The scalar mesons have caused much debate amongst hadronic physicists for many years. Even today the number of scalars is hotly contested, and there is almost no agreement on the composition of any of the experimentally observed states, except perhaps for the K*(_0) (1430). This thesis attempts to shed light on both of these problems via the application of analyticity to two different quantities. Recently a number of authors have proposed the existence of a light, strange, scalar meson known as the k. We perform a direct search of the best available πK scattering data to determine whether or not this resonance exists. This is done by constructing contour integrals from these data and determining the number of poles present inside the contour. We do not need to model either the internal dynamics of the state nor the form of the background scattering. The number of poles found tells us the number of resonances present and their positions allow us to estimate the resonance parameters. We find that there is only one resonance in scalar πK scattering below 1800 MeV and this is identified with the established K*(_0)(1430). We find no evidence for the k. Secondly, applying Cauchy's Theorem to the vacuum polarisation function leads to a relation between experimental and theoretical integrals known as a Finite Energy Sum Rule (FESR). FESRs are used to explore the scalar, isoscalar non-strange current and allow us to determine which of the experimentally observed scalar, isoscalar mesons is most likely to be the uũ + dd state. We find that the lightest scalar, isoscalar uũ dd state is not the fo(980) as suggested by some authors, but is rather the light, broad object known as the fo(400 - 1200). We are also able to estimate the average light quark mass and find m(_q)(l GeV(^2)) = 4.7 ± 0.9 MeV which is consistent with the recent estimates of this quantity from unquenched lattice QCD.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Neste trabalho calculamos os fatores de forma e constantes de acoplamento para os vértices B*sBK, B*BsK e BsBK* usando as Regras de Soma da Cromodinâmica Quântica (QCD). Ainda estão incluídos os diagramas não perturbativos. Nós usamos a técnica de considerar dois mésons fora da camada de massa para obter dois fatores de forma diferentes a fim de diminuir as incertezas. Os cálculos das incertezas foram incluídos neste trabalho. / In this work, we calculate the Form Factors and the Coupling Constants for the vertices B*sBK, BsB*K and BsBK* using the QCD Sum Rules. We use the technique of considering two mesons of shell to obtaining two differents form factors in order to give less uncertainty to the obtaining of the coupling constant. The evaluation of the uncertaints were included in this work.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Neste trabalho calculamos os fatores de forma e constantes de acoplamento para os vértices B*sBK, B*BsK e BsBK* usando as Regras de Soma da Cromodinâmica Quântica (QCD). Ainda estão incluídos os diagramas não perturbativos. Nós usamos a técnica de considerar dois mésons fora da camada de massa para obter dois fatores de forma diferentes a fim de diminuir as incertezas. Os cálculos das incertezas foram incluídos neste trabalho. / In this work, we calculate the Form Factors and the Coupling Constants for the vertices B*sBK, BsB*K and BsBK* using the QCD Sum Rules. We use the technique of considering two mesons of shell to obtaining two differents form factors in order to give less uncertainty to the obtaining of the coupling constant. The evaluation of the uncertaints were included in this work.

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.

Nesta tese de doutorado é utilizado o método das Regras de Soma da QCD para estudar a natureza dos novos estados ressonantes do charmonium: Y(3930), Y(4140), X(4350), Y(4260), Y(4360) e Y(4660). Há fortes evidências de que estes estados possuam estruturas hadrônicas não convencionais (ou exóticas) uma vez que as suas respectivas massas e canais de decaimento observados experimentalmente são inconsistentes com o que é esperado para o estado ressonante convencional do charmonium, J/psi. O mesmo fenômeno ocorre no setor do bottomonium, onde os novos estados Yb(10890) e Yb(11020) observados recentemente poderiam indicar a existência de novos estados exóticos do bottomonium. Neste sentido, verifica-se que o estado Y(4140) poderia ser descrito ou por uma estrutura molecular Ds*Ds* (0++) ou mesmo uma mistura entre estados moleculares Ds*Ds* (0++) e D*D* (0++). Já os estados Y(3930) e o X(4350) não podem ser descritos por correntes moleculares D*D* (0++) e Ds*Ds* (1-+), respectivamente. Verifica-se também que a estrutura molecular Psi(2S) f_0(980) (1--) descreve muito bem a massa do estado Y(4660). Uma extensão ao setor do bottomonium indica que o estado molecular Y(2S) f_0(980) é um bom candidato para descrever a estrutura do estado Yb(10890). É feita também uma estimativa para os possíveis estados moleculares formados por mésons D(*) e B(*), que poderão ser observados em futuros experimentos realizados pelo LHC. Um amplo estudo, utilizando o formalismo das Regras de Soma e também da Dupla Razão das Regras de Soma, é feito para calcular as massas dos bárions pesados na QCD. As estimativas para as massas dos bárions com um (Qqq) e com dois (QQq) quarks pesados são um excelente teste para a capacidade do método das regras de soma em prever a massa dos bárions que ainda não foram observados. / In this thesis, the QCD sum rules approach was used to study the nature of the new charmonium resonances: Y(3930), Y(4140), X(4350), Y(4260), Y(4360) and Y(4660). There is a strong evidence that these states have non-conventional (or exotic) hadronic structures since their respective masses and decay channels observed experimentally are inconsistent with what expected for a conventional charmonium state, J/psi. The same phenomenon occurs on the bottomonium sector, where new states like Yb(10890) and Yb(11020) observed recently could indicate the existence of new bottomonium exotic states. In this way, one verifies that the state Y(4140) could be described as a Ds*Ds* (0++) molecular state or even as a mixture of Ds*Ds* (0++) and D*D* (0++) molecular states. For the Y(3930) and X(4350) states, both cannot be described as a D*D* (0++) and Ds*Ds* (1-+), respectively. From a sum rule point of view, the Y(4660) state could be described as a Psi(2s) f_0(980) (1--) molecular state. The extension to the bottomonium sector is done in a straightforward way to demonstrate that the Y(2S) f_0(980) molecular state is a good candidate for describing the structure of the Yb(10890) state. In the following, one estimates the mass of the exotic Bc-like molecular states using QCD Sum Rules - these exotic states would correspond to bound states of D(*) and B(*) mesons. All of these mass predictions could (or not) be checked in a near future experiments at LHC. A large study using the Double Ratio of Sum Rules approach has been evaluated for the study of the heavy baryon masses in QCD. The obtained results for the unobserved heavy baryons, with one (Qqq) and two (QQq) heavy quarks will be an excellent test for the capability of the sum rule approach in predicting their masses.

In this thesis, we investigate the masses, form factors and magnetic dipole moments of some light octet, decuplet and heavy baryons containing a single heavy quark in the framework of the light cone QCD sum rules. The magnetic dipole moments can be measured considering radiative transitions within a multiplet or between multiplets. Analyzing the transitions among the baryons and calculating the above mentioned parameters can give us insight into the structure of those baryons. In analyzing the aforementioned processes, the transition form factors play a crucial role. In this thesis, the form factors for these transitions are calculated using the light cone QCD sum rules approach. In the limit when the light quark masses are equal, mu = md = ms, QCD has an SU(3) flavour symmetry which can be used to classify the light baryons. This classification results in the light decuplet, octet and singlet baryons. The baryons containing single heavy quark, on the other hand, can be classified according to the spin of the light degrees of freedom in the heavy quark limit, mQ -&gt / infinity. QCD at low energies, when the baryons are formed, is a non-perturbative theory. Hence, for phenomenology of the baryons, the QCD sum rules as a more powerful non-perturbative approach is used. Understanding the properties of nucleons is one of the main objectives of QCD. To investigate the properties of the nucleons, the axial N-Delta(1232) transition form factors are calculated within the light cone QCD sum rules method. A comparison of our results on those form factors with the predictions of lattice QCD and quark model is presented. The nucleon electromagnetic form factors are also calculated in the same framework using the most general form of the nucleon interpolating current. Using two forms of the distribution amplitudes (DA&rsquo / s), predictions for the form factors are presented and compared with existing experimental data. It is shown that our results describe the existing experimental data remarkably well. Another important property of the baryons is their magnetic moments. The magnetic moments of the heavy Xi_Q (Q = b or c) baryons containing a single charm or bottom quark are calculated within the light cone QCD sum rules approach. A comparison of our results with the predictions of other approaches, such as relativistic and nonrelativistic quark models, hyper central model, Chiral perturbation theory, soliton and skyrmion models is presented. Moreover, inspired by the results of recent experimental discoveries for charm and bottom baryons, the masses and magnetic moments of the heavy baryons with J^2P = 3/2^+ containing a single heavy quark are studied also within the light cone QCD sum rules method. Our results on the masses of heavy baryons are in good agreement with predictions of other approaches, as well as with the existing experimental values. Our predictions on the masses of the states, which are not experimentally discovered yet, can be tested in the future experiments. A comparison of our results on the magnetic moments of these baryons and the hyper central model predictions is also presented.

In the present work some hadronic properties of the scalar &kappa / meson are studied. Using the QCD sum rules approach, which is a nonperturbative method, the mass and the overlap amplitude of this meson are calculated. As well as the mass and the overlap amplitude, &kappa / &rarr / K^+&pi / ^&minus / decay is also studied. For this decay the coupling constant g_&kappa / K^+&pi / ^&minus / is obtained using light cone QCD sum rules which is an extension of the QCD sum rules method. Moreover, the coupling constant is calculated using the experimental decay width and it is compared with the value obtained in light cone QCD sum rules approach. The result of the calculation of g_&kappa / K^+&pi / ^&minus / , the one obtained from light cone QCD sum rules approach, is also applied to acquire the f_0 &minus / &sigma / scalar mixing angle, &theta / s, using the ratio g^2 (&kappa / &rarr / K^+&pi / ^&minus / )/g^2 (&sigma / &rarr / &pi / &pi / ) obtained from experimental decay width. The value of scalar mixing angle is also compared with its experimental results.

The modifications of hadronic properties caused by an ambient nuclear medium are investigated within the scope of QCD sum rules. This is exemplified for the cases of the omega meson, the nucleon and the D meson. By virtue of the sum rules, integrated spectral densities of these hadrons are linked to properties of the QCD ground state, quantified in condensates. For the cases of the omega meson and the nucleon it is discussed how the sum rules allow a restriction of the parameter range of poorly known four-quark condensates by a comparison of experimental and theoretical knowledge. The catalog of independent four-quark condensates is covered and relations among these condensates are revealed. The behavior of four-quark condensates under the chiral symmetry group and the relation to order parameters of spontaneous chiral symmetry breaking are outlined. In this respect, also the QCD condensates appearing in differences of sum rules of chiral partners are investigated. Finally, the effects of an ambient nuclear medium on the D meson are discussed and relevant condensates are identified. / Die Veränderungen von Hadroneneigenschaften durch ein umgebendes nukleares Medium (Kernmaterie) werden mit der Methode der QCD-Summenregeln untersucht. Dies wird am Beispiel des omega-Mesons, des Nukleons und des D-Mesons vorgeführt. Durch die Summenregeln werden integrierte Spektraldichten dieser Hadronen in Beziehung zu Eigenschaften des QCD-Grundzustandes, quantifiziert in Kondensaten, gesetzt. Diskutiert wird am Beispiel des omega-Mesons und des Nukleons, wie diese Summenregeln eine Einschränkung des Parameterbereiches von wenig bekannten Vierquark-Kondensaten durch Vergleich von experimentellen und theoretischen Erkenntnissen erlauben. Ein Katalog unabhängiger Vierquark-Kondensate wird aufgestellt und Relationen zwischen diesen Kondensaten werden deutlich gemacht. Das Verhalten der Vierquark-Kondensate unter der chiralen Symmetriegruppe und der Zusammenhang mit Ordnungsparametern spontaner chiraler Symmetriebrechung werden behandelt. In dieser Hinsicht werden auch die in Differenzen der Summenregeln chiraler Partner eingehenden QCD-Kondensate untersucht. Schließlich werden die Effekte endlicher Kerndichten beim D-Meson diskutiert und relevante Kondensate identifiziert.

Στη διατριβή αυτή μελετάται η μονοτονία και η κυρτότητα των ριζών ορισμένων οικογενειών associated ορθογωνίων q-πολυωνύμων που εμφανίζονται στο q-ανάλογο του σχήματος Askey. Για τη μελέτη της μονοτονίας και της κυρτότητας των ριζών χρησιμοποιείται μια συναρτησιακή αναλυτική μέθοδος η οποία βασίζεται στην αναδρομική σχέση τριών όρων που ικανοποιεί οποιαδήποτε οικογένεια ορθογωνίων πολυωνύμων. Επίσης για τον υπολογισμό των αθροισμάτων Newton των ριζών χρησιμοποιείται η συναρτησιακή αναλυτική μλεθοδος που παρουσιάστηκε από τους Υφαντή, Κοκολογιαννάκη και Σιαφαρίκα για τον υπολογισμό των αθροισμάτων Newton των ριζών των scaled corecursive associated ορθογωνίων πολυωνύμων. Επειδή τα ορθογώνια q-πολυώνυμα είναι q-ανάλογα κλασικών ορθογωνίων πολυωνύμων παίρνοντας το όριο q-1 προκύπτουν αντίστοιχα αποτελέσματα για τις ρίζες των κλασσικών ορθογωνίων πολυωνύμων. Τα αποτελέσματα αυτά γενικεύουν ενοποιούν και βελτιώνουν προηγούμενα αποτελέσματα. / In this thesis, we study the monotonicity properties and the convexity of the zeros of some families of associated orthogonal q-polynomials. Also, we calculate the Newton sum rules of these zeros. For the study of the monotonicity of the zeros, we use a functional analytic method based on the three terms recurrence relations satisfied by the associated orthogonal q-polynomials under consideration.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / A física de partículas vem atualmente estudando tópicos como o plasma de quarks e glúons (QGP), o bóson de Higgs e a matéria escura, que requerem experimentos de colisões entre partículas cada vez mais energéticas. Para isso, são necessários aceleradores capazes de gerar partículas projéteis a cada vez mais altas energias, o que pode levar a uma nova física. Quando novos dados surgem nos laboratórios, novos processos são necessários para explicar estes dados e algumas vezes a estrutura interna das partículas envolvidas é desconhecida. Nos modelos teóricos, usados para descrever estes processos de espalhamento, é comum introduzir o fator de forma. O fator de forma é simplesmente uma maneira de simular a sub-estrutura das partículas envolvidas nestes processos com função da energia ou momento. A obtenção dos atores de forma pode ser feita usando o método conhecido como Regras de Soma da QCD (RSQCD). Neste trabalho, será estudado o vértice D*Dp usando as RSQCD, de modo que seja possível obter os seus fatores de forma e sua constante de acoplamento. Para isso, foram estudados os casos em que o méson ρ e o méson D estão fora de suas camadas de massa. O vértice D*Dp é muito importante para entender melhor o ρπ Puzzle, onde o méson Ј/ψ decai ρπ em com um branching ratio maior do que o esperado (este é um processo suprimido pela regra de OZI). Estudando este processo com graus de liberdade mesnicos, é possível escapar da regra de OZI, uma vez que o processo Ј/ψ→ DD → ρπ não é suprimido por OZI. Ao se fazer isso, aparecerá, entre outros, o vértice D*Dp . Este é um vértice que também aparece em outros decaimentos, como por exemplo X(3872) →Ј/ψp e B→Ј/ψD. Ao final do desenvolvimento, os resultados obtidos neste trabalho para o vértice D*Dp foram comparados com outros encontrados na literatura, se mostrando compatíveis com estes outros trabalhos. / The particle physics have been studying topics like the Quark-Gluon Plasma (QGP), Higgs boson and dark matter, which require experiments in heavy-ion collisions. Therefore, accelerators capable of generate high energy particle beams are necessary and may generate new physics. When new data arise in the laboratories, new processes are necessary to explain this data and sometimes, the internal structure of the involved particles is unknow or are virtual. In the theoretical models, used to describe this scattering processes, is common to introduce the form factors. The form factor is a way to simulate the sub-structure of the involved particles as function of energy or momentum. The form factor can be obtained using a method called QCD Sum Rules (QCDSR). In this work, the vertex D*Dp will be studied using the QCDSR, in order to obtain its form factors and coupling constant.The D*Dp vertex is very important to understand the ρπ Puzzle, where the Ј/ψ meson decays in ρπ with a branching ratio bigger than expected (this is a suppressed process by the OZI Rule). Studying this process with hadronic degrees of freedom, its possible to escape of the OZI rule, once the Ј/ψ→ DD → ρπ is not suppressed by the OZI rule. In this process, the D*Dp vertex is necessary. There are other processes where this vertex is necessary: X(3872)→Ј/ψp and B→Ј/ψD for example. In this work, was only possible to obtain results from the ρ off-shell diagram. This results were compared with others obtained in the literature.