell skeleton``Renormierungsschema wird benutzt, um die erste vollstaendigeAnalyse der Eichinvarianz fuer den Prozess K_L->emuauszufuehren.

QCD-Strahlungskorrekturen zu Polarisationsobservablen in semileptonischen Zerfällen schwerer Quarks

In dieser Arbeit werden die QCD-Strahlungskorrekturen in erster Ordnung der starken Kopplungskonstanten für verschiedene Polarisationsobservablen zu semileptonischen Zerfällen eines bottom-Quarks in ein charm-Quark und ein Leptonpaar berechnet. Im ersten Teil wird der Zerfall eines unpolarisierten b-Quarks in ein polarisiertes c-Quark sowie ein geladenes Lepton und ein Antineutrino im Ruhesystem des b-Quarks analysiert. Es werden die Strahlungskorrekturen für den unpolarisierten und den polarisierten Beitrag zur differentiellen Zerfallsrate nach der Energie des c-Quarks berechnet, wobei das geladene Lepton als leicht angesehen und seine Masse daher vernachlässigt wird. Die inklusive differentielle Rate wird durch zwei Strukturfunktionen in analytischer Form dargestellt. Anschließend werden die Strukturfunktionen und die Polarisation des c-Quarks numerisch ausgewertet. Nach der Einführung der Helizitäts-Projektoren befaßt sich der zweite Teil mit dem kaskadenartigen Zerfall eines polarisierten b-Quarks in ein unpolarisiertes c-Quark und ein virtuelles W-Boson, welches weiter in ein Paar leichter Leptonen zerfällt. Es werden die inklusiven Strahlungskorrekturen zu drei unpolarisierten und fünf polarisierten Helizitäts-Strukturfunktionen in analytischer Form berechnet, welche die Winkelverteilung für die differentielle Zerfallsrate nach dem Viererimpulsquadrat des W-Bosons beschreiben. Die Strukturfunktionen enthalten die Informationen sowohl über die polare Winkelverteilung zwischen dem Spinvektor des b-Quarks und dem Impulsvektor des W-Bosons als auch über die räumliche Winkelverteilung zwischen den Impulsen des W-Bosons und des Leptonpaars. Der Impuls und der Spinvektor des b-Quarks sowie der Impuls des W-Bosons werden im b-Ruhesystem analysiert, während die Impulse des Leptonpaars im W-Ruhesystem ausgewertet werden. Zusätzlich zu den genannten Strukturfunktionen werden noch die unpolarisierte und die polarisierte skalare Strukturfunktion angegeben, die in Anwendungen bei hadronischen Zerfällen eine Rolle spielen. Anschließend folgt eine numerische Auswertung aller berechneten Strukturfunktionen. Im dritten Teil werden die nichtperturbativen HQET-Korrekturen zu inklusiven semileptonischen Zerfällen schwerer Hadronen diskutiert, welche ein b-Quark enthalten. Sie beschreiben hadronische Korrekturen, die durch die feste Bindung des b-Quarks in Hadronen hervorgerufen werden. Es werden insgesamt fünf unpolarisierte und neun polarisierte Helizitäts-Strukturfunktionen in analytischer Form angegeben, die auch eine endliche Masse und den Spin des geladenen Leptons berücksichtigen. Die Strukturfunktionen werden sowohl in differentieller Form in Abhängigkeit des quadrierten Viererimpulses des W-Bosons als auch in integrierter Form präsentiert. Zum Schluß werden die zuvor erhaltenen Resultate auf die semi-inklusiven hadronischen Zerfälle eines polarisierten Lambda_b-Baryons oder eines B-Mesons in ein D_s- oder ein D_s^*-Meson unter Berücksichtigung der D_s^*-Polarisation angewandt. Für die zugehörigen Winkelverteilungen werden die inklusiven QCD- und die nichtperturbativen HQET-Korrekturen zu den Helizitäts-Strukturfunktionen in analytischer Form angegeben und anschließend numerisch ausgewertet.

Renormalization of fermion mixing

Precision measurements of phenomena related to fermion mixing require the inclusion of higher order corrections in the calculation of corresponding theoretical predictions. For this, a complete renormalization scheme for models that allow for fermion mixing is highly required. The correct treatment of unstable particles makes this task difficult and yet, no satisfactory and general solution can be found in the literature. In the present work, we study the renormalization of the fermion Lagrange density with Dirac and Majorana particles in models that involve mixing. The first part of the thesis provides a general renormalization prescription for the Lagrangian, while the second one is an application to specific models. In a general framework, using the on-shell renormalization scheme, we identify the physical mass and the decay width of a fermion from its full propagator. The so-called wave function renormalization constants are determined such that the subtracted propagator is diagonal on-shell. As a consequence of absorptive parts in the self-energy, the constants that are supposed to renormalize the incoming fermion and the outgoing antifermion are different from the ones that should renormalize the outgoing fermion and the incoming antifermion and not related by hermiticity, as desired. Instead of defining field renormalization constants identical to the wave function renormalization ones, we differentiate the two by a set of finite constants. Using the additional freedom offered by this finite difference, we investigate the possibility of defining field renormalization constants related by hermiticity. We show that for Dirac fermions, unless the model has very special features, the hermiticity condition leads to ill-defined matrix elements due to self-energy corrections of external legs. In the case of Majorana fermions, the constraints for the model are less restrictive. Here one might have a better chance to define field renormalization constants related by hermiticity. After analysing the complete renormalized Lagrangian in a general theory including vector and scalar bosons with arbitrary renormalizable interactions, we consider two specific models: quark mixing in the electroweak Standard Model and mixing of Majorana neutrinos in the seesaw mechanism. A counter term for fermion mixing matrices can not be fixed by only taking into account self-energy corrections or fermion field renormalization constants. The presence of unstable particles in the theory can lead to a non-unitary renormalized mixing matrix or to a gauge parameter dependence in its counter term. Therefore, we propose to determine the mixing matrix counter term by fixing the complete correction terms for a physical process to experimental measurements. As an example, we calculate the decay rate of a top quark and of a heavy neutrino. We provide in each of the chosen models sample calculations that can be easily extended to other theories.

Characterization and optimization of an x-ray laser for the spectroscopy of Li-like heavy-ions

Recent developments in the theory of plasma-based collisionally excited x-ray lasers (XRL) have shown an optimization potential based on the dependence of the absorption region of the pumping laser on its angle of incidence on the plasma. For the experimental proof of this idea, a number of diagnostic schemes were developed, tested, qualified and applied. A high-resolution imaging system, yielding the keV emission profile perpendicular to the target surface, provided positions of the hottest plasma regions, interesting for the benchmarking of plasma simulation codes. The implementation of a highly efficient spectrometer for the plasma emission made it possible to gain information about the abundance of the ionization states necessary for the laser action in the plasma. The intensity distribution and deflection angle of the pump laser beam could be imaged for single XRL shots, giving access to its refraction process within the plasma. During a European collaboration campaign at the Lund Laser Center, Sweden, the optimization of the pumping laser incidence angle resulted in a reduction of the required pumping energy for a Ni-like Mo XRL, which enabled the operation at a repetition rate of 10 Hz. Using the experiences gained there, the XRL performance at the PHELIX facility, GSI Darmstadt with respect to achievable repetition rate and at wavelengths below 20 nm was significantly improved, and also important information for the development towards multi-100 eV plasma XRLs was acquired. Due to the setup improvements achieved during the work for this thesis, the PHELIX XRL system now has reached a degree of reproducibility and versatility which is sufficient for demanding applications like the XRL spectroscopy of heavy ions. In addition, a European research campaign, aiming towards plasma XRLs approaching the water-window (wavelengths below 5 nm) was initiated.

Deeply virtual Compton scattering in a relativistic quark model

This thesis is mainly concerned with a model calculation for generalized parton distributions (GPDs). We calculate vectorial- and axial GPDs for the N N and N Delta transition in the framework of a light front quark model. This requires the elaboration of a connection between transition amplitudes and GPDs. We provide the first quark model calculations for N Delta GPDs. The examination of transition amplitudes leads to various model independent consistency relations. These relations are not exactly obeyed by our model calculation since the use of the impulse approximation in the light front quark model leads to a violation of Poincare covariance. We explore the impact of this covariance breaking on the GPDs and form factors which we determine in our model calculation and find large effects. The reference frame dependence of our results which originates from the breaking of Poincare covariance can be eliminated by introducing spurious covariants. We extend this formalism in order to obtain frame independent results from our transition amplitudes.

Electronic transport in the heavy fermion superconductors UPd 2 Al 3 and UNi 2 Al 3

This work addresses the electronical properties of the superconductors UPd2Al3 and UNi2Al3 on the basis of thin film experiments. These isotructural compounds are ideal candiates to study the interplay of magnetism and superconductivity due to the differences of their magnetically ordered states, as well as the experimental evidence for a magnetic pairing mechanism in UPd2Al3. Epitaxial thin film samples of UPd2Al3 and UNi2Al3 were prepared using UHV Molecular Beam Epitaxy (MBE). For UPd2Al3, the change of the growth direction from the intrinsic (001) to epitaxial (100) was predicted and sucessfully demonstrated using LaAlO3 substrates cut in (110) direction. With optimized deposition process parameters for UPd2Al3 (100) on LaAlO3 (110) superconducting samples with critical temperatures up to Tc = 1.75K were obtained. UPd2Al3-AlOx-Ag mesa junctions with superconducting base electrode were prepared and shown to be in the tunneling regime. However, no signatures of a superconducting density of states were observed in the tunneling spectra. The resistive superconducting transition was probed for a possible dependence on the current direction. In contrast to UNi2Al3, the existence of such feature was excluded in UPd2Al3 (100) thin films. The second focus of this work is the dependence of the resisitive transition in UNi2Al3 (100) thin films on the current direction. The experimental fact that the resisitive transition occurs at slightly higher temperatures for I║a than for I║c can be explained within a model of two weakly coupled superconducting bands. Evidence is presented for the key assumption of the two-band model, namely that transport in and out of the ab-plane is generated on different, weakly coupled parts of the Fermi surface. Main indications are the angle dependence of the superconducting transition and the dependence of the upper critical field Bc2 on current and field orientation. Additionally, several possible alternative explanations for the directional splitting of the transition are excluded in this work. An origin due to scattering on crystal defects or impurities is ruled out, likewise a relation to ohmic heating or vortex dynamics. The shift of the transition temperature as function of the current density was found to behave as predicted by the Ginzburg-Landau theory for critical current depairing, which plays a significant role in the two-band model. In conclusion, the directional splitting of the resisitive transition has to be regarded an intrinsic and unique property of UNi2Al3 up to now. Therefore, UNi2Al3 is proposed as a role model for weakly coupled multiband superconductivity. Magnetoresistance in the normalconducting state was measured for UPd2Al3 and UNi2Al3. For UNi2Al3, a negative contribution was observed close to the antiferromagnetic ordering temperature TN only for I║a, which can be associated to reduced spin-disorder scattering. In agreement with previous results it is concluded that the magnetic moments have to be attributed to the same part of the Fermi surface which generates transport in the ab-plane.

Unconventional superconductivity of the heavy fermion compound UNi 2 Al 3

The heavy fermion compound UNi2Al3 exhibits the coexistence of superconductivity and magnetic order at low temperatures, stimulating speculations about possible exotic Cooper-pairing interaction in this superconductor. However, the preparation of good quality bulk single crystals of UNi2Al3 has proven to be a non-trivial task due to metallurgical problems, which result in the formation of an UAl2 impurity phase and hence a strongly reduced sample purity. The present work concentrates on the preparation, characterization and electronic properties investigation of UNi2Al3 single crystalline thin film samples. The preparation of thin films was accomplished in a molecular beam epitaxy (MBE) system. (100)-oriented epitaxial thin films of UNi2Al3 were grown on single crystalline YAlO3 substrates cut in (010)- or (112)-direction. The high crystallographic quality of the samples was proved by several characterisation methods, such as X-ray analysis, RHEED and TEM. To study the magnetic structure of epitaxial thin films resonant magnetic x-ray scattering was employed. The magnetic order of thin the film samples, the formation of magnetic domains with different moment directions, and the magnetic correlation length were discussed. The electronic properties of the UNi2Al3 thin films in the normal and superconducting states were investigated by means of transport measurements. A pronounced anisotropy of the temperature dependent resistivity ρ(T) was observed. Moreover, it was found that the temperature of the resistive superconducting transition depends on the current direction, providing evidence for multiband superconductivity in UNi2Al3. The initial slope of the upper critical field H′c2(T) of the thin film samples suggests an unconventional spin-singlet superconducting state, as opposed to bulk single crystal data. To probe the superconducting gap of UNi2Al3 directly by means of tunnelling spectroscopy many planar junctions of different design employing different techniques were prepared. Despite the tunneling regime of the junctions, no features of the superconducting density of state of UNi2Al3 were ever observed. It is assumed that the absence of UNi2Al3 gap features in the tunneling spectra was caused by imperfections of the tunnelling contacts. The superconductivity of UNi2Al3 was probably suppressed just in a degraded surface layer, resulting in tunneling into non superconducting UNi2Al3. However, alternative explanations such as intrinsic pair breaking effects at the interface to the barrier are also possible.

Highly accurate quantum chemistry : spin-orbit splittings via multireference coupled-cluster methods and applications in heavy-atom main-group chemistry

Diese Dissertation demonstriert und verbessert die Vorhersagekraft der Coupled-Cluster-Theorie im Hinblick auf die hochgenaue Berechnung von Moleküleigenschaften. Die Demonstration erfolgt mittels Extrapolations- und Additivitätstechniken in der Single-Referenz-Coupled-Cluster-Theorie, mit deren Hilfe die Existenz und Struktur von bisher unbekannten Molekülen mit schweren Hauptgruppenelementen vorhergesagt wird. Vor allem am Beispiel von cyclischem SiS_2, einem dreiatomigen Molekül mit 16 Valenzelektronen, wird deutlich, dass die Vorhersagekraft der Theorie sich heutzutage auf Augenhöhe mit dem Experiment befindet: Theoretische Überlegungen initiierten eine experimentelle Suche nach diesem Molekül, was schließlich zu dessen Detektion und Charakterisierung mittels Rotationsspektroskopie führte. Die Vorhersagekraft der Coupled-Cluster-Theorie wird verbessert, indem eine Multireferenz-Coupled-Cluster-Methode für die Berechnung von Spin-Bahn-Aufspaltungen erster Ordnung in 2^Pi-Zuständen entwickelt wird. Der Fokus hierbei liegt auf Mukherjee's Variante der Multireferenz-Coupled-Cluster-Theorie, aber prinzipiell ist das vorgeschlagene Berechnungsschema auf alle Varianten anwendbar. Die erwünschte Genauigkeit beträgt 10 cm^-1. Sie wird mit der neuen Methode erreicht, wenn Ein- und Zweielektroneneffekte und bei schweren Elementen auch skalarrelativistische Effekte berücksichtigt werden. Die Methode eignet sich daher in Kombination mit Coupled-Cluster-basierten Extrapolations-und Additivitätsschemata dafür, hochgenaue thermochemische Daten zu berechnen.

Hadronic correlation functions with quark-disconnected contributions in lattice QCD

One of the fundamental interactions in the Standard Model of particle physicsrnis the strong force, which can be formulated as a non-abelian gauge theoryrncalled Quantum Chromodynamics (QCD). rnIn the low-energy regime, where the QCD coupling becomes strong and quarksrnand gluons are confined to hadrons, a perturbativernexpansion in the coupling constant is not possible.rnHowever, the introduction of a four-dimensional Euclidean space-timernlattice allows for an textit{ab initio} treatment of QCD and provides arnpowerful tool to study the low-energy dynamics of hadrons.rnSome hadronic matrix elements of interest receive contributionsrnfrom diagrams including quark-disconnected loops, i.e. disconnected quarkrnlines from one lattice point back to the same point. The calculation of suchrnquark loops is computationally very demanding, because it requires knowledge ofrnthe all-to-all propagator. In this thesis we use stochastic sources and arnhopping parameter expansion to estimate such propagators.rnWe apply this technique to study two problems which relay crucially on therncalculation of quark-disconnected diagrams, namely the scalar form factor ofrnthe pion and the hadronic vacuum polarization contribution to the anomalousrnmagnet moment of the muon.rnThe scalar form factor of the pion describes the coupling of a charged pion torna scalar particle. We calculate the connected and the disconnected contributionrnto the scalar form factor for three different momentum transfers. The scalarrnradius of the pion is extracted from the momentum dependence of the form factor.rnThe use ofrnseveral different pion masses and lattice spacings allows for an extrapolationrnto the physical point. The chiral extrapolation is done using chiralrnperturbation theory ($chi$PT). We find that our pion mass dependence of thernscalar radius is consistent with $chi$PT at next-to-leading order.rnAdditionally, we are able to extract the low energy constant $ell_4$ from thernextrapolation, and ourrnresult is in agreement with results from other lattice determinations.rnFurthermore, our result for the scalar pion radius at the physical point isrnconsistent with a value that was extracted from $pipi$-scattering data. rnThe hadronic vacuum polarization (HVP) is the leading-order hadronicrncontribution to the anomalous magnetic moment $a_mu$ of the muon. The HVP canrnbe estimated from the correlation of two vector currents in the time-momentumrnrepresentation. We explicitly calculate the corresponding disconnectedrncontribution to the vector correlator. We find that the disconnectedrncontribution is consistent with zero within its statistical errors. This resultrncan be converted into an upper limit for the maximum contribution of therndisconnected diagram to $a_mu$ by using the expected time-dependence of therncorrelator and comparing it to the corresponding connected contribution. Wernfind the disconnected contribution to be smaller than $approx5%$ of thernconnected one. This value can be used as an estimate for a systematic errorrnthat arises from neglecting the disconnected contribution.rn