This dissertation concerns modeling two aspects of dynamics of complex networks: (1) response dynamics and (2) growth and formation. A particularly challenging class of networks are ones in which both nodes and links are evolving over time – the most prominent example is a financial network. In the first part of the dissertation we present a model for the response dynamics in networks near a metastable point. We start with a Landau-Ginzburg approach and show that the most general lowest order Lagrangians for dynamical weighted networks can be used to derive conditions for stability under external shocks. Using a closely related model, which is easier to solve numerically, we propose a powerful and intuitive set of equations for response dynamics of financial networks. We find the stability conditions of the model and find two phases: “calm” phase , in which changes are sub-exponential and where the system moves to a new, close-by equilibrium; “frantic” phase, where changes are exponential, with negative blows resulting in crashes and positive ones leading to formation of "bubbles". We empirically verify these claims by analyzing data from Eurozone crisis of 2009-2012 and stock markets. We show that the model correctly identifies the time-line of the Eurozone crisis, and in the stock market data it correctly reproduces the auto-correlations and phases observed in the data. The second half of the dissertation addresses the following question: Do networks that form due to local interactions (local in real space, or in an abstract parameter space) have characteristics different from networks formed of random or non-local interactions? Using interacting fields obeying Fokker-Planck equations we show that many network characteristics such as degree distribution, degree-degree correlation and clustering can either be derived analytically or there are analytical bounds on their behaviour. In particular, we derive recursive equations for all powers of the ensemble average of the adjacency matrix. We analyze a few real world networks and show that some networks that seem to form from local interactions indeed have characteristics almost identical to simulations based on our model, in contrast with many other networks.

Este estudo é dedicado ao entendimento do decaimento D+ K++. Desenvolvemos dois modelos que abordam aspectos complementares dos principais processos dinâmicos que atuam em tal decaimento: o v´ertice fraco, onde ocorre a transição c Ws, e as interações entre os três mesons no estado final. Este trabalho foi motivado por um resultado experimental importante sobre o decaimento D+ K++, no qual a fase em onda S de um par K do estado final não coincide com a fase do espalhamento K livre, chamado puzzle das fases. No primeiro modelo, as interações de estado final foram descritas por sucessivos reespalhamentos dos pares K, enquanto o vértice fraco foi aproximado por uma função sem estrutura. O espalhamento K é um ingrediente fundamental e é calculado usando uma lagrangiana efetiva quiral com ressonâncias. As amplitudes do decaimento são calculadas perturbativamente, ate a segunda ordem do reespalhamento K, para as três topologias acessíveis ao sistema. Os resultados do primeiro modelo mostram a importância das interações de estado finais, sendo o efeito da interação própria de três corpos essencial para a boa descrição dos dados experimentais obtida a partir de uma das topologias. No segundo modelo, o vértice fraco do decaimento é calculado a partir de uma teoria efetiva que acopla o setor leve de SU(3) ao setor do charme e descreve todas as interações, fortes e fracas, entre os dois setores. Esse modelo inclui a dependência correta de momento nos vértices e contém essencialmente três melhorias: (i) incorpora corretamente a estrutura de onda P no vértice fraco ao usar correntes do tipo V A; (ii) inclue o vértice V DK parametrizado em termos de fatores de forma monopolares; e (iii) inclue no vértice V a transição W intermediada pela ressonância , o que d´a origem a um fator de forma forte. Os resultados do segundo modelo mostram que o efeito dos fatores de forma no vértice D K são pequenos e mais importantes em altas energias. A inclusão do meson como uma ressonância é muito significativa e desloca a fase para 90o no limiar, o que explica o comportamento qualitativo dos dados experimentais na mesma região. / This study describer the D+ K++ decay. We developed two models for complementary issues of the main dynamic process in this system: the weak vertex, where the transition c Ws takes place, and the interactions between the three mesons in the final state. This work was motivated by important experimental results for D+ K++ decay in which the S wave phase for a K pair in the final state does not agree with the phase from K free scattering amplitude, which is here named phase puzzle. In the first model, the interaction in the final states are treated as successive rescattering between K pairs, and the weak vertex is approximated as structureless functions. The K amplitude is a fundamental ingredient and is calculated using an effective quiral lagrangian with resonances. The decay amplitudes were solved perturbatively up to second order in K rescattering for all the three topologies that can contribute. The results for the first model show the importance of final state interactions where the proper three body effect are essential for the good description of experimental data, obtained from one of the topologies. In the second model, the weak vertex is calculated using an effective theory that couples the light SU(3) sector to the charm sector and describes all interactions, strong and weak, between the two sectors. This model includes the correct momentum dependences at verticies and contain mainly three improvements: (i) correctly incorporates the P- wave momentum structure in the vertex through the use of V A currents; (ii) includes V DK vertex parametrized by monopoles form factors; and (iii) includes in the V vertex the W transition intermediated by a r resonance, which gives rise to a strong form factor. The results for the second model show that the form factors effects on D K vertex are small and more important at higher energy. The inclusion of the meson as a resonance is very significant and dislocates the phase shift from zero to 90o at threshold, which explains the qualitative experimental data behaviour in the same region.

Este estudo é dedicado ao entendimento do decaimento D+ K++. Desenvolvemos dois modelos que abordam aspectos complementares dos principais processos dinâmicos que atuam em tal decaimento: o v´ertice fraco, onde ocorre a transição c Ws, e as interações entre os três mesons no estado final. Este trabalho foi motivado por um resultado experimental importante sobre o decaimento D+ K++, no qual a fase em onda S de um par K do estado final não coincide com a fase do espalhamento K livre, chamado puzzle das fases. No primeiro modelo, as interações de estado final foram descritas por sucessivos reespalhamentos dos pares K, enquanto o vértice fraco foi aproximado por uma função sem estrutura. O espalhamento K é um ingrediente fundamental e é calculado usando uma lagrangiana efetiva quiral com ressonâncias. As amplitudes do decaimento são calculadas perturbativamente, ate a segunda ordem do reespalhamento K, para as três topologias acessíveis ao sistema. Os resultados do primeiro modelo mostram a importância das interações de estado finais, sendo o efeito da interação própria de três corpos essencial para a boa descrição dos dados experimentais obtida a partir de uma das topologias. No segundo modelo, o vértice fraco do decaimento é calculado a partir de uma teoria efetiva que acopla o setor leve de SU(3) ao setor do charme e descreve todas as interações, fortes e fracas, entre os dois setores. Esse modelo inclui a dependência correta de momento nos vértices e contém essencialmente três melhorias: (i) incorpora corretamente a estrutura de onda P no vértice fraco ao usar correntes do tipo V A; (ii) inclue o vértice V DK parametrizado em termos de fatores de forma monopolares; e (iii) inclue no vértice V a transição W intermediada pela ressonância , o que d´a origem a um fator de forma forte. Os resultados do segundo modelo mostram que o efeito dos fatores de forma no vértice D K são pequenos e mais importantes em altas energias. A inclusão do meson como uma ressonância é muito significativa e desloca a fase para 90o no limiar, o que explica o comportamento qualitativo dos dados experimentais na mesma região. / This study describer the D+ K++ decay. We developed two models for complementary issues of the main dynamic process in this system: the weak vertex, where the transition c Ws takes place, and the interactions between the three mesons in the final state. This work was motivated by important experimental results for D+ K++ decay in which the S wave phase for a K pair in the final state does not agree with the phase from K free scattering amplitude, which is here named phase puzzle. In the first model, the interaction in the final states are treated as successive rescattering between K pairs, and the weak vertex is approximated as structureless functions. The K amplitude is a fundamental ingredient and is calculated using an effective quiral lagrangian with resonances. The decay amplitudes were solved perturbatively up to second order in K rescattering for all the three topologies that can contribute. The results for the first model show the importance of final state interactions where the proper three body effect are essential for the good description of experimental data, obtained from one of the topologies. In the second model, the weak vertex is calculated using an effective theory that couples the light SU(3) sector to the charm sector and describes all interactions, strong and weak, between the two sectors. This model includes the correct momentum dependences at verticies and contain mainly three improvements: (i) correctly incorporates the P- wave momentum structure in the vertex through the use of V A currents; (ii) includes V DK vertex parametrized by monopoles form factors; and (iii) includes in the V vertex the W transition intermediated by a r resonance, which gives rise to a strong form factor. The results for the second model show that the form factors effects on D K vertex are small and more important at higher energy. The inclusion of the meson as a resonance is very significant and dislocates the phase shift from zero to 90o at threshold, which explains the qualitative experimental data behaviour in the same region.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第22247号 / 理博第4561号 / 新制||理||1655(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 畑 浩之, 教授 田中 貴浩, 教授 川合 光 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

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Der Autor hat das pastor-Softwarepaket für automatisierte Gitterstörungstheorie im Schrödingerfunktional entwickelt. Das pastor-Paket besteht aus zwei Bausteinen, die die Erzeugung von Vertexfunktionen und Feynmandiagrammen übernehmen. Ausgehend von recht generischen Formulierungen der Gitterwirkungen für Fermionen und Gluonen, die dem Vertexgenerator in symbolischer Form übergeben werden, erzeugt dieser Feynmanregeln zu beliebiger Ordnung in der nackten Kopplung. Dabei kann sowohl ein triviales als auch ein Abelsches Hintergrundfeld verwendet werden. Die vom zweiten Teil von pastor, einem Code-Generator, erzeugten Programme greifen auf den Vertexgenerator zu und berechnen alle Terme der perturbativen Entwicklung für eine Klasse von Schrödingerfunktional-Observablen bis zur Einschleifenordnung. Verbesserungsterme der Ordnung a werden dabei berücksichtigt. Wir werden die für die Funktionen der beiden Teile von pastor relevanten Algorithmen detailliert beschrieben und die Korrektheit unserer Implementierung mit einer Reihe von Vergleichen mit perturbativen und nichtperturbativen Daten belegen. Wir werden darauf die Nützlichkeit von pastor Anhand einiger Beispiele aus dem Abgleich von Heavy Quark Effective Theory mit Quantenchromodynamik demonstrieren. Wir haben unter Anderem eine Einschleifenrechnung zweier Kandidaten für Observablen, die aller Voraussicht nach in Zukunft für den Abgleich verwendet werden, zügig und mit geringem Aufwand durchgeführt. Dies zeigt die Stärken eines Softwarepakets für automatisierte Störungsrechnungen. Unsere Resultate werden als nützliche Richtschnur für zukünftige nichtperturbative Berechnungen dienen. / The author developed the pastor software package for automated lattice perturbation theory calculations in the Schrödinger functional scheme. The pastor code consists of two building blocks, dealing with the generation of Feynman rules and Feynman diagrams respectively. Accepting a rather generic class of lattice gauge and fermion actions, passed to the code in a symbolic form as input, a low level part of pastor will generate Feynman rules to an arbitrary order in the bare coupling with a trivial or an Abelian background field. The second, high level part of pastor is a code generator whose output relies on the vertex generator. It writes programs that evaluate Feynman diagrams for a class of Schrödinger functional observables up to one loop order automatically, the relevant O(a) improvement terms are taken into account. We will describe the algorithms used for implementation of both parts of the code in detail, and provide cross checks with perturbative and non-perturbative data to demonstrate the correctness of our code. We demonstrate the usefulness of the pastor package through various applications taken from the matching process of heavy quark effective theory with quantum chromodynamics. We have e.g. completed a one loop analysis for new candidates for matching observables timely and with rather small effort, highlighting two advantages of an automated software setup. The results that were obtained so far will be useful as a guideline for further non-perturbative studies.

Effective field theories can be used to describe measurements at e⁺e⁻ colliders over a wide kinematic range while allowing reliable error predictions and systematic extensions. We show this in two physical situations. First, we give a factorization formula for the e⁺e⁻ thrust distribution dσ/dτ with thrust T and τ = 1 − T based on soft collinear effective theory. The result is applicable for all τ, i.e. in the peak, tail, and far-tail regions. We present a global analysis of all available thrust distribution data measured at center-of-mass energies Q = 35 to 207 GeV in the tail region, where a two parameter fit to the strong coupling constant α(s)(m(Z)) and the leading power correction parameter Ω₁ suffices. We find α(s)(m(Z)) = 0.1135 ± (0.0002)expt ± (0.0005)hadr ± (0.0009)pert, with x²/dof = 0.91, where the displayed 1-sigma errors are the total experimental error, the hadronization uncertainty, and the perturbative theory uncertainty, respectively. In addition, we consider cumulants of the thrust distribution using predictions of the full spectrum for thrust. From a global fit to the first thrust moment we extract α(s)(m(Z)) and Ω₁. We obtain α(s)(m(Z)) = 0.1140 ± (0.0004)exp ± (0.0013)hadr ± (0.0007)pert which is compatible with the value from our tail region fit. The n-th thrust cumulants for n ≥ 2 are completely insensitive to Ω₁, and therefore a good instrument for extracting information on higher order power corrections, Ω'(n)/Qⁿ, from moment data. We find (˜Ω₂)^1/2 = 0.74 ± (0.11)exp ± (0.09)pert GeV. Second, we study the differential cross section dσ/dx of e⁺e⁻-collisions producing a heavy hadron with energy fraction x of the beam energy in the center-of-mass frame. Using a sequence of effective field theories we give a definition of the heavy quark fragmentation function in the endpoint region x → 1. From the perspective of our effective field theory approach we revisit the heavy quark fragmentation function away from the endpoint and outline how to develop a description of the heavy quark fragmentation function valid for all x. Our analysis is focused on Z-boson decays producing one B-meson. Finally, we will give a short outlook of how we want to apply our approach to determine the leading nonperturbative power corrections of the b-quark fragmentation function from LEP experiments.

In this thesis jet production and cosmological constraints on decaying dark matter are studied. The powerful framework of effective field theory is applied in both cases to further our knowledge of particle physics. We first discuss how to apply the Soft Collinear Effective Theory (SCET) for calculating hadronic jet production rate. By applying SCET power counting, we develop a consistent approach to perform phase space integrations. This approach is then successfully applied to one-loop calculations with regard to a variety of jet algorithms. This allows us to study if the soft contribution can be factorized from the collinear ones. In particular we point out the connection between such factorization and the choice of ultraviolet regulator. We then further our study of the (exclusive) kt and C/A jet algorithms in SCET with the introduction of an additional regulator. Regularizing the virtualities and rapidities of graphs in SCET, we are able to write the next-to-leading-order dijet cross section as the product of separate hard, jet, and soft contributions. We show how to reproduce the Sudakov form factor to next-to-leading logarithmic accuracy previously calculated by the coherent branching formalism. Our resummed expression only depends on the renormalization group evolution of the hard function, rather than on that of the hard and jet functions as is usual in SCET. Finally we present a complete analysis of the cosmological constraints on decaying dark matter. For this, we have updated and extended previous analyses to include Lyman-alpha forest, large scale structure, and weak lensing observations. Astrophysical constraints are not considered in this thesis. The bounds on the lifetime of decaying dark matter are dominated by either the late-time integrated Sachs-Wolfe effect for the scenario with weak reionization, or CMB polarisation observations when there is significant reionization. For the respective scenarios, the lifetimes for decaying dark matter are constrained by Gamma^{-1} > 100 Gyr and (f*Gamma)^{-1} > 5.3 x 10^8 Gyr (at 95.4% confidence level), where the phenomenological parameter f is the fraction of decay energy deposited into the baryonic gas. This allows us to constrain particle physics models with dark matter candidates, by analyzing effective operators responsible for the dark matter decays into Standard Model particles.

In this thesis jet production and cosmological constraints on decaying dark matter are studied. The powerful framework of effective field theory is applied in both cases to further our knowledge of particle physics. We first discuss how to apply the Soft Collinear Effective Theory (SCET) for calculating hadronic jet production rate. By applying SCET power counting, we develop a consistent approach to perform phase space integrations. This approach is then successfully applied to one-loop calculations with regard to a variety of jet algorithms. This allows us to study if the soft contribution can be factorized from the collinear ones. In particular we point out the connection between such factorization and the choice of ultraviolet regulator. We then further our study of the (exclusive) kt and C/A jet algorithms in SCET with the introduction of an additional regulator. Regularizing the virtualities and rapidities of graphs in SCET, we are able to write the next-to-leading-order dijet cross section as the product of separate hard, jet, and soft contributions. We show how to reproduce the Sudakov form factor to next-to-leading logarithmic accuracy previously calculated by the coherent branching formalism. Our resummed expression only depends on the renormalization group evolution of the hard function, rather than on that of the hard and jet functions as is usual in SCET. Finally we present a complete analysis of the cosmological constraints on decaying dark matter. For this, we have updated and extended previous analyses to include Lyman-alpha forest, large scale structure, and weak lensing observations. Astrophysical constraints are not considered in this thesis. The bounds on the lifetime of decaying dark matter are dominated by either the late-time integrated Sachs-Wolfe effect for the scenario with weak reionization, or CMB polarisation observations when there is significant reionization. For the respective scenarios, the lifetimes for decaying dark matter are constrained by Gamma^{-1} > 100 Gyr and (f*Gamma)^{-1} > 5.3 x 10^8 Gyr (at 95.4% confidence level), where the phenomenological parameter f is the fraction of decay energy deposited into the baryonic gas. This allows us to constrain particle physics models with dark matter candidates, by analyzing effective operators responsible for the dark matter decays into Standard Model particles.

Theoretical predictions for generic multi-scale observables in Quantum Chromodynamics (QCD) typically suffer from large Sudakov logarithms associated with the emission of soft or collinear radiation, whose presence spoils the perturbative expansion in the coupling strength which underlies most calculations in QCD. A canonical way to improve predictions wherever these logarithms appear is to resum them to all perturbative orders, which can conveniently be achieved using Effective Field Theory (EFT) methods. In an age of increasing automation using computers, this task is still mostly performed manually, observable-by-observable. In this thesis we identify the 2-loop soft function as a crucial ingredient for the resummation of QCD Sudakov logarithms to Next-to-next-to-leading logarithmic (NNLL) accuracy in Soft-Collinear Effective Theory (SCET), for wide classes of observables involving two massless colour-charged energetic particles, such as dijet event shapes at lepton colliders, or colour singlet production at hadron colliders. We develop a method to evaluate these soft functions using numerical methods based on sector decomposition and the choice of a convenient parametrisation for the phase space. This allows the factorisation of all implicit (real emission) and explicit (virtual correction) divergences made manifest by dimensional and analytic regularisation. The regulator pole coefficients can then be evaluated numerically following a subtraction and expansion, and two computational tools are presented to perform these numerical integrations, one based on publicly available tools, the other based on our own code. Some technical improvements over naive straightforward numerical evaluation are demonstrated and implemented. This allows us to compute and verify two of three colour structures of the 2-loop bare soft functions for wide ranges of observables with a factorisation theorem. A number of example results - both new and already known - are shown to demonstrate the reach of this approach, and a few possible extensions are sketched. This thesis therefore represents a crucial step towards automation of resummation for generic observables to NNLL accuracy in SCET.