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<p> After an introduction to the variational principle of three body systems via the Helium atom, we present general analytical formulas for the radial parts of integrals that occur when three body systems are described using wave functions that consist of powers and exponentials in all three interparticle Hylleraas coordinates [Hylleraas1929]. This work is an extension of integrals given by Harris, Frolov and Smith, Jr. [Harris2004]. Specifically included are radial integrals encountered in calculations involving the dipole moment matrix element in Hylleraas coordinates that contain a function <i>f(kr </i>₁) (such as a spherical Bessel function) in addition to a plane wave, a hydrogenic orbital and exponentials in all three interparticle coordinates.</p>

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<p> Large vacuum fluctuations of a quantum stress tensor can be described by the asymptotic behavior of its probability distribution. Here we focus on stress tensor operators which have been averaged with a sampling function in time. The Minkowski vacuum state is not an eigenstate of the time-averaged operator, but can be expanded in terms of its eigenstates. We calculate the probability distribution and the cumulative probability distribution for obtaining a given value in a measurement of the time-averaged operator taken in the vacuum state. In these calculations, we use the normal ordered square of the time derivative of a massless scalar field in Minkowski spacetime as an example of a stress tensor operator. We analyze the rate of decrease of the tail of the probability distribution for different temporal sampling functions, such as compactly supported functions and the Lorentzian function. We find that the tails decrease relatively slowly, as exponentials of fractional powers, in agreement with previous work using the moments of the distribution. Our results lead additional support to the conclusion that large vacuum stress tensor fluctuations are more probable than large thermal fluctuations, and may have observable effects.</p><p>

<p> Elastic lepton scattering off of a nucleon has proven to be an efficient tool to study the structure of the hadron. In particular, the spatial distributions of the nucleon's charge and magnetization can be accessed through measurements of its electric (<i>G_E</i>) and magnetic (<i>G_M</i>) form factors. These form factors can be extracted from unpolarized cross sections measurements by using the Rosenbluth separation technique. At the current level of accuracy, a determination of <i>G_E</i> and <i>G_M</i> from an analysis of elastic lepton-nucleon scattering data requires effects beyond the leading-order (Born) approximation to be taken into account. </p><p> In this work, I study higher-order QED corrections to elastic lepton-nucleon scattering. First of all, I perform a model-independent calculation of conventional charge-dependent contributions in unpolarized lepton-proton scattering without making use of ultra-relativistic approximations. Second, in a connection to the future MUSE experiment in Switzerland, I estimate helicity-flip meson exchanges that make a difference in a comparison of ultra-relativistic vs non-ultra-relativistic lepton-proton scattering. Finally, I present a model calculation of the target-normal single-spin asymmetry in elastic electron-nucleon scattering. Such an asymmetry gives us a direct tool to studies of the imaginary part of the two-photon exchange amplitude.</p><p>

<p> We are at the dawn of a data-driven era in astrophysics and cosmology. A large number of ongoing and forthcoming experiments combined with an increasingly open approach to data availability offer great potential in unlocking some of the deepest mysteries of the Universe. Among these is understanding the nature of dark matter (DM)&mdash;one of the major unsolved problems in particle physics. Characterizing DM through its astrophysical signatures will require a robust understanding of its distribution in the sky and the use of novel statistical methods. </p><p> The first part of this thesis describes the implementation of a novel statistical technique which leverages the &ldquo;clumpiness&rdquo; of photons originating from point sources (PSs) to derive the properties of PS populations hidden in astrophysical datasets. This is applied to data from the <i> Fermi</i> satellite at high latitudes (|<i>b</i>| &ge; 30&deg;) to characterize the contribution of PSs of extragalactic origin. We find that the majority of extragalactic gamma-ray emission can be ascribed to unresolved PSs having properties consistent with known sources such as active galactic nuclei. This leaves considerably less room for significant dark matter contribution. </p><p> The second part of this thesis poses the question: &ldquo;what is the best way to look for annihilating dark matter in extragalactic sources?&rdquo; and attempts to answer it by constructing a pipeline to robustly map out the distribution of dark matter outside the Milky Way using galaxy group catalogs. This framework is then applied to <i>Fermi</i> data and existing group catalogs to search for annihilating dark matter in extragalactic galaxies and clusters.</p><p>

Esta tese tem como objetivo apresentar e discutir resultados de um estudo sobre os fenômenos de polarização de híperons e de anti-híperons em processos inclusivos resultantes de interações próton-núcleo e altas energias (centenas de GeV). É proposto um modelo que acreditamos ser o principal responsável pela polarização de anti-híperons em tais processos. A polarização é resultante das interações finais entre os anti-híperons e outras partículas produzidas no processo (que na sua maioria são píons). O modelo baseia-se então em dois elementos: as interações píon-híperon a baixas energias (que estudamos através da lagrangianas efetivas) e das flutuações estatísticas do meio em expansão. O estudo deste meio baseia-se no modelo hidrodinâmico, que considera a formação de matéria hadronica quente durante tais colisões. Os resultados estão em bom acordo com os dados experimentais e conseguem explicar pela primeira vez a polarização de anti-híperons. / We present and discuss in this thesís results of a study on the hyperon and antihyperon polarization phenomena in high-energy (hundreds of GeV) proton-nudeus inclusive reactions. We propose a model that we believe is the main source of the anti-hyperon polarization in these processes. The polarization is originated by the final-state interactions between the antí-hyperons and other produced particles in these collisions (predominantly píons) and based on two elements: the low-energy pion-hyperon interaction (descriebed by effective lagrangians) and the statistical fluctuations plus expansion of the background matter. The results agree quite well wíth the experimental data and gíve for the first time a convencing explanatíon of the anti-hyperon polarization.