When calculating scattering processes in theories involving massless gauge bosons, such as gluons in Quantum Chromodynamics (QCD), one encounters infrared (IR), or soft, divergences. To obtain precise predictions, it is important to have exact expressions for these IR divergences, which are present in any on-shell scattering amplitude. Due to their long wavelength, soft gluons factorise with respect to short-distance, or hard, interactions and can be captured by correlators of semi-infinite Wilson lines. The latter obey a renormalisation group equation, which gives rise to exponentiation. The exponent can be represented diagrammatically in terms of weighted sums of Feynman diagrams, called webs. A web with L external legs, each with ni gluon attachments, is denoted (n1; n2; : : : ; nL). In this way all soft gluon interactions can be described by a soft anomalous dimension. It is currently known at three loops with lightlike kinematics, and at two loops with general kinematics. Our work is a step towards a three-loop result in general kinematics. In recent years, much progress has been made in understanding the general physical properties of scattering amplitudes and in exploiting these properties to calculate specific amplitudes. At the same time, we have discovered a lot of structure underpinning the space of multiple polylogarithms, the functions in terms of which most known amplitudes can be written. General properties include analyticity, implying that scattering amplitudes are analytic functions except on certain branch cuts, and unitarity, or conservation of probability. These two properties are both exploited by unitarity cuts. Unitarity cuts provide a diagrammatic way of calculating the discontinuities of a Feynman diagram across its branch cuts, which is often simpler than calculating the diagram itself. From this discontinuity, the original function can be reconstructed by performing a dispersive integral. In this work, we extend the formalism of unitarity cuts to incorporate diagrams involving Wilson-line propagators, where the inverse propagator is linear in the loop momenta, rather than the quadratic case which has been studied before. To exploit this for the calculation of the soft anomalous dimension, we first found a suitable momentum-space IR regulator and corresponding prescription, and then derived the appropriate largest time equation (LTE). We find that, as in the case of the scalar diagrams, most terms contributing to the LTE turn out to be zero, albeit for different reasons. This simplifies calculations considerably. This formalism is then applied to the calculation of webs with non-lightlike Wilson lines. As a test, we first looked at webs that have been previously studied using other methods. It emerges that, when using the correct variables, the dispersive integrals one encounters here are trivial, illustrating why unitarity cuts are a particularly useful tool for the calculation of webs. We observe that our technique is especially efficient when looking at diagrams involving three-gluon vertices, such as the (1; 1; 1) web and the Y diagram between two lines. We then focus on three-loop diagrams connecting three or four external non-lightlike lines and involving a three-gluon vertex. We calculate the previously unknown three-loop three-leg (1; 1; 3) web in general kinematics. We obtain a result which agrees with the recently calculated lightlike limit. We also develop a technique to test our results numerically using the computer program SecDec, and we find agreement with our analytical result. The result for the (1; 1; 3) web can then be exploited to gain insight into the more complicated three-loop four-leg (1; 1; 1; 2) web. Indeed, the (1; 1; 1; 2) web reduces to the (1; 1; 3) web in a certain collinear limit. We propose an ansatz for the (1; 1; 1; 2) web in general kinematics, based on a conjectured basis of multiple polylogarithms. The result for the (1; 1; 3) web, together with the known result for the lightlike limit of the (1; 1; 1; 2) web, imposes strong constraints on the ansatz. Using these constraints, we manage to fix all but four coefficients in the ansatz. We fit the remaining coefficients numerically, but find that the quality of the fit is not good. We find possible explanations for this poor quality. This calculation is still a work in progress. Our results provide a major step towards the full calculation of the three-loop soft anomalous dimension for non-lightlike Wilson lines. We calculated new results for three-loop webs, and also deepened the understanding of webs in general. We confirm a conjecture about the functional dependence of the soft anomalous dimension on the cusp angles. We also confirm earlier findings about the symbol alphabet of the relevant functions. This confirms the remarkable simplicity found earlier in the expressions for the soft anomalous dimension.

The Large Hadron Collider (LHC) has provided, and will continue to provide, data for collisions at the highest energies ever seen in a particle accelerator. A strong knowledge of the properties of amplitudes for Quantum Chromodynamics in the High Energy Limit is therefore important to interpret this data. We study this limit in the context of the High Energy Jets (HEJ) formalism. This formalism resums terms in the perturbative expansion of the cross-section that behave like αn/s log (s/-t)ⁿ¯¹, which are enhanced in this limit. Understanding this region is particularly important in certain key analyses at the LHC: for example, Higgs-boson- plus-dijet analyses where cuts are applied to pick out events with a large mjj and in many searches for new physics. In this thesis, we discuss two directions in which HEJ's accuracy has been improved. Firstly, we look at adding descriptions of partonic subprocesses which are formally sub-leading in the jet cross-section but Leading Logarithmic (LL) in the particular subprocess itself. This required the derivation of new effective vertices that describe the emission of a quark/anti-quark pair in a way that is consistent with the resummation procedure. The inclusion of such processes reduces HEJ's dependence on fixed-order calculations and marks an important step towards full Next-to-Leading Logarithmic (NLL) accuracy in the inclusive dijet cross-section. The second extension was to improve our description of events involving the emission of a Higgs boson along with jets. Specifically, we derive new effective vertices which keep the full dependence on the quark mass that appears in the loops that naturally arise in such amplitudes. The formalism is also simple enough to allow for any number of extra nal state jets in the process. Therefore, HEJ is unique in its ability to provide predictions for high-multiplicity Higgs-plus-jets processes with full nite quark mass e ects. Such a calculation is far beyond the reach of any xed order approach.

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

Made available in DSpace on 2014-06-11T19:25:30Z (GMT). No. of bitstreams: 0 Previous issue date: 2002-03Bitstream added on 2014-06-13T19:26:30Z : No. of bitstreams: 1 morales_ps_me_ift.pdf: 900348 bytes, checksum: 11b8ab9b4c422ec3a42face91d5074e6 (MD5) / O mecanismo de rearranjo de tubos de fluxo predito no limite de acoplamento forte da formulação Hamiltoniana da QCD na rede foi implementado num modelo de quarks constituintes e suas consequências investigadas para o espalhamento méson-méson. O rearranjo de tubos de fluxo leva a efeitos similares aos tradicionais efeitos de troca de quarks com troca de um glúon em interações hádron-hádron. Contudo, enquanto o primeiro está relacionado ao regime de confinamento da QCD, o último está relacionado ao regime de liberdade assintótica desta teoria. Mostra-se aqui que ambos mecanismos levam a resultados qualitativamente similares quando o potencial de rearranjo pode ser escrito como a soma de interações locais quark-quark, antiquark-antiquark e quark-antiquark. Para interações gerais, não locais e de longo alcance, o rearranjo de tubos de fluxo leva a resultados qualitativa e quantitativamente diferentes dos resultados de troca de quarks com troca de um glúon. As consequências disso para a fenomenologia das interações hádron-hádron são discutidas. / The mechanism of link rearrangement predicted in the strong coupling limit of Hamiltonian lattice QCD is implemented in a constituent quark model and its consequences for meson-meson scattering are investigated. Link rearrangement leads to effects similar to the traditional quark exchange with one gluon exchange in hadron-hadron interactions. However while the first is related to the confinement regime of QCD, the latter is related to the asymptotic freedom regime of this theory. It is shown here that both mechanisms lead to identical qualitative results when the rearrangement potential can be written as a sum of local quark-quark, antiqurk-antiquark e quark-antiquark. For general, long-range nonlocal interactions, link rearrangement leads to results qualitative and quantitatively different from those of quark exchange with one gluon exchange. The consequences of this for the phenomenology of hadron-hadron interactions are discussed.

Made available in DSpace on 2015-06-17T19:34:08Z (GMT). No. of bitstreams: 0 Previous issue date: 2013-06-11. Added 1 bitstream(s) on 2015-06-18T12:47:23Z : No. of bitstreams: 1 000809991.pdf: 663835 bytes, checksum: 99dfc3fa4c492e16d50e3e8a8ae1cf08 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / The rainbow-ladder approximation is a simple nonperturbative truncation scheme for nonperturbative calculations in Quantum Chromodynamics (QCD). It provides satisfactory results for the ground-states of light pseudoscalar and vector mesons, but for excited and exotic states, as well as for heavy-light mesons, this truncation provides less accurate results. In the present dissertation we have proposed a novel approach to go beyond the rainbow-ladder truncation, which we name dressed perturbation theory. The guiding principle of the approach is to modify the quadratic part of the QCD action by the addition of self-energy terms for the quarks and gluons, and perform perturbative calculations with the interaction action subtracted by the same self-energies. Instead of noninteracting propagators of traditional perturbative QCD calculations, the novel perturbative scheme is performed with dressed propagators. The self-energies used in the dressed propagators can be taken from the ladder approximation, or from lattice QCD simulations. Our main concern in the dissertation is the application of the formalism to the the quark propagator. The lowest nontrivial order corrections are two-loop vertex corrections. Numerical results are obtained for quark mass function and pion properties in the chiral limit for a simple ansatz for the gluon self-energy

Orientador: Gastão Inácio Krein / Banca: Arlene Cristina Aguilar / Banca: Bruno El-Bennich / Resumo:A aproximação "rainbow-ladder" (arcoíris-escada) é um esquema de truncamento não-perturbativo simples para cálculos não-perturbativos na cromodinâmica quântica (QCD). Ela fornece resultados satisfatórios para os estados fundamentais de mésons pseudo-escalares e vetoriais, mas para estados excitados e estados exóticos, como também para mésons pesados-leves, este esquema de truncamento fornece resultados menos precisos. Na presente dissertação propomos um novo método que vai além do truncamento "rainbow-ladder", que denominamos "dressed perturbation theory" (teoria de perturbação vestida). O princípio norteador do método é modificar a parte quadrática da ação da QCD pela adição de termos de autoenergia para os quarks e glúons e efetuar teoria de perturbação com a parte de interação da ação, subtraída das mesmas auto-energias. Ao invés de propagadores não-interagentes dos tradicionais cálculos de QCD perturbativa, o novo esquema perturbativo é implementado com propagadores vestidos. As auto-energias empregadas nos propagadores vestidos podem ser tomadas da aproximação "ladder", ou de simulações de QCD na rede. Nossa preocupação principal nesta dissertação é a aplicação do novo formalismo ao propagador dos quarks. As correções não-triviais de ordem mais baixa são correções de vértice. Resultados numéricos são obtidos para a função de massa dos quarks e propriedades do píon no limite quiral para um ansatz simples para a auto-energia do glúon / Abstract:The rainbow-ladder approximation is a simple nonperturbative truncation scheme for nonperturbative calculations in Quantum Chromodynamics (QCD). It provides satisfactory results for the ground-states of light pseudoscalar and vector mesons, but for excited and exotic states, as well as for heavy-light mesons, this truncation provides less accurate results. In the present dissertation we have proposed a novel approach to go beyond the rainbow-ladder truncation, which we name dressed perturbation theory. The guiding principle of the approach is to modify the quadratic part of the QCD action by the addition of self-energy terms for the quarks and gluons, and perform perturbative calculations with the interaction action subtracted by the same self-energies. Instead of noninteracting propagators of traditional perturbative QCD calculations, the novel perturbative scheme is performed with dressed propagators. The self-energies used in the dressed propagators can be taken from the ladder approximation, or from lattice QCD simulations. Our main concern in the dissertation is the application of the formalism to the the quark propagator. The lowest nontrivial order corrections are two-loop vertex corrections. Numerical results are obtained for quark mass function and pion properties in the chiral limit for a simple ansatz for the gluon self-energy / Mestre

Neste trabalho, nós estudamos a hadroprodução de charmonium em experimentos de alvo fixo com os três modelos: modelo de singleto de cor (CSM), modelo de evaporação de cor (CEM) e QCD não relativística (NRQCD). Os ajustes feitos aos dados experimentais nos permitiram concluir que o CSM subestima o valor da seção de choque de produção dos estados de charmonium J/ e (2S) e, portanto, não descreve adequadamente a hadroprodução nestes casos. Os modelos CEM e NRQCD por outro lado descreveram satisfatoriamente os dados, no entanto, o fato dos resultados experimentais possuírem grandes incertezas não nos permitiu comparar diretamente os dois modelos e desta forma concluir qual dos dois é mais adequado. / ln this work we evaluate the charmonium production at fixed-target experiments with three different models: the color singlet model (CSM), the color evaporation model (CEM) and the nonrelativistic quantum chromodynamics (NRQCD). We verify that the results of CSM under-preditcs the production cross-section for J / and (2S), thus, in this case, the CSM is an inadequate model. In addition, we find that the two models CEM and NRQCD satisfactorily predict the charmonium hadro-production. However, due to the fact that the experimental uncertainties are large we can not compare the two models.

In this dissertation we use the gauge/gravity duality approach to study the dynamics of strongly coupled non-Abelian plasmas. Ultimately, we want to understand the properties of the quark-gluon plasma (QGP), whose scientifc interest by the scientific community escalated exponentially after its discovery in the 2000\'s through the collision of ultrarelativistic heavy ions. One can enrich the dynamics of the QGP by adding an external field, such as the baryon chemical potential (needed to study the QCD phase diagram), or a magnetic field. In this dissertation, we choose to investigate the magnetic effects. Indeed, there are compelling evidences that strong magnetic fields of the order $eB\\sim 10 m_\\pi^2$ are created in the early stages of ultrarelativistic heavy ion collisions. The chosen observable to scan possible effects of the magnetic field on the QGP was the viscosity, due to the famous result $\\eta/s=1/4\\pi$ obtained via holography. In a first approach we use a caricature of the QGP, the $\\mathcal=4$ super Yang-Mills plasma to calculate the deviations of the viscosity as we add a magnetic field. We must emphasize, though, that a magnetized plasma has a priori seven viscosity coefficients (five shears and two bulks). In addition, we also study in this same model the anisotropic heavy quark-antiquark potential in the presence of a magnetic field. In the end, we propose a phenomenological holographic QCD-like model, which is built upon the lattice QCD data, to study the thermodynamics and the viscosity of the QGP with an external strong magnetic field. / Nesta dissertação utilizamos uma abordagem via dualidade gauge/gravity para estudar a dinâmica de plasmas não-Abelianos fortemente interagentes. Nosso objetivo último visa aplicações para o plasma de quarks e glúons (QGP), cujo interesse científico cresceu exponencialmente depois de sua descoberta em meados dos anos 2000 ao colidir-se íons ultrarelativísticos. Podemos enriquecer a dinâmica do QGP ao adicionarmos campos externos, como o potencial químico (para exploração do diagrama de fases hadrônico), ou um campo magnético. Nesta dissertação, tomamos como norte a exploração dos efeitos magnéticos. De fato, acredita-se que campos magnéticos da ordem de $eB\\sim 10 m_\\pi^2$ sejam criados nos estágios iniciais do QGP. O observável escolhido para sondar possíveis efeitos do campo magnético no QGP foi a viscosidade, em partes pelo famoso resultado $\\eta/s=1/4\\pi$ obtido holograficamente. Utilizamos num primeiro momento uma caricatura da QCD, a $\\mathcal=4$ super Yang-Mills para calcular o que muda na viscosidade com o advento do campo magnético. Devemos salientar, contudo, que um plasma altamente magnetizado possui a priori sete coeficientes de viscosidade (cinco de cisalhamento e duas volumétricas). Também exploramos, nesse mesmo modelo, o potencial de um par pesado de quark-antiquark na presença de um campo magnético. Por fim, propomos um modelo holográfico fenomenológico mais semelhante a QCD, sendo ele ``calibrado\'\' pelos dados da QCD na rede, para estudar a termodinâmica e a viscosidade do QGP imerso num forte campo magnético.

O advento dos colisores modernos tem proporcionado novas possibilidades de estudo em física de partículas como, por exemplo, a busca por nova física e o estudo de novos estados da matéria hadrônica. Em particular, em colisões de íons pesados em altas energias, acredita-se que um novo estado da matéria seja formado antes da colisão, o chamado condensado de vidros de cor. Tal estado seria a condição inicial de um plasma de quarks e glúons e é caracterizado por altas densidades de pártons (quarks e glúons). De fato, as equações de evolução da Cromodinâmica Quântica predizem que, para virtualidades moderadas e altas energias, os hádrons se tornam sistemas extremamente densos devido ao crescimento das distribuições de glúons nessas condições. Um crescimento indefinido das distribuições de glúons poderia levar à violação do vínculo de unitariedade. Para evitar essa violação, existe um mecanismo chamado de saturação de pártons o qual contém o crescimento das distribuições de quarks e glúons de forma a respeitar o vínculo de unitariedade. Teoricamente, no limite de altas energias, observa-se que os hádrons são populados especialmente por glúons. Experimentalmente, existem indícios da saturação em colisões ep, pp, pA e AA, contudo, isso ainda é uma questão em aberto. Portanto, no limite de altas densidades, espera- se que a física não linear, a qual leva em conta efeitos de recombinações de glúon, passe a se manifestar. Uma alternativa para o estudo da saturação em colisores hadrônicos são os processos foto-induzidos, os quais ocorrem em interações ultraperiféricas. Em uma colisão ultraperiférica entre dois hádrons, o parâmetro de impacto é maior do que a soma dos raios dos hádrons, de forma que interações fortes são suprimidas. Dessa forma os hádrons atuam como fontes de fótons (quase reais) podendo ocorrer interações fóton-hádron e fóton-fóton. Nesse trabalho estudamos a fotoprodução difrativa de mésons vetoriais em energias do LHC para colisões ultraperiféricas próton-próton, próton-núcleo e núcleo-núcleo e a produção dupla de mésons vetoriais em colisões fóton-fóton e devido ao mecanismo de duplo espalhamento fóton-p(A). Mostramos como esses processos podem ser usados para estudar a física de altas energias e os efeitos de saturação. Os efeitos de saturação em nossos cálculos são levados em conta através do formalismo de dipolo de cor, que é uma das ferramentas básicas usadas nessa tese. O tratamento de colisões ultraperiféricas hádron-hádron foi feito com a aproximação de fótons equivalentes que assim como o formalismo de dipolo, foi extensamente usada. Nossos resultados apontam que o estudo fenomenológico e experimental dos tipos de processos citados acima são factíveis e podem ser usados para vincular a dinâmica da QCD em altas energias. / The advent of the modern colliders has provided new possibilities of study in particle physics as, for example, the search for new physics and the study of new states of the hadronic matter. In particular, in high energy heavy ion collisions is expected that a new state can be formed before the collision, the so called Color Glass Condensate. This state would be the initial condition of the Quark Gluon Plasma and is characterized by high parton (quarks and gluons) densities. Indeed, the Quantum Chromodynamics evolution equations predict that, for moderate virtualities and high energies, the hadrons become extremely dense systems due to the growth of the parton distribution in these conditions. An indefinite growth of the parton distributions could lead to the violation of the unitarity bound. To avoid this violation, there is a mechanism called parton saturation which tames the growth of the parton distributions to satisfy the unitarity bound. Theoretically, in the high energy limit, one can see that the hadrons are populated mainly by gluons. Experimentally, there are indications of the saturation in ep, pp, pA and AA collisions, however, this is an open question. So, in the high density limit, we expect that the nonlinear physics, which takes into account gluon recombination effects start to manifest itself. An alternative for the study of the saturation at hadronic colliders are the photon-induced processes, which occurs in ultra-peripheral collisions. In a ultra-peripheral collision between two hadrons the impact parameter is greater than the sum of the radii of the hadrons, so the strong interaction is suppressed. Thus, the hadrons act as sources of (almost real) photons and may occur photon-hadron and photon-photon interactions. In this work we study the diffractive photoproduction of vector mesons at LHC and future colliders energies in ultra-peripheral proton-proton, proton-nucleus and nucleus-nucleus collisions and the double vector meson production in photon-photon collisions and due to the double photon-p(A) scattering mechanism. We show how these processes can be used to study the high energy physics and the saturation effects. These effects are considered in our calculations through the color dipole formalism, which is one of the basic tools used in this thesis. The treatment of the ultra-peripheral hadron-hadron collisions was done through the equivalent photon approximation that just as in the dipole formalism, was widely used. Our results point that the phenomenological and experimental studies of the processes cited above are feasible and can be used to constraint the QCD dynamics in high energies.

Orientador: Marcio Jose Menon / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin / Made available in DSpace on 2018-08-04T20:13:10Z (GMT). No. of bitstreams: 1 Luna_EmersonGustavodeSouza_D.pdf: 10516190 bytes, checksum: 28a19c18006994f354667c230156c034 (MD5) Previous issue date: 2005 / Resumo: Não informado / Abstract: Not informed. / Doutorado / Física das Particulas Elementares e Campos / Doutor em Ciências