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.

UHP metamorphic rocks of the Eastern Rhodope Massif, NE Greece: new constraints from petrology, geochemistry and zircon ages

In this PhD thesis, a multidisciplinary study has been carried out on metagranitoids and paragneisses from the Eastern Rhodope Massif, northern Greece, to decipher the pre-Alpine magmatic and geodynamic evolution of the Rhodope Massif and to correlate the eastern part with the western/central parts of the orogen. The Rhodope Massif, which occupies the major part of NE Greece and S Bulgaria, represents the easternmost part of the Internal Hellenides. It is regarded as a nappe stack of high-grade units, which is classically subdivided into an upper unit and a lower unit, separated by a SSE-NNW trending thrust plane, the Nestos thrust. Recent research in the central Greek Rhodope Massif revealed that the two units correspond to two distinct terranes of different age, the Permo-Carboniferous Thracia Terrane, which was overthrusted by the Late Jurassic/Early Cretaceous Rhodope Terrane. These terranes are separated by the Nestos suture, a composite zone comprising metapelites, metabasites, metagranitoids and marbles, which record high-pressure and even ultrahigh-pressure metamorphism in places. Similar characteristic rock associations were investigated during this study along several well-constrained cross sections in vincity to the Ada, Sidiro and Kimi villages in the Greek Eastern Rhodope Massif. Field evidence revealed that the contact zone of the two terranes in the Eastern Rhodope Massif is characterized by a mélange of metapelites, migmatitic amphibolites/eclogites, strongly sheared orthogneisses and marbles. The systematical occurrence of this characteristic rock association between the terranes implies that the Nestos suture is a continuous belt throughout the Greek Rhodope Massif. In this study, a new UHP locality could be established and for the first time in the Greek Rhodope, metamorphic microdiamonds were identified in situ in their host zircons using Laser-Raman spectroscopy. The presence of the diamonds as well as element distribution patterns of the zircons, obtained by TOF-SIMS, indicate metamorphic conditions of T > 1000 °C and P > 4 GPa. The high-pressure and ultrahigh-pressure rocks of the mélange zone are considered to have formed during the subduction of the Nestos Ocean in Jurassic times at ~150 Ma. Melting of metapelitic rocks at UHP conditions facilitated the exhumation to lower crustal levels. To identify major crust forming events, basement granitoids were dated by LA-SF-ICPMS and SHRIMP-II U-Pb analyses of zircons. The geochronological results revealed that the Eastern Rhodope Massif consists of two crustal units, a structurally lower Permo-Carboniferous unit corresponding to the Thracia Terrane and a structurally upper Late Jurassic/Early Cretaceous unit corresponding to the Rhodope Terrane, like it was documented for the Central Rhodope Massif. Inherited zircons in the orthogneisses from the Thracia Terrane of the Eastern Rhodope Massif indicate the presence of a pre-existing Neoproterozoic and Ordovician-Silurian basement in this region. Triassic magmatism is witnessed by the zircons of few orthogneisses from the easternmost Rhodope Massif and is interpreted to be related to rifting processes. Whole-rock major and trace element analyses indicate that the metagranitoids from both terranes originated in a subduction-related magmatic-arc environment. The Sr-Nd isotope data for both terranes of the Eastern and Central Rhodope Massif suggest a mixed crust-mantle source with variable contributions of older crustal material as already indicated by the presence of inherited zircons. Geochemical and isotopic similarity of the basement of the Thracia Terrane and the Pelagonian Zone implies that the Thracia Terrane is a fragment of a formerly unique Permo-Carboniferous basement, separated by rifting and opening of the Meliata-Maliac ocean system in Triassic times. A branch of the Meliata-Maliac ocean system, the Nestos Ocean, subducted northwards in Late Jurassic times leading to the formation of the Late Jurassic/Early Cretaceous Rhodope magmatic arc on remnants of the Thracia Terrane as suggested by inherited Permo-Carboniferous zircons. The ~150 Ma zircon ages of the orthogneisses from the Rhodope Terrane indicate that subduction-related magmatism and HP/UHP metamorphism occurred during the same subduction phase. Subduction ceased due to the closure of the Nestos Ocean in the Late Jurassic/Early Cretaceous. The post-Jurassic evolution of the Rhodope Massif is characterized by the exhumation of the Rhodope core complex in the course of extensional tectonics associated with late granite intrusions in Eocene to Miocene times.

Elastizität porenüberspannender Membranen: eine kraftmikroskopische Studie

Membranen spielen eine essentielle Rolle bei vielen wichtigen zellulären Prozessen. Sie ermöglichen die Erzeugung von chemischen Gradienten zwischen dem Zellinneren und der Umgebung. Die Zellmembran übernimmt wesentliche Aufgaben bei der intra- und extrazellulären Signalweiterleitung und der Adhäsion an Oberflächen. Durch Prozesse wie Endozytose und Exozytose werden Stoffe in oder aus der Zelle transportiert, eingehüllt in Vesikel, welche aus der Zellmembran geformt werden. Zusätzlich bietet sie auch Schutz für das Zellinnere. Der Hauptbestandteil einer Zellmembran ist die Lipiddoppelschicht, eine zweidimensionale fluide Matrix mit einer heterogenen Zusammensetzung aus unterschiedlichen Lipiden. In dieser Matrix befinden sich weitere Bausteine, wie z.B. Proteine. An der Innenseite der Zelle ist die Membran über Ankerproteine an das Zytoskelett gekoppelt. Dieses Polymernetzwerk erhöht unter anderem die Stabilität, beeinflusst die Form der Zelle und übernimmt Funktionenrnbei der Zellbewegung. Zellmembranen sind keine homogenen Strukturen, je nach Funktion sind unterschiedliche Lipide und Proteine in mikrsokopischen Domänen angereichert.Um die grundlegenden mechanischen Eigenschaften der Zellmembran zu verstehen wurde im Rahmen dieser Arbeit das Modellsystem der porenüberspannenden Membranen verwendet.Die Entwicklung der porenüberspannenden Membranen ermöglicht die Untersuchung von mechanischen Eigenschaften von Membranen im mikro- bis nanoskopischen Bereich mit rasterkraftmikroskopischen Methoden. Hierbei bestimmen Porosität und Porengröße des Substrates die räumliche Auflösung, mit welcher die mechanischen Parameter untersucht werdenrnkönnen. Porenüberspannende Lipiddoppelschichten und Zellmembranen auf neuartigen porösen Siliziumsubstraten mit Porenradien von 225 nm bis 600 nm und Porositäten bis zu 30% wurden untersucht. Es wird ein Weg zu einer umfassenden theoretischen Modellierung der lokalen Indentationsexperimente und der Bestimmung der dominierenden energetischen Beiträge in der Mechanik von porenüberspannenden Membranen aufgezeigt. Porenüberspannende Membranen zeigen eine linear ansteigende Kraft mit zunehmender Indentationstiefe. Durch Untersuchung verschiedener Oberflächen, Porengrößen und Membranen unterschiedlicher Zusammensetzung war es für freistehende Lipiddoppelschichten möglich, den Einfluss der Oberflächeneigenschaften und Geometrie des Substrates, sowie der Membranphase und des Lösungsmittels auf die mechanischen Eigenschaften zu bestimmen. Es ist möglich, die experimentellen Daten mit einem theoretischen Modell zu beschreiben. Hierbei werden Parameter wie die laterale Spannung und das Biegemodul der Membran bestimmt. In Abhängigkeit der Substrateigenschaften wurden für freitragende Lipiddoppelschichten laterale Spannungen von 150 μN/m bis zu 31 mN/m gefunden für Biegemodulde zwischen 10^(−19) J bis 10^(−18) J. Durch Kraft-Indentations-Experimente an porenüberspannenden Zellmembranen wurde ein Vergleich zwischen dem Modell der freistehenden Lipiddoppelschichten und nativen Membranen herbeigeführt. Die lateralen Spannungen für native freitragende Membranen wurden zu 50 μN/m bestimmt. Weiterhin konnte der Einfluss des Zytoskeletts und der extrazellulä-rnren Matrix auf die mechanischen Eigenschaften bestimmt und innerhalb eines basolateralen Zellmembranfragments kartiert werden, wobei die Periodizität und der Porendurchmesser des Substrates das räumliche Auflösungsvermögen bestimmen. Durch Fixierung der freistehenden Zellmembran wurde das Biegemodul der Membran um bis zu einem Faktor 10 erhöht. Diese Arbeit zeigt wie lokal aufgelöste, mechanische Eigenschaften mittels des Modellsystems der porenüberspannenden Membranen gemessen und quantifiziert werden können. Weiterhin werden die dominierenden energetischen Einflüsse diskutiert, und eine Vergleichbarkeit zurnnatürlichen Membranen hergestellt.rn

Contributions to exact approaches in combinatorial optimization

The focus of this thesis is to contribute to the development of new, exact solution approaches to different combinatorial optimization problems. In particular, we derive dedicated algorithms for a special class of Traveling Tournament Problems (TTPs), the Dial-A-Ride Problem (DARP), and the Vehicle Routing Problem with Time Windows and Temporal Synchronized Pickup and Delivery (VRPTWTSPD). Furthermore, we extend the concept of using dual-optimal inequalities for stabilized Column Generation (CG) and detail its application to improved CG algorithms for the cutting stock problem, the bin packing problem, the vertex coloring problem, and the bin packing problem with conflicts. In all approaches, we make use of some knowledge about the structure of the problem at hand to individualize and enhance existing algorithms. Specifically, we utilize knowledge about the input data (TTP), problem-specific constraints (DARP and VRPTWTSPD), and the dual solution space (stabilized CG). Extensive computational results proving the usefulness of the proposed methods are reported.

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