<p>The lifetime of $^{19}$Ne is an important parameter in precision tests of the Standard Model. Improvement in the uncertainty of experimental observables of this and other $T=\frac{1}{2}$ mirror isotopes would allow for an extraction of</p><p>V$_{ud}$ at a similar precision to that obtained by superallowed $0^+\rightarrow0^+$ Fermi decays. We report on a new high precision measurement of the lifetime of $^{19}$Ne, performed at the Kernfysich Versneller Instituut (KVI) in Groningen, the Netherlands. A 10.5 $\frac{MeV}{A}$ $^{19}$F beam was used to produce $^{19}$Ne using inverse reaction kinematics in a H$_2$ gas target. Contaminant productions were eliminated using the TRI$\mu$P magnetic isotope separator. The $^{19}$Ne beam was implanted into a thick aluminum tape, which was translated to a shielded detection region by a custom tape drive system. Collinear annihilation radiation from the emitted decay positrons were detected by two high purity germanium (HPGe) detectors. Event pulse waveforms were digitized and stored using a CAEN V1724 Digitizer. Systematic studies were performed to characterize rate-dependent data acquisition effects, diffusion, backgrounds, and contamination from the separator. We have obtained the result for the lifetime of $\tau = 24.9344 \pm 0.0073(stat) \pm 0.0083(sys)$ seconds.</p> / Dissertation

The study of scattering amplitudes beyond one loop is necessary for precision phenomenology for the Large Hadron Collider and may also provide deeper insights into the theoretical foundations of quantum field theory. In this thesis we develop a new method for computing two-loop amplitudes, based on unitarity rather than Feynman diagrams. In this approach, the two-loop amplitude is first expanded in a linearly independent basis of integrals. The process dependence thereby resides in the coefficients of the integrals. These expansion coefficients are then the object of calculation. Our main results include explicit formulas for a subset of the integral coefficients, expressing them as products of tree-level amplitudes integrated over specific contours in the complex plane. We give a general selection principle for determining these contours. This principle is then applied to obtain the coefficients of integrals with the topology of a double box. We show that, for four-particle scattering, each double-box integral in the two-loop basis is associated with a uniquely defined complex contour, referred to as its master contour. We provide a classification of the solutions to setting all propagators of the general double-box integral on-shell. Depending on the number of external momenta at the vertices of the graph, these solutions are given as a chain of pointwise intersecting Riemann spheres, or a torus. This classification is needed to define master contours for amplitudes with arbitrary multiplicities. We point out that a basis of two-loop integrals with as many infrared finite elements as possible allows substantial technical simplications, in terms of obtaining the coefficients of the integrals, as well as for the analytic evaluation of the integrals themselves. We compute two such integrals at four points, obtaining remarkably compact expressions. Finally, we provide a check on a recently developed recursion relation for the all-loop integrand of the amplitudes of N=4 supersymmetric Yang-Mills theory, examining the two-loop six-gluon MHV amplitude and finding agreement. The validity of the approach to two-loop amplitudes developed in this thesis extends to all four-dimensional gauge theories, in particular QCD. The approach is suited for obtaining compact analytical expressions as well as for numerical implementations.

Este trabalho é dedicado ao estudo da unitariedade em teoria de campos não comuta- tiva. Inicialmente, são apresentadas as ferramentas básicas para abordar o problema da unitariedade em teorias não comutativas, incluindo as regras de corte e uma introdução à não comutatividade. Em seguida, foi feita a análise do modelo Á3 não comutativo. Empregando o esquema perturbativo usual da teoria de campos, foi verificado que o modelo é unitário quando a não comutatividade envolve apenas o espaço. Por outro lado, quando a não comutatividade envolve o espaço e o tempo verificou-se uma violação da unitariedade, fato esse bem conhecido tratando-se de teorias não comutativas. Partimos então para uma abordagem proposta na literatura, em que a teoria de perturbação é adaptada para teorias não comutativas. Dentro desse esquema, o modelo Á3 foi estudado novamente verificando assim a unitariedade para um diagrama de um laço e segunda ordem na constante de acoplamento mesmo quando a não comutatividade envolve o espaço e o tempo. Baseado nesse método, estendemos a análise para uma teoria contendo além de um campo escalar um campo fermiônico, mais precisamente o modelo de Yukawa, no qual também foi verificada a unitariedade a um laço e segunda ordem na constante de acoplamento. / This work is dedicated to study unitarity in noncommutative field theory. Initially, the basic tools to handle the problem of unitarity in noncommutative theories are discussed, including the cutting rules and an introduction to noncommutativity. Then, we analised the noncommutative Á3 model. Using the usual perturbative framework of field theory, we verified that the model preserves unitarity when the noncommutativity is restrict to the spatial coordinates. On the other hand, when the noncommutativity includes both, space and time, we found a violation of the unitarity, a well known fact in noncommutative field theory. Next, we turn to an approach proposed in the literature, in wich perturbation theory is adapted for noncommutative field theory. Whitin this approach, the Á3 model was studied again and the unitarity was verified for one loop diagram and second order in the coupling constant even in the case when noncommutativity affects both space and time. Following this, we extended the analysis to a field theory with fermionic and scalar fields, namely, Yukawa\'s model, again verifing unitarity at one loop and second order in the coupling constant.

A existência de um méson escalar-isoescalar leve, conhecido como ?, foi proposta pela primeira vez na década de 60. A partícula tinha então um papel importante na construção teórica das interações ?? mas, apesar dos esforços experimentais, ela não foi detectada nos anos que se seguiram. Essa situação foi radicalmente alterada em 2001, quando uma ressonância escalar foi descoberta nos canais ?+?- do decaimento D+ -> ?+?-?+ e recebeu o rótulo ?(500). Sua existência é bem estabelecida hoje em dia. Contudo, no tratamento dos dados dos vários grupos experimentais são empregadas expressões com pouca base teórica e, por isso, os valores de sua massa e largura ainda são mal conhecidos. Neste tipo de decaimento, a formação da ressonância pode se dar no vértice fraco. Em sua subseqüente propagação, ocorrem as chamadas interações de estado final, cuja descrição não é trivial. Normalmente, essas interações não são levadas em conta de maneira criteriosa na análise de dados experimentais. Neste trabalho introduzimos uma função _(s) que descreve a propagação e decaimento da ressonância em presença das interações de estado final. No regime elástico, a fase de _(s) é determinada pelo chamado teorema de Watson, segundo o qual ela deve ser a mesma do espalhamento. Conseguimos estabelecer, sem ambigüidades, como a informação do espalhamento deve ser usada de forma a determinar não somente a fase de _(s), mas também seu módulo. Nosso principal resultado é uma expressão para _(s) em termos da fase elástica e de uma outra fase relacionada a uma integral de loop bem controlada. Três casos particulares foram explorados numericamente: os modelos sigma linear e não linear e ainda um modelo fenomenológico que leva em conta o acoplamento de canais p´?on-p´?on e k´aon-k´aon. Em consonância com a teoria quântica de campos, nosso resultado incorpora a unitariedade, considera a ressonância como grau de liberdade explícito e representa, ainda, uma generalização do procedimento usual de unitarizacao pela matriz K. Por permitir uma ligação clara entre espalhamento e produção, a função _(s) pode ser útil na análise de dados experimentais e ajudar na determinação da posição do pólo do ? e de outras ressonâncias escalares. / The existence of a light scalar-isoscalar meson, known as ?, was suggested in the 60\'s. This particle played an important role in the theoretical construction of ?? interactions but, in spite of all experimental effort, it failed to be detected. This scenario changed radically in 2001, when a scalar-isoscalar resonance was discovered in the ?+?- channel of the D+ -> ?+?-?+ decay and was called ?(500). Nowadays, its existence is rather well established. However, in the analysis of experimental data, expressions loosely based on theory are employed and therefore its mass and width are still not well known. In this kind of decay, the production of the resonance may occur at the weak vertex. When it propagates, final state interactions take place. Usually these interactions are not properly taken into account in data analysis. In this work, we introduce a function _(s), which describes the propagation and decay of the resonance in the presence of the final state interactions. In the elastic regime, the phase of _(s) is determined by the Watson\'s theorem, which states that it must be the same as the scattering phase. We were able to establish, unambiguously, how the information from scattering should be used to determine not only the phase of _(s) but also its modulus. Our main result is an expression for _(s) in terms of the elastic phase and another one related to a well controlled loop integral. Three special cases are explored numerically, namely: the linear and non linear sigma models and a phenomenological model that takes into account the coupling between pion-pion and kaon-kaon channels. In agreement with quantum field theory, our result encompasses unitarity, treats the resonance as an explicit degree of freedom and, moreover, corresponds to a generalisation of the usual K-matrix unitarization procedure. Since it represents a clear way to relate scattering and production, our function _(s) can be useful in data analysis and may be instrumental in the determination of the pole position of the ? as well as other scalar resonances.

A existência de um méson escalar-isoescalar leve, conhecido como ?, foi proposta pela primeira vez na década de 60. A partícula tinha então um papel importante na construção teórica das interações ?? mas, apesar dos esforços experimentais, ela não foi detectada nos anos que se seguiram. Essa situação foi radicalmente alterada em 2001, quando uma ressonância escalar foi descoberta nos canais ?+?- do decaimento D+ -> ?+?-?+ e recebeu o rótulo ?(500). Sua existência é bem estabelecida hoje em dia. Contudo, no tratamento dos dados dos vários grupos experimentais são empregadas expressões com pouca base teórica e, por isso, os valores de sua massa e largura ainda são mal conhecidos. Neste tipo de decaimento, a formação da ressonância pode se dar no vértice fraco. Em sua subseqüente propagação, ocorrem as chamadas interações de estado final, cuja descrição não é trivial. Normalmente, essas interações não são levadas em conta de maneira criteriosa na análise de dados experimentais. Neste trabalho introduzimos uma função _(s) que descreve a propagação e decaimento da ressonância em presença das interações de estado final. No regime elástico, a fase de _(s) é determinada pelo chamado teorema de Watson, segundo o qual ela deve ser a mesma do espalhamento. Conseguimos estabelecer, sem ambigüidades, como a informação do espalhamento deve ser usada de forma a determinar não somente a fase de _(s), mas também seu módulo. Nosso principal resultado é uma expressão para _(s) em termos da fase elástica e de uma outra fase relacionada a uma integral de loop bem controlada. Três casos particulares foram explorados numericamente: os modelos sigma linear e não linear e ainda um modelo fenomenológico que leva em conta o acoplamento de canais p´?on-p´?on e k´aon-k´aon. Em consonância com a teoria quântica de campos, nosso resultado incorpora a unitariedade, considera a ressonância como grau de liberdade explícito e representa, ainda, uma generalização do procedimento usual de unitarizacao pela matriz K. Por permitir uma ligação clara entre espalhamento e produção, a função _(s) pode ser útil na análise de dados experimentais e ajudar na determinação da posição do pólo do ? e de outras ressonâncias escalares. / The existence of a light scalar-isoscalar meson, known as ?, was suggested in the 60\'s. This particle played an important role in the theoretical construction of ?? interactions but, in spite of all experimental effort, it failed to be detected. This scenario changed radically in 2001, when a scalar-isoscalar resonance was discovered in the ?+?- channel of the D+ -> ?+?-?+ decay and was called ?(500). Nowadays, its existence is rather well established. However, in the analysis of experimental data, expressions loosely based on theory are employed and therefore its mass and width are still not well known. In this kind of decay, the production of the resonance may occur at the weak vertex. When it propagates, final state interactions take place. Usually these interactions are not properly taken into account in data analysis. In this work, we introduce a function _(s), which describes the propagation and decay of the resonance in the presence of the final state interactions. In the elastic regime, the phase of _(s) is determined by the Watson\'s theorem, which states that it must be the same as the scattering phase. We were able to establish, unambiguously, how the information from scattering should be used to determine not only the phase of _(s) but also its modulus. Our main result is an expression for _(s) in terms of the elastic phase and another one related to a well controlled loop integral. Three special cases are explored numerically, namely: the linear and non linear sigma models and a phenomenological model that takes into account the coupling between pion-pion and kaon-kaon channels. In agreement with quantum field theory, our result encompasses unitarity, treats the resonance as an explicit degree of freedom and, moreover, corresponds to a generalisation of the usual K-matrix unitarization procedure. Since it represents a clear way to relate scattering and production, our function _(s) can be useful in data analysis and may be instrumental in the determination of the pole position of the ? as well as other scalar resonances.

Este trabalho é dedicado ao estudo da unitariedade em teoria de campos não comuta- tiva. Inicialmente, são apresentadas as ferramentas básicas para abordar o problema da unitariedade em teorias não comutativas, incluindo as regras de corte e uma introdução à não comutatividade. Em seguida, foi feita a análise do modelo Á3 não comutativo. Empregando o esquema perturbativo usual da teoria de campos, foi verificado que o modelo é unitário quando a não comutatividade envolve apenas o espaço. Por outro lado, quando a não comutatividade envolve o espaço e o tempo verificou-se uma violação da unitariedade, fato esse bem conhecido tratando-se de teorias não comutativas. Partimos então para uma abordagem proposta na literatura, em que a teoria de perturbação é adaptada para teorias não comutativas. Dentro desse esquema, o modelo Á3 foi estudado novamente verificando assim a unitariedade para um diagrama de um laço e segunda ordem na constante de acoplamento mesmo quando a não comutatividade envolve o espaço e o tempo. Baseado nesse método, estendemos a análise para uma teoria contendo além de um campo escalar um campo fermiônico, mais precisamente o modelo de Yukawa, no qual também foi verificada a unitariedade a um laço e segunda ordem na constante de acoplamento. / This work is dedicated to study unitarity in noncommutative field theory. Initially, the basic tools to handle the problem of unitarity in noncommutative theories are discussed, including the cutting rules and an introduction to noncommutativity. Then, we analised the noncommutative Á3 model. Using the usual perturbative framework of field theory, we verified that the model preserves unitarity when the noncommutativity is restrict to the spatial coordinates. On the other hand, when the noncommutativity includes both, space and time, we found a violation of the unitarity, a well known fact in noncommutative field theory. Next, we turn to an approach proposed in the literature, in wich perturbation theory is adapted for noncommutative field theory. Whitin this approach, the Á3 model was studied again and the unitarity was verified for one loop diagram and second order in the coupling constant even in the case when noncommutativity affects both space and time. Following this, we extended the analysis to a field theory with fermionic and scalar fields, namely, Yukawa\'s model, again verifing unitarity at one loop and second order in the coupling constant.

Neste trabalho consideramos extensões do Modelo Padrão contendo vértices quárticos anômalos parametrizados por operadores efetivos de dimensão oito. Estes alteram o comportamento das amplitudes do tipo VV VV , onde V pode ser o fóton, o bóson Z, o bóson W ou o Higgs. Para essa extensão ser consistente, ela tem que obedecer o teorema ótico. Entretanto, as amplitudes geradas por estes operadores efetivos tendem a aumentar conforme a energia do centro de massa aumenta. Estudaremos o comportamento dessas amplitudes e determinaremos se há violação de unitariedade. Para isso utilizamos também o formalismo da base de helicidade. / In this work we consider Standard Model extensions containing anomalous quartic vertex parametrized by effective dimension-eight operators. These modify the behaviour of the scat- tering amplitudes VV VV , where V can be photon, Z boson, W boson and Higgs. To this extension be consistent, it has to obey the optical theorem. However, the amplitudes generated by these effective operators tends to grow as the center of mass energy increase. We will study the behaviour of these amplitudes and we will determine if there is unitarity violation. For this it was also used the helicity base formalism.

In this thesis massive higher derivative gravity theories are analyzed in some detail. One-particle scattering amplitude between two covariantly conserved sources mediated by a graviton exchange is found at tree-level in D dimensional (Anti)-de Sitter and flat spacetimes for the most general quadratic curvature theory augmented with the Pauli-Fierz mass term. From the amplitude expression, the Newtonian potential energies are calculated for various cases. Also, from this amplitude and the propagator structure, a three dimensional unitary theory is identified. In the second part of the thesis, the found three dimensional unitary theory is studied in more detail from a canonical point of view. The general higher order action is written in terms of gauge-invariant functions both in flat and de Sitter backgrounds. The analysis is extended by adding static sources, spinning masses and the gravitational Chern-Simons term separately to the theory in the case of flat spacetime. For all cases the microscopic spectrum and the masses are found. In the discussion of curved spacetime, the masses are found in the relativistic and non-relativistic limits. In the Appendix, some useful calculations that are frequently used in the bulk of the thesis are given.

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.

abstract: With the discovery of the Higgs Boson in 2012, particle physics has decidedly moved beyond the Standard Model into a new epoch. Though the Standard Model particle content is now completely accounted for, there remain many theoretical issues about the structure of the theory in need of resolution. Among these is the hierarchy problem: since the renormalized Higgs mass receives quadratic corrections from a higher cutoff scale, what keeps the Higgs boson light? Many possible solutions to this problem have been advanced, such as supersymmetry, Randall-Sundrum models, or sub-millimeter corrections to gravity. One such solution has been advanced by the Lee-Wick Standard Model. In this theory, higher-derivative operators are added to the Lagrangian for each Standard Model field, which result in propagators that possess two physical poles and fall off more rapidly in the ultraviolet regime. It can be shown by an auxiliary field transformation that the higher-derivative theory is identical to positing a second, manifestly renormalizable theory in which new fields with opposite-sign kinetic and mass terms are found. These so-called Lee-Wick fields have opposite-sign propagators, and famously cancel off the quadratic divergences that plague the renormalized Higgs mass. The states in the Hilbert space corresponding to Lee-Wick particles have negative norm, and implications for causality and unitarity are examined. This dissertation explores a variant of the theory called the N = 3 Lee-Wick Standard Model. The Lagrangian of this theory features a yet-higher derivative operator, which produces a propagator with three physical poles and possesses even better high-energy behavior than the minimal Lee-Wick theory. An analogous auxiliary field transformation takes this higher-derivative theory into a renormalizable theory with states of alternating positive, negative, and positive norm. The phenomenology of this theory is examined in detail, with particular emphasis on the collider signatures of Lee-Wick particles, electroweak precision constraints on the masses that the new particles can take on, and scenarios in early-universe cosmology in which Lee-Wick particles can play a significant role. / Dissertation/Thesis / Doctoral Dissertation Physics 2015