Submitted by MATHEUS LOSS LIZE (matheuslize@icloud.com) on 2018-06-25T14:57:23Z No. of bitstreams: 1 Thesis Final.pdf: 1131929 bytes, checksum: a010126b1d56e2526a965d0e67aed302 (MD5) / Rejected by Hellen Sayuri Sato null (hellen@ift.unesp.br), reason: Solicitamos que realize correções na submissão seguindo as orientações abaixo: - título e titulo alternativo estão em inglês. Título alternativo, neste caso, deve ser em português. Por favor, utilize maiúscula apenas na palavra inicial do titulo e em caso de siglas ou nomes próprio - Seu nome foi preenchido Loss Lize, Matheus. Loss é o sobrenome do seu pai? A entrada deve ser pelo sobrenome do pai. Acho que no seu caso, o correto seria Lize, Matheus Loss on 2018-06-29T17:55:18Z (GMT) / Submitted by MATHEUS LOSS LIZE (matheuslize@icloud.com) on 2018-06-29T18:23:23Z No. of bitstreams: 1 Thesis Final.pdf: 1131929 bytes, checksum: a010126b1d56e2526a965d0e67aed302 (MD5) / Approved for entry into archive by Hellen Sayuri Sato null (hellen@ift.unesp.br) on 2018-06-29T18:45:49Z (GMT) No. of bitstreams: 1 lize_ml_dr_ift.pdf: 1131929 bytes, checksum: a010126b1d56e2526a965d0e67aed302 (MD5) / Made available in DSpace on 2018-06-29T18:45:49Z (GMT). No. of bitstreams: 1 lize_ml_dr_ift.pdf: 1131929 bytes, checksum: a010126b1d56e2526a965d0e67aed302 (MD5) Previous issue date: 2017-02-23 / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / Neste trabalho revisamos as amplitudes de MHV no contexto da teoria de super-Yang-Mills. Nós estudamos as simetrias das amplitudes de MHV no espaço de twistors como uma motivação para introduzir a teoria de cordas com twistors . A teoria de cordas com twistors feita por Nathan Berkovits [3] é revisada e uma fórmula geral é dada para calcular amplitudes de espalhamento com n gluons. No final, a partir desta fórmula deduzimos a amplitude de MHV. / In this work we review the maximal helicity violating (MHV) scattering amplitude in the context of super-Yang-Mills theory. We study the symmetries of the MHV amplitude in the twistor space as a motivation to introduce the twistor string theory. The twistor string action introduced by Nathan Berkovits [3] is reviewed and also a general formula is given for the scattering amplitude with n gluons. In the end, the MHV amplitude is derived from this formula. / CNPq: 132620/2015-4.

Amplitudes in theories with a massless gauge boson suffer from so-called infrared divergences where off-shell states become asymptotically close to the mass-shell in loop or phase-space momentum integrals. These singularities have been shown to cancel intricately order-by-order in the perturbative expansion. However, in order to obtain meaningful and precise predictions for physical observables, we must understand and compute such divergences to high orders. This can be accomplished by calculating webs: weighted sets of Feynman diagrams which, when exponentiated give the complete infrared singular component of the amplitude, known as the soft function. This quantity is formally equivalent to a vacuum expectation value of a product of Wilson lines. In this thesis we shall study webs correlating multiple Wilson lines, which differs from the two line case due to the possibility of non-trivial colour flows. This renders the soft function matrix valued in the space of colour flows, thus making its calculation and renormalisation non-trivial. At present, the infrared singularities of non-abelian, multiparton scattering amplitudes are known only to two loops in general kinematics, and to three loops in a simplifying kinematic limit. This thesis will thus form part of a program of work aimed at calculating and understanding the three-loop singularities in general kinematics and in doing so we aim to gain all-order insights into the pertubative structure of non-abelian gauge theories. We first specialise to a subset of webs which we have called Multiple Gluon Exchange Webs (MGEWs), which contain only those diagrams with direct exchanges of soft gauge bosons directly between Wilson lines with no intervening three- or four- boson vertices. Studing their properties allows us to construct a basis of functions which describes all examples of such webs, and we conjecture will continue to do so at any order. Furthermore, we find that the basis functions can be described by a simple, one-dimensional integral over only logarithms. We go on to compute several examples providing evidence for the validity of our basis and demonstrate the utility of the framework we have built by computing a four-loop web and providing some all-order results for particular classes of MGEW. We then consider a step beyond MGEWs, that is, webs which contain a single three-gluon vertex sub-diagram. In particular we study the simplest web in this class correlating four lines at three loops and attempt to calculate it through the numerical fitting of a physically motivated ansatz. We show that this web cannot carry kinematic dependence through conformal invariant cross ratios, which arise when connected subdiagrams correlate at least four lines. Hence, it is subject to the same constraints as MGEWs with regards to their symbol alphabet, from the physical considerations in their lightlike limit and spacelike/timelike analytic continuation. Like all other known webs satisfying such constraints, we therefore argue that it can be written in terms of sums of products of MGEW basis functions. Symmetries inherent to our parameterisation of the cusp angles, Bose symmetry and transcendental weight further constrain this ansatz, resulting in forty parameters for which we present preliminary results of a numerical fit.

The tree amplitudes of string theory low-energy effective actions admit a diagrammatic expansion in terms of higher-than-cubic contact terms. These tree amplitudes can be used to build loop amplitudes using unitary cuts or the forward limit. In this thesis we study the possibility of constructing four-point cubic representations for the resulting one-loop contact terms that obey the Bern-Carrasco-Johansson (BCJ) color-kinematics relation. From the string theory effective action we study the contact terms carrying ζ2, ζ3, ζ4, and ζ5. For the even ζ2 and ζ4 cases we find that the cubic representations are incompatible with the BCJ relations, as expected from their disappearance in the closed-string effective action. We find a unique, local set of numerators at ζ3 that obey the BCJ relations. For ζ5 we find two choices of representations: one obeys BCJ but requires non-trivial contributions for the tadpole; the other contains no tadpoles but breaks one of the BCJ relations.

In this text we explore the case of pure Yang-Mills amplitudes in 5 spacetime dimensions for vector particles. Extending current toolsets such as the Spinor-Helicity formalism in 5D would be beneficial to the study of the various cases of super Yang-Mills and supergravity. In this text we provide an expression for the 5D BCFW shifts and test them in the 4-point setting. A method for obtaining the 5-point gluon amplitude is presented as well as a way to classify possible building blocks of the ansatz. We also provide a non-trivial expression for the 5-point case. The text begins with a short review of Spinor-Helicity formalism in 4D is given at the beginning followed by a discussion of its extension to 5D. Next, we review the pure Yang-Mills theory and modern methods of amplitude calculations. Finally we discuss our methods and results. / Vi utforskar fallet med rena Yang-Mills-amplituder i 5 rymdtidsdimensioner för vektorpartiklar. Utvidgningen av Spinor-Helicity-formalismen i 5D skulle vara fördelaktig för studiet av de olika fallen av super Yang-Mills och supergravitation. I denna avhandling ger vi ett uttryck för 5D BCFW-skiften och tillämpar dem i 4-punktsinställningen. Vi presenterar en metod för att erhålla 5-punkts gluonamplituden och ett sätt att klassificera möjliga byggstenar i ansatsen. Med hjälp av dessa utvecklar vi ett icke-trivialt uttryck för 5-punktsfallet i 5D SH-variabler. Texten börjar med en kortöversikt över Spinor-Helicity-formalismen i 4D som ges i början följt av en diskussion om dess utvidgning till 5D. Därefter granskar vi den rena Yang-Mills-teorin och moderna metoder för amplitudberäkningar och slutligen diskuterar vi våra metoder och resultat

Nous étudions des fluctuations qui sont omniprésentes dans des collisions entre particules aux hautes énergies. Ces fluctuations peuvent être de nature classique ou quantique et nous allons considérer ces deux cas. D'abord, nous étudions les fluctuations quantiques qui sont présentes dans des collisions entre protons. Celles-ci sont calculables en théorie quantique des champs, et nous allons nous concentrer sur une certaine classe de diagrammes dans ce cadre. Dans un second temps nous allons étudier des fluctuations qui sont présentes dans des collisions entre particules plus lourdes que le proton. Celles-ci sont décrites par les lois quantiques de la nature qui donnent les positions des nucléons dans le noyau, ou bien des fluctuations classiques, d'origine thermique, qui affectent l'évolution hydrodynamique du milieu produit dans une collision. Les fluctuations dans des collisions entre protons peuvent être calculées analytiquement jusqu'à un certain ordre en théorie quantique des champs. Nous allons nous concentrer sur des diagrammes à une boucle, d'une topologie donnée. Ces diagrammes aux boucles donnent des intégrales, qui typiquement sont difficiles à calculer. Nous allons démontrer comment des outils des mathématiques modernes peuvent être utilisés pour faciliter leur évaluation. En particulier, nous allons étudier des relations entre des coupures d'un diagramme, la discontinuité à travers d'un branchement et le coproduit. Nous allons démontrer comment l'intégrale originale peut être reconstruit à partir de l'information contenue dans le coproduit. Nous nous attendons à ce que ces méthodes seront utiles pour le calcul des diagrammes avec des topologies plus difficiles et ainsi aident au calcul des nouvelles amplitudes de diffusion. A la fin, nous étudions les deux types de fluctuations qui ont lieu dans des collisions entre ions lourds. Celles-ci sont liées soit à l'état initial de la matière, soit à l'état intermédiaire produit dans une telle collision. Les fluctuations de l'état initial ont été mesurées expérimentalement, et on voit qu'elles donnent lieu à des non-Gaussianités dans le spectre final de particules. Nous allons démontrer comment ces non-Gaussianités peuvent être comprises comme des positions et des énergies d'interaction aléatoires des 'sources' dans les noyaux entrant en collision. En plus, nous étudions le bruit hydrodynamique dans le milieu produit juste après une collision. Le comportement de ce milieu est celui d'un fluide à basse viscosité. / We study fluctuations that are omnipresent in high-energy particle collisions. These fluctuations can be either of either classical or quantum origin and we will study both. Firstly, we consider the type of quantum fluctuations that arise in proton-proton collisions. These are computable perturbatively in quantum field theory and we will focus on a specific class of diagrams in this set-up. Secondly, we will consider the fluctuations that are present in collisions between nuclei that can be heavier than protons. These are the quantum laws of nature that describe the positions of nucleons within a nucleus, but also the hydrodynamic fluctuations of classical, thermal origin that affect the evolution of the medium produced in heavy-ion collisions. The fluctuations arising in proton-proton collisions can be computed analytically up to a certain order in perturbative quantum field theory. We will focus on one-loop diagrams of a fixed topology. Loop diagrams give rise to integrals that typically are hard to evaluate. We show how modern mathematical methods can be used to ease their computation. We will study the relations among unitarity cuts of a diagram, the discontinuity across the corresponding branch cut and the coproduct. We show how the original integral corresponding to a given diagram can be reconstructed from the information contained in the coproduct. We expect that these methods can be applied to solve more complicated topologies and help in the computation of new amplitudes in the future. Finally, we study the two types of fluctuations arising in heavy-ion collisions. These are related either to the initial state or the intermediate state of matter produced in such collisions. The initial state fluctuations are experimentally observed to give rise to non-Gaussianities in the final-state spectra. We show how these non-Gaussianities can be explained by the random position and interaction energy of `sources' in the colliding nuclei. Furthermore, we investigate the effect of hydrodynamical noise in the evolution of the medium produced just after a collision. This medium behaves like a fluid with a very low viscosity, and so the corresponding evolution is hydrodynamical.

Le sujet de cette thèse sont les amplitudes d'hélicités de la leptoproduction exclusive et diffractive du méson rho dans la limite de Regge perturbative et au-delà du twist dominant. La compréhension de pareils processus exclusifs en termes des constituants élémentaires de QCD est un important défi pour comprendre la structure des hadrons. On présente ici deux nouveaux modèles phénoménologiques basés sur la kT-factorisation des amplitudes d'hélicités en un facteur d'impact γ*(λ) → ρ(λ'), où λ et λ' dénotent les polarisations du photon virtuel et du méson rho, et le facteur d'impact du nucléon cible. Les facteurs d'impacts γ*(λ) → ρ(λ') sont calculés en utilisant la factorisation colinéaire pour séparer la partie molle du méson rho. Le premier modèle est obtenu en combinant les résultats respectivement de twist 2 et twist 3 des facteurs d'impacts où les deux polarisations sont longitudinales ou transverses, avec un modèle pour le facteur d'impact du nucléon et un modèle pour les distributions d'amplitudes du méson rho. Dans la seconde approche présentée dans cette thèse, on calcule ces facteurs d'impacts dans l'espace des paramètres d'impacts et on montre que l'amplitude de diffusion d'un dipôle de couleur avec le nucléon se factorise, permettant de combiner nos résultats avec un modèle de section efficace de dipôle. On obtient en très bon accord avec les données de H1 et ZEUS pour des virtualités plus grandes que quelques GeV. Nous discutons les résultats obtenus et les comparons à d'autres modèles existants. / This thesis deals with the computation of the helicity amplitudes of the exclusive diffractive rho meson leptoproduction in the perturbative Regge limit beyond the leading twist. The understanding of such exclusive processes in terms of the elementary constituents of QCD is a serious challenge to understand the hadronic structure. We present two new phenomenological models based on the kT-factorization of the helicity amplitudes in a γ*(λ) → ρ(λ') impact factor, where λ and λ' denote the polarizations of the virtual photon and the rho meson, and the nucleon target impact factor. The γ*(λ) → ρ(λ') impact factors are then computed using the collinear factorization of the rho meson soft part. The first model relies on the combination of the results respectively up to twist 2 and twist 3 for the impact factors where both polarizations are longitudinal or transverse, with a model for the nucleon impact factor and a model for the distribution amplitudes of the rho meson. In the second approach presented in this thesis, we derive these impact factors in impact parameter space and show that the color dipole scattering amplitude with the nucleon factorizes, allowing to use our results in combination with dipole cross-section models. We get a very good agreement with the data from H1 and ZEUS collaborations for virtualities higher than a few GeV. We discuss our results and compare them to other models.

This thesis concerns a range of aspects of theoretical physics. It is composed of two parts. In the first part we motivate our line of research, and introduce and discuss the relevant concepts. In the second part, four research papers are collected. The first paper deals with a possible extension of general relativity, namely the recently discovered classically consistent bimetric theory. In this paper we study the behavior of perturbations of the metric(s) around cosmologically viable background solutions. In the second paper, we explore possibilities for particle physics with low-scale supersymmetry. In particular we consider the addition of supersymmetric higher-dimensional operators to the minimal supersymmetric standard model, and study collider phenomenology in this class of models. The third paper deals with a possible extension of the notion of Lie algebras within category theory. Considering Lie algebras as objects in additive symmetric ribbon categories we define the proper Killing form morphism and explore its role towards a structure theory of Lie algebras in this setting. Finally, the last paper is concerned with the computation of string amplitudes in four dimensional models with reduced supersymmetry. In particular, we develop general techniques to compute amplitudes involving gauge bosons and gravitons and explicitly compute the corresponding three- and four-point functions. On the one hand, these results can be used to extract important pieces of the effective actions that string theory dictates, on the other they can be used as a tool to compute the corresponding field theory amplitudes. / Over the last twenty years there have been spectacular observations and experimental achievements in fundamental physics. Nevertheless all the physical phenomena observed so far can still be explained in terms of two old models, namely the Standard Model of particle physics and the ΛCDM cosmological model. These models are based on profoundly different theories, quantum field theory and the general theory of relativity. There are many reasons to believe that the SM and the ΛCDM are effective models, that is they are valid at the energy scales probed so far but need to be extended and generalized to account of phenomena at higher energies. There are several proposals to extend these models and one promising theory that unifies all the fundamental interactions of nature: string theory. With the research documented in this thesis we contribute with four tiny drops to the filling of the fundamental physics research pot. When the pot will be saturated, the next fundamental discovery will take place.

This thesis reviews the method of Mafra, Schlotterer, and Stieberger (2011) for computing the full colour ordered N-point open superstring amplitude using the Pure Spinor formalism. We introduce relevant elements of super Yang-Mills theory and examine the basics of the Pure Spinor formalism, with a focus on tools for amplitude computation. We then define a series of objects with increasingly useful BRST transformation properties, which greatly simplify the calculations, and show how these properties can be determined using a diagrammatic method. Finally, we use the explicit four- and five-point amplitude computations as stepping stones to compute the general N-point amplitude, which factors into a set of kinematic integrals multiplying SYM subamplitudes.

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