In this dissertation, a low energy theory approach is applied to the studies of Dark Matter direct detection experiments and two-dimensional Quantum Chromodynamics (QCD) spectra. We build a general framework of non-relativistic effective field theory of Dark Matter direct detection using non-relativistic operators. Any Dark Matter particle theory can be translated into the coefficients of an effective operator and any effective operator can be related to a most general description of the nuclear response. Response functions are evaluated for common Dark Matter targets. Based on the effective field theory we perform an analysis of the experimental constraints on the full parameter space of elastically scattering Dark Matter. We also formulate an analytic approach to solving two-dimensional gauge theories. We find that in theories with confinement, in a conformal operator basis, the decoupling of high scaling-dimension operators from the low-energy spectrum occurs exponentially fast in their scaling-dimension. Consequently the low-energy spectrum of a strongly coupled system like QCD can be calculated using a truncated conformal basis, to an accuracy parametrized exponentially by the cutoff dimension. We apply the conformal basis approach in two models, a two-dimensional QCD with an adjoint fermion at large N, and a two-dimensional QCD with a fundamental fermion at finite N. It is shown that the low energy spectrum converges efficiently in both cases.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20901号 / 理博第4353号 / 新制||理||1625(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 川合 光, 教授 青木 慎也, 准教授 菅沼 秀夫 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

No description available.

No description available.

No description available.

No description available.

Depuis les années 1930, on sait que le noyau des atomes est composé de deux types de particules: les protons et les neutrons. Ces deux particules sont très similaires: d'une part le neutron est subtilement plus lourd (un pour mille) que le proton et d'autre part le proton porte une charge électrique positive tandis que le neutron est neutre. La petite différence de masse entre le neutron et le proton fourni l'énergie suffisante pour autoriser désintégration où un neutron se désintègre en un proton en émettant un électron et un anti-neutrino électronique. Aussi, le fait que le proton ne se désintègre pas assure la stabilité de l'atome d'hydrogène. De plus, on sait empiriquement que les paramètres de la désintégration déterminent la composition des noyaux d'atomes stables plus lourds que l'hydrogène. Il est donc raisonnable de penser que si la différence de masse entre le neutron et le proton était de signe opposé ou seulement légèrement différente, l'Univers visible serait surement très différent de celui que l'on connait. Il est donc essentiel de comprendre l'origine de cette différence de masse à partir des principes premiers de la physique. C'est à ce problème, et à des problèmes liés à celui-ci, qu'essaye de répondre ce travail. Dans la compréhension actuelle de la physique, les neutrons et les protons sont des particules composées de particules élémentaires appelées quark up (symbole u) et quark down (symbole d). Le proton est un état lié uud et le neutron est un état lié udd. Les quarks up et down sont deux particules similaires: elles sont toutes deux légères (de l'ordre de quelques MeV) et leurs charges électriques sont différentes. / .

Les mésons lourd-légers jouent un rôle majeur dans la recherche de nouvelle physique au delà du modèle standard. En particulier, les propriétés du méson B sont utilisées pour contraindre la matrice Cabibbo-Kobayashi-Maskawa (CKM) qui décrit les changements de saveur d’un quark lors d’une interaction faible.Les interactions entre quarks et gluons sont décrites par la théorie de l'interaction forte (QCD). Cette dernière prédit, qu'à faible énergie, le couplage de la théorie croît rendant tout traitement perturbatif impossible. La QCD sur réseau est une régularisation non-perturbative de la QCD adaptée aux simulations numériques. Néanmoins, l'étude des mésons lourd-légers est particulièrement délicate puisqu'elle nécessite la prise en compte de nombreuses échelles d'énergies. La théorie effective des quarks lourds (HQET) peut alors être utilisée : elle consiste en une expansion systématique du Lagrangien QCD et des fonctions de corrélation en puissance de 1/m où m est la masse du quark lourd.Après avoir présenté les outils de la QCD sur réseaux, un calcul de la masse du quark b avec nf=2 quarks dynamiques est présentée. Toutes les étapes sont réalisées de manière non-perturbative et le résultat est une importante vérification de la valeur actuellement citée par le PDG et qui repose essentiellement sur des calculs perturbatifs.Dans la seconde partie de la thèse, après avoir présenté les Lagrangiens décrivant les mésons lourd-légers dans la limite chirale, je présente le calcul de deux couplages. Le premier couplage est associé à la transition hadronique B* '→Bπ où B* 'est la première excitation radiale du méson B vecteur. Il est obtenue en étudiant le rapport de fonctions de corrélation à trois et deux points et le problème aux valeurs propres généralisées (GEVP) est utilisé pour isoler la contribution de l'état excité. Dans un second temps, le couplage h décrivant la transition entre des mésons B scalaire et pseudoscalaire est calculé. Ce couplage intervient dans les extrapolations chirales de différentes quantités, comme la constante de désintégration du méson B scalaire. Nous verrons que le couplage h est important et qu'il ne peux pas être négligé.Finalement, je présenterai nos résultats concernant le calcul de la masse et de la constant d'annihilation de la première excitation radiale du méson D. Je comparerai la masse obtenue avec celle du nouvel état récemment découvert par la Collaboration BaBar et j'expliquerai comment le calcul de la constante d'annihilation peut aider dans la résolution du problème "1/2 vs. 3/2''. Tout au long de ce travail, le GEVP est utilisé pour réduire la contribution des états excités. De plus les extrapolations chirales et la limite du continue sont étudiées afin de tenir compte des différentes sources d'erreurs statistiques. / Heavy-light mesons play an important role in the search of new physics beyond the Standard Model. In particular B-mesons properties can be used to put constraints on the matrix elements of the Cabibbo-Kobayashi-Maskawa (CKM) mixing matrix governing flavour-changing weak decays.The dynamics of quarks and gluons are described by Quantum Chromodynamic (QCD). This theory predicts that, at low energies, the associated coupling constant increases, making the use of perturbative methods ineffective. Lattice QCD is a non-perturbative regularization scheme of QCD, suitable for numerical simulations. However, studying heavy-light mesons remains a challenging task due to the many different energy scales that must be considered simultaneously on the lattice. In this work, I use the Heavy Quark Effective Theory (HQET), which consists in a systematic expansion of the QCD Lagrangian and correlation functions in 1/m where m is the mass of the heavy quark.After a presentation of the main techniques used in lattice simulations, a computation of the b-quark mass with nf=2 dynamical quarks is presented. All the steps are performed non-perturbatively, offering an important cross-check of the value cited in the PDG which mainly relies on perturbation theory. A computation of the B-meson decay constant at static and first orders in HQET will be also presented and phenomenological implication are discussed.In the second part of this thesis, after introducing the Heavy Meson Chiral Lagrangians and its different couplings, I present the lattice computation of two such couplings. The first one is associated to the hadronic transitionB* '→Bπ where B* 'is the radial excitation of the vector B meson. The Generalized Eigenvalue Problem (GEVP) will be used to extract information about the excited state from the ratio of three-point to two-point correlation functions and I will discuss the phenomenological implications of our results. Then, I will present the computation of the coupling h between the scalar and the pseudoscalar B mesons using two-point correlation functions. This coupling enters the formulae used to guide the chiral extrapolations when positive parity states are taken into account. We will see that h is large compared to the other couplings and that B meson orbital excitation degrees of freedom cannot be missed in chiral loops.Finally, I will present the lattice computation of the mass and decay constant of the first radial excitation of the D meson. The mass will be compared with the recently observed state by the BaBar Collaboration and I show how the decay constant can help to solve the so-called "1/2 vs. 3/2'' puzzle. In this work, the GEVP is used to control the contribution from higher excited states and continuum and chiral extrapolations are performed to take intro account systematic errors.

Nesta dissertação nós revisamos aspectos gerais de teorias de gauge, os princípios da formulação de rede da cromodinâmica quântica (QCD) e algumas propriedades de quarkônios pesados, i.e. estados ligados de um quark pesado e seu antiquark. Como um exemplo de simulações de Monte Carlo de modelos de rede, apresentamos aplicações nos casos do oscilador harmônico e teorias de gauge SU(2). Nós estudamos o efeito de incorporar o propagador de gluon de simulações na rede em um modelo de potencial para a descrição do quarkônio, no caso do botômomio e do charmônio. Nós usamos em ambos os casos uma abordagem numérica para calcular as massas dos estados de quarkônio. O espectro resultante é comparado em ambos os casos com cálculos usando o potencial de Coulomb mais linear (ou potencial Cornell). / In this dissertation we review general aspects of gauge theories, the principles of the lattice formulation of quantum chromodynamics (QCD) and some properties of heavy quarkonia, i.e. bound states of a heavy quark and its antiquark. As an illustration of Monte Carlo simulations of lattice models, we present applications in the case of the harmonic oscillator and SU(2) gauge theory. We study the effect of incorporating the gluon propagator from lattice simulations into a potential model for the description of quarkonium, in the case of bottomonium and charmonium. We use a numerical approach to evaluate masses of quarkonium states. The resulting spectrum is compared in both cases to calculations using the Coulomb plus linear (or Cornell) potential.

Nesta tese, discutimos em detalhes a técnica das Regras de Soma da QCD (RSQCD) e suas aplicações em sistemas hadrônicos situados na região de massa do charmônio. Em particular, calculamos a massa, as constantes de decaimento e acoplamento, bem como a largura de decaimento dos estados $Y(4260)$,$Y(3940)$ e $Z_c^+(3900)$. Além disso, consideramos a existência do parceiro estranho deste último, o $Z^+_{cs}(3970)$, e calculamos sua largura de decaimento de modo a prever seu valor em futuros experimentos. Usamos modelos ditos exóticos para descrever tais estados. Para o $Y(4260)$ e o $Y(3940)$ usamos correntes de mistura charmônio - tetraquarks. Para os estados carregados usamos uma corrente de tetraquarks. Como resultado das aplicações das RSQCD nesses sistemas, obtivemos valores de massa e largura compatíveis com os valores experimentais medidos pelas colaborações BESIII, Belle, Babar e CLEO-c. Dessa forma, podemos afirmar que os modelos utilizados fornecem uma boa interpretação para esses estados. Investigamos também, aplicando técnicas de teorias efetivas, os estados carregados $Z^+_c(4025)$ e novamente o $Z_c^+(3900)$, além dos estados no setor do bottom $Z^+_b(10610)$ e $Z_b^+(10650)$. Usamos as Lagrangianas da Simetria Oculta de Calibre Local (HGS) e também as regras da Simetria de Spin do Quark Pesado (HQSS) para determinarmos as interações $D\\bar{D}^*$, $D^*\\bar{D}^*$, $B\\bar{B}^*$ e $B^*\\bar{B}^*$ via troca de mésons vetoriais pesados e devido à troca de dois píons correlacionados e não correlacionados entre si. Determinamos o potencial para cada interação e, com isso, procuramos por pólos na solução da matriz $T$ na equação de Bethe-Salpeter, cujo kernel é dado pelo potencial. Como resultado desses estudos, obtivemos para as interações no setor do charme, estados ligados cuja massa e largura estão em razoável acordo com os estados carregados $Z^+_c(4025)$ e $Z_c^+(3900)$. Para as interações no setor do bottom, obtemos um estado fracamente ligado próximo do limiar de massa $B\\bar{B}^*$ cuja largura e massa são compatíveis com a estrutura $Z_b^+(10610)$ observada pela Colaboração Belle. Obtivemos um cusp no limiar de massa $B^*\\bar{B}^*$ próximo do valor da estrutura $Z_b^ (10650)$ / In this thesis, we discuss in details the QCD Sum Rules (QCDSR) technique and its application to the study of hadronic systems situated in the charmonium mass region. In particular, we applied QCDSR to calculate hadronic properties such as the mass, the coupling contants as well as the total decay width of the $Y(4260)$, $Y(3940)$ and $Z_c^+(3900)$ charmoniumlike states. We have also predicted the decay width of the strange partner of the $Z_c^+(3900)$, called $Z_{cs}^+(3970)$, to be searched in future experiments. In order to describe these states, we used exotic models. For $Y(4260)$ and $Y(3940)$ states we used mixed charmonium-tetraquarks interpolating currents. For the charged states we used tetraquark currents. As a result of the application of QCDSR to these systems, we obtained masses and decay widths in good agreement with the experimental values measured by BESIII, Babar, and CLEO-c collaborations. Therefore, the currents we used within QCDSR approach provide a good interpretation for these states. Furthermore, applying effective field theories techniques, we also investigated the charged states $Z_c^+(4025)$ and $Z_c^+(3900)$, in addition to $Z^+_b(10610)$ and $Z_b^+(10650)$ in the bottom sector. Specifically, we used hidden local symmetry Lagrangians (HGS) together with heavy quark spin symmetry rules (HQSS) in order to study the interactions $D\\bar{D}^*$, $D^*\\bar{D}^*$, $B\\bar{B}^*$ and $B^*\\bar{B}^*$ by means of the heavy vector exchange and also from the exchange of two pions, interacting and noninteracting among themselves. We obtained the potencial for each interaction, then we used them as a kernel of the Bethe-Salpeter equation in order to look for poles in the $T$-matrix. Our aim was to relate these poles with the charmoniumlike states of interest. As a result, in the charm sector, we obtained bound states whoses masses and widths are in a good agreement with the charged states we have studied. With respect to the bottom sector, we have found a loosely bound state very close to the $B\\bar{B}^*$ threshold with mass and width compatible with the structure $Z_b(10610)$ observed by Belle colaboration. We have obtained a cusp in the $B^*\\bar{B}^*$ threshold very close to the mass of the $Z_b^+(10650)$ state.