Exotic B-c-like molecules in QCD sum rules

We use the QCD sum rules to study possible B-c-like molecular states. We consider isoscalar J(P) = 0(+) and J(P) = 1(+) D(*) B(*) molecular currents. We consider the contributions of condensates up to dimension eight and we work at leading order in alpha(s). We obtain for these states masses around 7 GeV. (C) 2012 Elsevier B.V. All rights reserved.

1(--) and 0(++) heavy four-quark and molecule states in QCD

We estimate the masses of the 1(--) heavy four-quark and molecule states by combining exponential Laplace (LSR) and finite energy (FESR) sum rules known perturbatively to lowest order (LO) in alpha(s) but including non-perturbative terms up to the complete dimension-six condensate contributions. This approach allows to fix more precisely the value of the QCD continuum threshold (often taken ad hoc) at which the optimal result is extracted. We use double ratio of sum rules (DRSR) for determining the SU(3) breakings terms. We also study the effects of the heavy quark mass definitions on these LO results. The SU(3) mass-splittings of about (50-110) MeV and the ones of about (250-300) MeV between the lowest ground states and their 1st radial excitations are (almost) heavy-flavor independent. The mass predictions summarized in Table 4 are compared with the ones in the literature (when available) and with the three Y-c(4260, 4360, 4660) and Y-b(10890) 1(--) experimental candidates. We conclude (to this order approximation) that the lowest observed state cannot be a pure 1(--) four-quark nor a pure molecule but may result from their mixings. We extend the above analyzes to the 0(++) four-quark and molecule states which are about (0.5-1) GeV heavier than the corresponding 1(--) states, while the splittings between the 0(++) lowest ground state and the 1st radial excitation is about (300-500) MeV. We complete the analysis by estimating the decay constants of the 1(--) and 0(++) four-quark states which are tiny and which exhibit a 1/M-Q behavior. Our predictions can be further tested using some alternative non-perturbative approaches or/and at LHCb and some other hadron factories. (c) 2012 Elsevier B.V. All rights reserved.

Self-bound interacting QCD matter in compact stars

The quark gluon plasma (QGP) at zero temperature and high baryon number is a system that may be present inside compact stars. It is quite possible that this cold QGP shares some relevant features with the hot QGP observed in heavy ion collisions, being also a strongly interacting system. In a previous work we have derived from the QCD Lagrangian an equation of state (EOS) for the cold QGP, which can be considered an improved version of the MIT bag-model EOS. Compared to the latter, our EOS reaches higher values of the pressure at comparable baryon densities. This feature is due to perturbative corrections and also to nonperturbative effects. Here we apply this EOS to the study of neutron stars, discussing the absolute stability of quark matter and computing the mass-radius relation for self-bound (strange) stars. The maximum masses of the sequences exceed two solar masses, in agreement with the recently measured values of the mass of the pulsar PSR J1614-2230, and the corresponding radii of around 10-11 km.

QCD sum rules for the 'Z POT + IND C' (3900) state.

We use the QCD sum rules to study the recently observed charmonium-like structure Z+ c (3900) as a tetraquark state. We evaluate the three-point function and extract the coupling constants of the Z+ c J/ψ π+, Z+ c ηc ρ+ and Z+ c D+ ¯D∗0 vertices and the corresponding decay widths in these channels. The results obtained are in good agreement with the experimental data and supports to the tetraquark picture of this state.

The charmed pentaquark Θc(3250) from QCD sum rules.

We study, using the QCD sum rule framework, the possible existence of a charmed pentaquark that we call Θc(3250). In the QCD side we work at leading order in αs and consider condensates up to dimension 10. The mass obtained: mΘc = (3.21±0.13) GeV, is compatible with the mass of the structure seen by BaBar Collaboration in the decay channel B− → ￣p Σ++ c π−π−.

Relation between Tcc,bb and Xc,b from QCD.

We have studied, using double ratio of QCD (spectral) sum rules, the ratio between the masses of Tcc and X(3872) assuming that they are respectively described by the D−D∗ and D− ¯D∗ molecular currents. We found (within our approximation) that the masses of these two states are almost degenerate. Since the pion exchange interaction between these mesons is exactly the same, we conclude that if the observed X(3872) meson is a D ¯D∗ + c.c. molecule, then the DD∗ molecule should also exist with approximately the same mass. An extension of the analysis to the b-quark case leads to the same conclusion. We also study the SU(3) breakings for the T s Q Q /TQ Q mass ratios. Motivated by the recent Belle observation of two Zb states, we revise our determination of Xb by combining results from exponential and FESR sum rules.

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.

Transport properties of YBa 2 Cu 3 O 7, PrBa 2 Cu 3 O 7-superlattices

The understanding of the coupling between superconducting YBa2Cu3O7 (YBCO) layers decoupled by non superconducting PrBa2Cu3O7 (PBCO) layers in c-axis oriented superlattices was the aim of this thesis. For this purpose two conceptually different kind of transport experiments have been performed. rnrnIn the first type of transport experiments the current is flowing parallel to the layers. Here the coupling is probed indirectly using magnetic vortex lines, which are penetrating the superlattice. Movement of the vortex segments in neighbouring YBCO layers is more or less coherent depending on the thickness of both the superconducting and non superconducting layers. This in-plane transport was measured either by sending an external current through bridges patterned in the superlattice or by an induced internal current. rnThe vortex-creep activation energy U was determined by analysis of the in-plane resistive transition in an external magnetic field B oriented along the c-axis. The activation energies for two series of superlattices were investigated. In one series the thickness of the YBCO layers was constant (nY=4 unit cells) and the number of the PBCO unit cells was varied, while in the other the number of PBCO layers was constant (nP=4) and nY varied. The correlation length of the vortex system was determined to be 80 nm along the c-axis direction. It was found that even a single PBCO unit cell in a superlattice effectively cuts the flux lines into shorter weakly coupled segments, and the coupling of the vortex systems in neighbouring layers is negligible already for a thickness of four unit cells of the PBCO layers. A characteristic variation of the activation energy for the two series of superlattices was found, where U0 is proportional to the YBCO thickness. A change in the variation of U0 with the current I in the specimen was observed, which can be explained in terms of a crossover in the vortex creep process, generated by the transport current. At low I values the dislocations mediated (plastic) vortex creep leads to thermally assisted flux-flow behaviour, whereas at high current the dc transport measurements are dominated by elastic (collective) creep.rnThe analysis of standard dc magnetization relaxation data obtained for a series superlattices revealed the occurrence of a crossover from elastic (collective) vortex creep at low temperature to plastic vortex creep at high T. The crossover is generated by the T dependent macroscopic currents induced in the sample. The existence of this creep crossover suggests that, compared with the well known Maley technique, the use of the normalized vortex creep activation energy is a better solution for the determination of vortex creep parameters.rnrnThe second type of transport experiments was to measure directly a possible Josephson coupling between superconducting CuO2 double planes in the superlattices by investigation of the transport properties perpendicular to the superconducting planes. Here three different experiments have been performed. The first one was to pattern mesa structures photolithographically as in previous works. The second used three-dimensional nanostructures cut by a focused ion beam. For the these two experiments insufficient patterning capabilities prevented an observation of the Josephson effect in the current voltage curves. rnA third experiment used a-axis and (110) oriented YBCO films, where in-plane patterning can in principle be sufficient to measure transport perpendicular to the superconducting planes. Therefore the deposition of films with this unusual growth orientation was optimized and investigated. The structural and microstructural evolution of c-axis to a-axis orientation was monitored using x-ray diffraction, scanning electron microscopy and magnetization measurements. Films with full a-axis alignment parallel to the substrate normal could be achieved on (100)SrTiO3. Due to the symmetry of the substrate the c-axis direction in-plane is twofold. Transferring the deposition conditions to films grown on (110)SrTiO3 allowed the growth of (110) oriented YBCO films with a unique in-plane c-axis orientation. While these films were of high quality by crystallographic and macroscopic visual inspection, electron microscopy revealed a coherent crack pattern on a nanoscale. Therefore the actual current path in the sample was not determined by the macroscopic patterning which prohibited investigations of the in-plane anisotropy in this case.rn

Microstructure of epitaxial thin films of the ferromagnetic shape memory alloy Ni 2 MnGa

Gegenstand dieser Arbeit ist die Präparation und die ausführliche Charakterisierung epitaktischer Dünnschicht-Proben der Heusler Verbindung Ni2MnGa. Diese intermetallische Verbindung zeigt einen magnetischen Formgedächtnis-Effekt (MFG), der sowohl im Bezug auf mögliche Anwendungen, als auch im Kontext der Grundlagenforschung äußerst interessant ist. In Einkristallen nahe der Stöchiometrie Ni2MnGa wurden riesige magnetfeldinduzierte Dehnungen von bis zu 10 % nachgewiesen. Der zugrundeliegende Mechanismus basiert auf einer Umverteilung von kristallographischen Zwillings-Varianten, die eine tetragonale oder orthorhombische Symmetrie besitzen. Unter dem Einfluss des Magnetfeldes bewegen sich die Zwillingsgrenzen durch den Kristall, was eine makroskopische Formänderung mit sich bringt. Die somit erzeugten reversiblen Längenänderungen können mit hoher Frequenz geschaltet werden, was Ni2MnGa zu einem vielversprechenden Aktuatorwerkstoff macht. rnDa der Effekt auf einem intrinsischen Prozess beruht, eignen sich Bauteile aus MFG Legierungen zur Integration in Mikrosystemen (z.B. im Bereich der Mikrofluidik). rnrnBislang konnten große magnetfeldinduzierte Dehnungen nur für Einkristalle und Polykristalle mit hoher Porosität („foams") nachgewiesen werden. Um den Effekt für Anwendungen nutzbar zu machen, werden allerdings Konzepte zur Miniaturisierung benötigt. Eine Möglichkeit bieten epitaktische dünne Filme, die im Rahmen dieser Arbeit hergestellt und untersucht werden sollen. Im Fokus stehen dabei die Optimierung der Herstellungsparameter, sowie die Präparation von freitragenden Schichten. Zudem werden verschiedene Konzepte zur Herstellung freistehender Mikrostrukturen erprobt. Mittels Röntgendiffraktometrie konnte die komplizierte Kristallstruktur für verschiedene Wachstumsrichtungen verstanden und die genaue Verteilung der Zwillingsvarianten aufgedeckt werden. In Verbindung mit Mikroskopie-Methoden konnte so die Zwillingsstruktur auf verschiedenen Längenskalen geklärt werden. Die Ergebnisse erklären das Ausbleiben des MFG Effekts in den Proben mit (100) Orientierung. Andererseits wurde für Schichten mit (110) Wachstum eine vielversprechende Mikrostruktur entdeckt, die einen guten Ausgangspunkt für weitere Untersuchungen bietet.rnDurch die spezielle Geometrie der Proben war es möglich, Spektroskopie-Experimente in Transmission durchzuführen. Die Ergebnisse stellen den ersten experimentellen Nachweis der Änderungen in der elektronischen Struktur einer metallischen Verbindung während des martensitischen Phasenübergangs dar. Durch Messen des magnetischen Zirkulardichroismus in der Röntgenabsorption konnten quantitative Aussagen über die magnetischen Momente von Ni und Mn getroffen werden. Die Methode erlaubt überdies die Beiträge von Spin- und Bahn-Moment separat zu bestimmen. Durch winkelabhängige Messungen gelang es, die mikroskopische Ursache der magnetischen Anisotropie aufzuklären. Diese Ergebnisse tragen wesentlich zum Verständnis der komplexen magnetischen und strukturellen Eigenschaften von Ni2MnGa bei.rn

Baryons in the chiral regime

Quantum Chromodynamics (QCD) is the theory of strong interactions, one of the four fundamental forces in our Universe. It describes the interaction of gluons and quarks which build up hadrons like protons and neutrons. Most of the visible matter in our universe is made of protons and neutrons. Hence, we are interested in their fundamental properties like their masses, their distribution of charge and their shape. \\rnThe only known theoretical, non-perturbative and {\it ab initio} method to investigate hadron properties at low energies is lattice Quantum Chromodynamics (lattice QCD). However, up-to-date simulations (especially for baryonic quantities) do not achieve the accuracy of experiments. In fact, current simulations do not even reproduce the experimental values for the form factors. The question arises wether these deviations can be explained by systematic effects in lattice QCD simulations.rnrnThis thesis is about the computation of nucleon form factors and other hadronic quantities from lattice QCD. So called Wilson fermions are used and the u- and d-quarks are treated fully dynamically. The simulations were performed using gauge ensembles with a range of lattice spacings, volumes and pion masses.\\rnFirst of all, the lattice spacing was set to be able to make contact between the lattice results and their experimental complement and to be able to perform a continuum extrapolation. The light quark mass has been computed and found to be $m_{ud}^{\overline{\text{MS}}}(2\text{ GeV}) = 3.03(17)(38)\text{ MeV}$. This value is in good agreement with values from experiments and other lattice determinations.\\rnElectro-magnetic and axial form factors of the nucleon have been calculated. From these form factors the nucleon radii and the coupling constants were computed. The different ensembles enabled us to investigate systematically the dependence of these quantities on the volume, the lattice spacing and the pion mass.\newpage Finally we perform a continuum extrapolation and chiral extrapolations to the physical point.\\rnIn addition, we investigated so called excited state contributions to these observables. A technique was used, the summation method, which reduces these effects significantly and a much better agreement with experimental data was achieved. On the lattice, the Dirac radius and the axial charge are usually found to be much smaller than the experimental values. However, due to the carefully investigation of all the afore-mentioned systematic effects we get $\langle r_1^2\rangle_{u-d}=0.627(54)\text{ fm}^2$ and $g_A=1.218(92)$, which is in agreement with the experimental values within the errors.rnrnThe first three chapters introduce the theoretical background of form factors of the nucleon and lattice QCD in general. In chapter four the lattice spacing is determined. The computation of nucleon form factors is described in chapter five where systematic effects are investigated. All results are presented in chapter six. The thesis ends with a summary of the results and identifies options to complement and extend the calculations presented. rn

Chirale effektive Feldtheorie mit Vektormesonen : vom elektromagnetischen Formfaktor zur virtuellen Compton-Streuung

Die vorliegende Arbeit beschäftigt sich mit der Modellierung niederenergetischer elektromagnetischer und hadronischer Prozesse im Rahmen einer manifest lorentzinvarianten, chiralen effektiven Feldtheorie unter expliziter, dynamischer Berücksichtigung resonanter, das heißt vektormesonischer Freiheitsgrade. Diese effektive Theorie kann daher als Approximation der grundlegenden Quantenchromodynamik bei kleinen Energien verstanden werden. Besonderes Augenmerk wird dabei auf das verwendete Zähl- sowie Renormierungschema gelegt, wodurch eine konsistente Beschreibung mesonischer Prozesse bis zu Energien von etwa 1GeV ermöglicht wird. Das verwendete Zählschema beruht dabei im Wesentlichen auf einem Argument für großes N_c (Anzahl der Farbfreiheitsgrade) und lässt eine äquivalente Behandlung von Goldstonebosonen (Pionen) und Resonanzen (Rho- und Omegamesonen) zu. Als Renormierungsschema wird das für (bezüglich der starken Wechselwirkung) instabile Teilchen besonders geeignete complex-mass scheme als Erweiterung des extended on-mass-shell scheme verwendet, welches in Kombination mit dem BPHZ-Renormierungsverfahren (benannt nach Bogoliubov, Parasiuk, Hepp und Zimmermann) ein leistungsfähiges Konzept zur Berechnung von Quantenkorrekturen in dieser chiralen effektiven Feldtheorie darstellt. Sämtliche vorgenommenen Rechnungen schließen Terme der chiralen Ordnung vier sowie einfache Schleifen in Feynman-Diagrammen ein. Betrachtet werden unter anderem der Vektorformfaktor des Pions im zeitartigen Bereich, die reelle Compton-Streuung (beziehungsweise Photonenfusion) im neutralen und geladenen Kanal sowie die virtuelle Compton-Streuung, eingebettet in die Elektron-Positron-Annihilation. Zur Extraktion der Niederenergiekopplungskonstanten der Theorie wird letztendlich eine Reihe experimenteller Datensätze verschiedenartiger Observablen verwendet. Die hier entwickelten Methoden und Prozeduren - und insbesondere deren technische Implementierung - sind sehr allgemeiner Natur und können daher auch an weitere Problemstellungen aus diesem Gebiet der niederenergetischen Quantenchromodynamik angepasst werden.

Hadronic matrix elements in lattice QCD

The lattice formulation of Quantum ChromoDynamics (QCD) has become a reliable tool providing an ab initio calculation of low-energy quantities. Despite numerous successes, systematic uncertainties, such as discretisation effects, finite-size effects, and contaminations from excited states, are inherent in any lattice calculation. Simulations with controlled systematic uncertainties and close to the physical pion mass have become state-of-the-art. We present such a calculation for various hadronic matrix elements using non-perturbatively O(a)-improved Wilson fermions with two dynamical light quark flavours. The main topics covered in this thesis are the axial charge of the nucleon, the electro-magnetic form factors of the nucleon, and the leading hadronic contributions to the anomalous magnetic moment of the muon. Lattice simulations typically tend to underestimate the axial charge of the nucleon by 5 − 10%. We show that including excited state contaminations using the summed operator insertion method leads to agreement with the experimentally determined value. Further studies of systematic uncertainties reveal only small discretisation effects. For the electro-magnetic form factors of the nucleon, we see a similar contamination from excited states as for the axial charge. The electro-magnetic radii, extracted from a dipole fit to the momentum dependence of the form factors, show no indication of finite-size or cutoff effects. If we include excited states using the summed operator insertion method, we achieve better agreement with the radii from phenomenology. The anomalous magnetic moment of the muon can be measured and predicted to very high precision. The theoretical prediction of the anomalous magnetic moment receives contribution from strong, weak, and electro-magnetic interactions, where the hadronic contributions dominate the uncertainties. A persistent 3σ tension between the experimental determination and the theoretical calculation is found, which is considered to be an indication for physics beyond the Standard Model. We present a calculation of the connected part of the hadronic vacuum polarisation using lattice QCD. Partially twisted boundary conditions lead to a significant improvement of the vacuum polarisation in the region of small momentum transfer, which is crucial in the extraction of the hadronic vacuum polarisation.

Helicity methods in LO and NLO QCD calculations

The goal of this thesis is the acceleration of numerical calculations of QCD observables, both at leading order and next–to–leading order in the coupling constant. In particular, the optimization of helicity and spin summation in the context of VEGAS Monte Carlo algorithms is investigated. In the literature, two such methods are mentioned but without detailed analyses. Only one of these methods can be used at next–to–leading order. This work presents a total of five different methods that replace the helicity sums with a Monte Carlo integration. This integration can be combined with the existing phase space integral, in the hope that this causes less overhead than the complete summation. For three of these methods, an extension to existing subtraction terms is developed which is required to enable next–to–leading order calculations. All methods are analyzed with respect to efficiency, accuracy, and ease of implementation before they are compared with each other. In this process, one method shows clear advantages in relation to all others.

Efficient algorithms for NLO QCD event generators

In this thesis we present techniques that can be used to speed up the calculation of perturbative matrix elements for observables with many legs ($n = 3, 4, 5, 6, 7, ldots$). We investigate several ways to achieve this, including the use of Monte Carlo methods, the leading-color approximation, numerically less precise but faster operations, and SSE-vectorization. An important idea is the use of enquote{random polarizations} for which we derive subtraction terms for the real corrections in next-to-leading order calculations. We present the effectiveness of all these methods in the context of electron-positron scattering to $n$ jets, $n$ ranging from two to seven.