Quantum Chromodynamics(QCD) is part of the Standard Model(SM) that describes the interaction of fundamental particles. In QCD, due to the fact that strong coupling constant is large at low energies, perturbative approaches do not work. For this reason, non-perturbative approaches have to be used for studying the properties of hadrons. Among several non-perturbative approaches, QCD sum rules is one of the reliable methods which is applied to understand the properties of hadrons and their interactions. In this thesis, the semileptonic rare decays of $B$ meson to $K_{1}(1270)$ and $K_{1} (1400)$ are analyzed in the framework of three point QCD sum rules approach. The $Brightarrow K_{1} (1270,1400) ell^+ ell^-$ decays are significant flavor changing neutral current (FCNC) decays of the $B$ meson, since FCNC processes are forbidden at tree level at SM. These decays are sensitive to the new physics beyond SM. The radiative $Brightarrow K_{1}(1270) gamma$ decay is observed experimentally. Although semileptonic $Bto K_1(1270,1400)$ decays are still not observed, they are expected to be observed at future B factories. These decays happens at the quark level with $brightarrow s ell^+ ell^- $ transition, providing new opportunities for calculating CKM matrix elements: $V_{tb}$ and $V_{ts}$. Applying three point QCD sum rules to $Brightarrow K_{1} (1270,1400) ell^+ ell^-$ decays is tricky, due to the fact that the $K_{1} (1270)$ and $K_{1} (1400)$ states are the mixtures of ideal $^{3}P_{1}(K_{1}^{A})$ and $^{1}P_{1}(K_{1}^{B})$ orbital angular momentum states. First, by taking axial vector and tensor current definitions for $K_1$ mesons, the transition form factors of $Brightarrow K_{1A} ell^+ ell^-$ and $Brightarrow K_{1B} ell^+ ell^-$ are calculated. Then using the definitions for $K_1$ mixing, the transition form factors of $Brightarrow K_{1} (1270,1400) ell^+ ell^-$ decays are obtained. The results of these form factors are used to estimate the branching ratio of $B$ meson into $K_1(1270)$ and $K_1(1400)$. The results obtained for form factors and branching fractions are also compared with the ones in the literature.

The idea of effective field theory (EFT) was developed decades ago in low-energy strong-interaction - hadronic and nuclear - physics. After introducing chiral perturbation theory (ChPT), we focus in this dissertation on three non-perturbative cases that standard ChPT cannot deal with by itself. First, we investigate pion-nucleon (πN) scattering around the delta resonance, which is an important non-perturbative feature of low-energy nuclear physics. We show that in order to describe πN scattering around the delta peak, a power counting is necessary that goes beyond the power counting of ChPT. Using this new power counting, we calculate the phase shifts in the spin-3/2 P-wave channel up to next-to-next-to-leading order (NNLO). Second, in order to clarify the issue of renormalization and power counting of nucleon-nucleon potentials, we use a toy model to illustrate how to build effective theories for singular potentials, which some nuclear potentials belong to. We consider a central attractive 1/r² potential perturbed by a 1/r⁴ correction. We show that leading-order counterterms are needed in all partial waves where the potential overcomes the centrifugal barrier, and that the additional counterterms at next-to-leading order are the ones expected on the basis of dimensional analysis. Finally, we illustrate how non-perturbative EFT can be used to study neutron-antineutron oscillation inside the deuteron. We build an EFT for a model-independent, systematic study of two-unit baryon-number (|ΔB| = 2) violation in the context of nuclear physics. To cope with the non-perturbative deuteron structure, we apply the pionless version of this EFT to calculate deuteron decay. The decay width is obtained up to next-to-leading order. We show that the contribution of direct two-nucleon annihilation to the deuteron decay appears only at NNLO.

Made available in DSpace on 2014-06-11T19:25:30Z (GMT). No. of bitstreams: 0 Previous issue date: 2011-03-30Bitstream added on 2014-06-13T19:32:39Z : No. of bitstreams: 1 machado_fa_me_ift.pdf: 655529 bytes, checksum: 09aa0eb55f5a6e66c8c52d66ea1e85e7 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / O presente trabalho diz respeito ao vértice ghost-gluon da Cromodinâmica Quântica, o qual, de acordo com a identidade de Taylor, não possui correções perturbativas no calibre de Landau para uma determinada configuração de momentos. Estudamos este vértice numa configuração para a qual não há provas de um tal resultado, que é para o momento do gluon igual a zero. Para tanto, adotamos a abordagem da Teoria Dinâmica de Perturbação, que consiste em inserir características não perturbativas da teoria em sua expansão perturbativa. Trata-se de uma tentativa de caráter fenomenológico apenas, que objetiva explorar propriedades da teoria no domínio infravermelho por meio de cálculos de loop. Utilizamos duas informações não perturbativas: Primeiramente, uma massa finita do gluon, visto que há consideráveis indicações de que ele apresente uma massa, embora esta seja o que se chama de dinâmica – ela, inerentemente, varia de um valor finito no infravermelho para zero no ultravioleta. Em segundo, um resultado recente acerca da carga efetiva da Cromodinâmica Quântica, na qual é considerada uma massa dinâmica do gluon. Calculamos então a correção, a 1 loop, do vértice ghost-gluon, com o fim de verificar o quão próxima a função de renormalização (~Z1) desse vértice é de 1. O resultado obtido foi positivo neste sentido: ~Z1 difere pouco de 1, como mostrado no Cap. 5. O resultado, ainda, é melhor ajustado aos dados da rede quando consideramos a referida carga efetiva, do que quando usamos a constante de acoplamento como um parâmetro de ajuste. Portanto, nossa abordagem um tanto fenomenológica, baseada numa massa dinâmica do gluon, é ao menos consistente e dá suporte à aproximação ~Z1 1, comumente efetuada no estudo das equações de Schwinger-Dyson da Cromodinâmica Quântica / The present work concerns the ghost-gluon vertex of Quantum Chromodynamics, which, according to the Taylor identity, has no perturbative corrections to any order, in the Landau gauge and for a specific momentum configuration. We study this vertex for a momentum configuration for which there is no proof of such a result, which is the one with a zero gluon momentum. The framework we adopt for it is the Dynamical Perturbation Theory approach, which consists of inserting some nonperturbative information of the theory into its perturbative expansion. It is a phenomenological attempt only, intended to probe infrared properties of the theory by means of loop calculations. We have made use of two nonperturbative informations: First, a finite gluon mass, since there are even more indications that the gluon presents a mass, though it is a dynamical one – it intrinsically changes from finite in the infrared, to zero in the ultraviolet. Second, a recent result on the effective charge of Quantum Chromodynamics, which itself considers a dynamical gluon mass. We calculate the 1-loop correction to the ghost-gluon vertex, aiming at verifying how close to 1 the ghost-gluon vertex renormalization function (~Z1) is. The result obtained was positive in this direction: ~Z1 does not differ much from unity, as shown in Chap.5. Moreover, our result ts better the lattice data when we consider the mentioned effective charge, than when we set the coupling constant as a t parameter. Therefore, our somewhat phenomenological approach based on a dynamical gluon mass is, at least, consistent, and supports the approximation ~Z1 1, usually performed in the study of the Schwinger-Dyson equations of Quantum Chromodynamics

Strongly coupled systems are elusive and not suitable to be described by conventional perturbative approaches. However, they are ubiquitous in nature, especially in particle physics. The lattice formulation of quantum field theories provided a unique framework in which the physical content of these systems could be precisely determined. Combined with numerical techniques, the lattice formalism allowed to precisely determined physical quantities describing the thermodynamics, as well as the spectroscopy of strongly interacting theories. In this work, the lattice formulation has been employed to probe the effectiveness of a recently proposed method, which aims at determining the renormalized energy-momentum tensor in non perturbative regimes. The latter plays a fundamental role to quantitatively describe the thermodynamics and fluid-dynamics of hot, dense systems, or to characterize theories that enlarge the actual standard model. In all these aspects, only a non perturbative approach provides physically reliable results: hence a non perturbative determination of the energy momentum tensor is fundamental. The new method consists in defining suitable lattice Ward identities probed by observables built with the gradient flow. The new set of identities exhibits many interesting qualities, arising from the UV finiteness of such probes, and allows to define a numerical strategy for estimating the renormalization constants of the lattice energy-momentum tensor. In this work the method has been tested within two different quantum theories, with the purpose of understanding its effectiveness and reliability.

O objetivo deste trabalho foi incluir o méson escalar $\\kappa$ na núvem de mésons estranhos do próton e verificar se, desta forma, a contribuição de estranheza para as suas propriedades eletromagnéticas poderia ser explicada pelo modelo da núvem mesônica. Os observáveis que quantificam tal contribuição são os fatores de forma estranhos elétrico ($G_E^s$) e magnético ($G_M^s$), que têm sido objeto de grande interesse experimental nos últimos 10 anos. Usando a versão da nuvem que inclui o méson $\\kappa$, nós calculamos $G_E^s$ e $G_M^s$ em função do momento transferido dentro do intervalo 0 $\\leq Q^2 \\leq$ 1,2 GeV$^2$, de modo a abranger toda a gama de dados disponíveis no momento. Comparamos nossos resultados com os dados existentes para $G_E^s$ e $G_M^s$ e encontramos um ótimo acordo entre experimento e modelo, demonstrando que a inclusão do $\\kappa$ na núvem de mésons do próton é fundamental para que o seu conteúdo de estranheza possa ser compreendido. / The goal of this work was to include the scalar $\\kappa$ meson on the meson cloud of the proton, and then to verify if the strangeness contribution to the electromagnetic properties of the proton could be explained by the meson cloud model. The observables that quantify such a contribution are the electric ($G_E^s$) and magnetic ($G_M^s$) strange form factors, which have been subject of great experimental interest in the last 10 years. Using the version of the cloud which includes the $\\kappa$ meson, we calculated $G_E^s$ and $G_M^s$ as a function of the transferred momentum in the interval 0 $\\leq Q^2 \\leq$ 1.2 GeV$^2$, to cover the full range of available data at the time. We compared our results with existing data for $G_E^s$ and $G_M^s$ and we found a good agreement between experiment and model, showing that including $\\kappa$ on the meson cloud of the proton is crucial to understand its strangeness content.

Afin de poursuivre la croissance imposée par la loi de Moore, les circuits numériques deviennent de plus en plus parallèles, avec un nombre important d’unités de calcul distinctes. L’utilisation de l’optique peut s’avérer intéressante pour leur assurer une bande passante élevée. Au contraire, les liens traditionnels (électriques) commencent à montrer leurs limites en terme de consommation par unité d’information échangée. Dans un tel contexte, il est alors nécessaire de développer des interconnexions optiques dont les procédés de fabrication restent compatibles avec le standard CMOS. Si le transport de la lumière est aisé à obtenir au voisinage de 1.55 μm avec le couple Silicium/Silice, l’obtention de sources LASER est nettement plus difficile puisque le silicium (gap indirect) ne permet pas de réaliser le gain optique requis. Une solution consiste alors à reporter par collage moléculaire des vignettes de composés à base de semi-conducteurs III-V.Dans cette thèse, nous nous intéresserons uniquement à une source bien particulière, basée sur les modes de galerie (WGM) dans les résonateurs à symétrie circulaire, de quelques micromètres de rayon. Nous verrons comment tirer profit des éléments a priori perturbateurs que sont les contacts électriques (absorbants) de sorte à diminuer le seuil LASER. La mise en place d’un modèle semianalytique permet d’obtenir un dimensionnement ultra-rapide de la source monolithique obtenue, en optimisant la géométrie et la position des électrodes de contact. La collection de la lumière dans un guide par couplage évanescent donne lieu à de complexes interactions. Là encore, une modélisation à partir de la théorie des modes couplés a permis d’en comprendre les rouages, et d’en tirer profit. Le guide lui-même peut alors servir à favoriser une seule et unique longueur d’onde d’émission. Avec des éléments actifs situés à proximité de ces guides, on peut même obtenir une source ultra-compacte et modulable dont on contrôle la longueur d’onde d’émission par un élément extérieur au LASER. La dernière partie de cette thèse fournit des résultats expérimentaux, obtenus avec une chaine "pilote" sur des wafers 200 mm (CEA LETI) en se limitant à des procédés CMOS. On démontre donc la faisabilité des sources proposées dans les chapitres précédents ainsi que la possibilité de les intégrer un lien optique complet (source, routage et détection). / To follow the evolution imposed by Moore’s law, digital circuits are becoming more and more parallelized with a large number of independent computational units. Optics may be used to provide them the necessary very high bandwidth, as traditional electrical links begin to suffer from their high consumption per transferred bit. In such cases, developing CMOS compatible optical interconnects can be necessary. If light transport around wavelength 1.55 μm is quite easily obtained thanks to the Silicon/Silica couple, obtaining laser sources is much more difficult because silicon (indirect gap) can not be used to provide optical gain. An alternate solution consists in using molecular bonding of III-V semiconductor based dies onto silicon wafers. In this thesis, we only focus on a very specific source based on Whispering Galery Modes (WGM) inresonators with circular symmetry, with a few micrometers radius. We will see how to take advantage of perturbative elements such as the electrical contacts (necessary absorbing) to decrease the lasing threshold. The use of a semi analytical model provides ultra fast design of these monolithic source, optimizing the the geometry and position of the contacting electrodes. Light collection in an optical waveguide by evanescent coupling to the source leads to complexinteractions. Modelling them from Coupled Mode Theory demonstrates how it works, and how to take advantage of them to control the lasing wavelength. The optical waveguide itself can then be used to promote a single wavelength emission. Laying out active elements around the collecting waveguide, one can get modulated and ultra-compact sources for wavelength tuning or mode hoping applications, with an external active control. The last part of this thesis provides experimental results obtained with a 200 mm pilot line at CEALETI, using CMOS compatible processes. Feasibility of the sources suggested in the previous chapters is demonstrated with their integration in a complete optical link (source, routing and detection).

Surface electromyography records the motor unit action potential signals in the vicinity of the electrode to reveal information on muscle activation. Decomposition of sEMG signals for characterization of constituent motor unit action potentials in terms of amplitude and firing times is useful for clinical research as well as diagnosis of neurological disorders. Successful decomposition of sEMG signals would allow for pertinent motor unit action potential information to be acquired without discomfort to the subject or the need for a well-trained operator (compared with intramuscular EMG). To determine amplitudes and firing times for motor unit action potentials in an sEMG recording, Szlavik's perturbation based decomposition may be applied. The decomposition was initially applied to synthetic sEMG signals and then to experimental data collected from the biceps brachii. Szlavik's decomposition estimator yields satisfactory results for synthetic and experimental sEMG signals with reasonable complexity.

This licentiate thesis addresses two important aspects of the van der Waals and the Casimir-Polder ground-state and excited-state (resonance) interactions between two atoms or molecules. The first is the finite-size effect and the second is the non-perturbative effect. Going beyond the usual assumption of atoms and molecules as point particles and adopting a description of finite size, the divergence inherent in such interaction energies in the limit of zero separation distance between the two interacting atoms or molecules is removed. The attainment of finite interaction energy at such close separation distance facilitates the estimation of van der Waals force contribution to the binding energy of the molecules, and towards surfaces. This is particularly important for noble atoms. We investigate in detail for a pair of helium (He) atoms and krypton (Kr) atoms, and for a pair of methane (CH4) molecules considering its environmental importance. The application of finite size further leads to finite self energies of the atoms. The expression of the interaction energy, as is discussed in detail in this thesis, typically contains a logarithmic factor of the form ln(1-x). Formerly, in evaluating the interaction energies, this factor is customarily series-expanded and truncated in the leading order with certain assumptions. This thesis explores the effect of using the full expression, which we refer to as the non-perturbative (or, the non-expanded) theory, analytically wherever possible as well as numerically. The combined application of the finite-size theory and the non-perturbative theory results in as much as 100% correction in the self energy of atoms in vacuum. This may give rise to significant physical consequences, for example, in the permeabilities of atoms across dielectric membranes. The non-perturbative theory, in addition, exhibits interesting behaviour in the retarded resonance interaction. / <p>QC 20160509</p>

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第19496号 / 理博第4156号 / 新制||理||1597(附属図書館) / 32532 / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)准教授 笹倉 直樹, 教授 田中 貴浩, 教授 杉本 茂樹 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

Despite its history of more than one hundred years, the phenomenon of superconductivity has not lost any of its allure. During that time the concept and perception of the superconducting state - both from an experimental and theoretical point of view - has evolved in way that has triggered increasing interest. What was initially believed to simply be the disappearance of electrical resistivity, turned out to be a universal and inevitable result of quantum statistics, characterized by many more aspects apart from its zero resistivity. The insights of BCS-theory eventually helped to uncover its deep connection to particle physics and consequently led to the formulation of the Anderson-Higgs-mechanism. The very core of this theory is the concept of gauge symmetry (breaking). Within the framework of condensed-matter theory, gauge invariance is only one of several symmetry groups which are crucial for the description and classification of superconducting states. \\ In this thesis, we employ time-reversal, inversion, point group and spin symmetries to investigate and derive possible Hamiltonians featuring spin-orbit interaction in two and three spatial dimensions. In particular, this thesis aims at a generalization of existing numerical concepts to open up the path to spin-orbit coupled (non)centrosymmetric superconductors in multi-orbital models. This is done in a two-fold way: On the one hand, we formulate - based on the Kohn-Luttinger effect - the perturbative renormalization group in the weak-coupling limit. On the other hand, we define the spinful flow equations of the effective action in the framework of functional renormalization, which is valid for finite interaction strength as well. Both perturbative and functional renormalization groups produce a low-energy effective (spinful) theory that eventually gives rise to a particular superconducting state, which is investigated on the level of the irreducible two-particle vertex. The symbiotic relationship between both perturbative and functional renormalization can be traced back to the fact that, while the perturbative renormalization at infinitesimal coupling is only capable of dealing with the Cooper instability, the functional renormalization can investigate a plethora of instabilities both in the particle-particle and particle-hole channels. \\ Time-reversal and inversion are the two key symmetries, which are being used to discriminate between two scenarios. If both time-reversal and inversion symmetry are present, the Fermi surface will be two-fold degenerate and characterized by a pseudospin degree of freedom. In contrast, if inversion symmetry is broken, the Fermi surface will be spin-split and labeled by helicity. In both cases, we construct the symmetry allowed states in the particle-particle as well as the particle-hole channel. The methods presented are formally unified and implemented in a modern object-oriented reusable and extendable C++ code. This methodological implementation is employed to one member of both families of pseudospin and helicity characterized systems. For the pseudospin case, we choose the intriguing matter of strontium ruthenate, which has been heavily investigated for already twenty-four years, but still keeps puzzling researchers. Finally, as the helicity based application, we consider the oxide heterostructure LaAlO$_{3}$/SrTiO$_{3}$, which became famous for its highly mobile two- dimensional electron gas and is suspected to host topological superconductivity. / Trotz seiner über hundertjährigen Geschichte seit seiner Entdeckung hat das Phänomen der Supraleitung nichts von seiner ursprünglichen Faszination eingebüßt. Vielmehr hat sich in der Zwischenzeit der Begriff und das Verständnis des supraleitenden Zustandes in einer Weise weiterentwickelt, die das Interesse daran eher hat zunehmen lassen. Was anfänglich ausschließlich für ein Verschwinden des elektrischen Widerstands gehalten wurde, ist tatsächlich ein universelles und unvermeidliches Resultat der Quantenstatistik und besitzt viel mehr bemerkenswerte Eigenschaften als nur den widerstandslosen elektrischen Transport. Die Erkenntnisse der BCS-Theorie haben schließlich dazu geführt die tiefe Verbindung zur Teilchenphysik zu offenbaren und trugen entscheidend zur Formulierung des Anderson-Higgs-Mechanismus bei. Der wichtigste Baustein dieser Theorie ist das Konzept der (Brechung der) Eichsymmetrie. Im Rahmen der Festkörperphysik ist die Eichsymmetrie nur eine von mehreren Symmetrien, die eine essentielle Rolle für die Beschreibung und Einordnung von Phänomenen der Supraleitung spielen. \\ In dieser Arbeit wenden wir Zeitumkehr-, (räumliche) Inversions-, Punktgruppen- und Spin-Symmetrien an, um mögliche Hamilton-Operatoren in zwei und drei räumlichen Dimensionen, welche Spin-Bahn-Kopplung enthalten, herzuleiten und zu untersuchen. Diese Arbeit zielt auf eine Verallgemeinerung von existierenden numerischen Konzepten ab und erschließt den Weg die supraleitenden Eigenschaften von Modellen mit starker Spin-Bahn-Kopplung und mit oder ohne Inversionszentrum zu untersuchen. Dies geschieht mit Hilfe zweier methodischer Ansätze. Erstens formulieren wir aufbauend auf dem Kohn-Luttinger Effekt die störungstheoretische Renormierungsgruppe im Limes schwacher Kopplung. Zweitens verwenden wir die spinaufgelösten Flussgleichungen der effektiven Wirkung im Rahmen der funktionalen Renormierungsgruppe, die auch für endliche Wechselwirkungsstärke gültig sind. Die symbiotische Ergänzung der perturbativen und funktionalen Renormierungsgruppen ist darauf zurückzuführen, dass es mit der perturbativen Methode zwar möglich ist die Cooper Instabilität bei infinitesimaler Wechselwirkung numerisch exakt zu berechnen, aber nur die funktionale Renormierungsgruppe auch Teilchen-Loch Kondensate zugänglich macht. \\ Zeitumkehr- und Inversionssymmetrie sind die beiden Schlüsselsymmetrien, die verwendet werden, um zwei Szenarien zu unterscheiden. Falls sowohl Zeitumkehr- als auch Inversionssymmetrie gültig sind, sind die Fermiflächen zweifach entartet und durch einen Pseudospin-Freiheitsgrad charakterisiert. Im Gegensatz dazu führt der Verlust der Inversionssymmetrie zur Spinaufspaltung der Fermiflächen, die dann durch die sogenannte Helizität gekennzeichnet sind. In beiden Fällen leiten wir alle symmetrie-erlaubten Zustände her, welche die entsprechenden Teilchen-Teilchen und Teilchen-Loch Kondensate beschreiben. Die vorstellten und verallgemeinerten Methoden sind im Rahmen dieser Arbeit formal miteinander verbunden und in einem modernen objektorientierten C++ Quellcode implementiert worden. \\ Als erste vorläufige Anwendungen für diese methodische Implementierung betrachten wir zwei Systeme, die jeweils einer der beiden Familien zugeordnet werden können. Zum einen berechnen wir in der Pseudospin-Formulierung der perturbativen und funktionalen Renormierungsgruppen die Instabilitäten eines Dreiorbital-Modells für Strontiumruthenat, das seit seiner erstmaligen Synthese trotz intensiver Forschung immer noch Rätsel aufgibt. Zum anderen betrachten wir das zweidimensionale Elektronengas, das sich an der Schnittstelle zwischen LaAlO$_{3}$ und SrTiO$_{3}$ bildet und welches durch seine hohe Ladungsträgermobilität bekannt geworden ist.